9.1 TIME DIMENSION OF WHOLE-FARM PLANNING
9.2 GENERAL PLANNING OBJECTIVES AND PROCEDURES
9.3 PLANNING METHODS AND THEIR APPLICABILITY
9.4 ALLOCATION BUDGETING
9.5 SIMPLIFIED PROGRAMMING
9.6 LINEAR PROGRAMMING
9.7 REFERENCES
'The news are not good. We must start from fresh.'Pun Seet Leen, Johor girl
Methods of formulating plans for the construction or reconstruction of whole-farm systems of Order Level 10 are presented in this chapter. It consolidates the discussion of previous chapters which were concerned with lower Order Level systems and such relevant elements as planning objectives, performance evaluation criteria, enterprises, activities, resources and the optimization of resource use within activities. The planning problem is to integrate these elements into a whole-farm system which, relative to the objectives of the farm household, optimizes farm resource use.
There are two main types of whole-farm planning: agro-economic planning, which is discussed here, and physical farm planning, which is not discussed. Agro-economic planning amounts to the preparation of blueprints for farm production. Physical farm planning is aimed at providing a physical base for the production activities and thus is concerned with structuring or restructuring the farm service matrix, a system of Order Level 9 (Figure 1.2) - e.g., providing irrigation and drainage facilities, soil conservation, crop storage etc. Physical farm planning with its focus on engineering and construction of farm infrastructure is outside the scope of this book. Note, however, that the kind of physical capital which will initially be needed on a farm will be determined by the requirements of its several activities and might change as these change. Necessary adjustments to this capital might also be uncovered from time to time by the comparative analysis of whole-system performance (Chapter 7). Special purpose planning might also be needed in areas such as livestock breeding but, except in the case of mono-activity farms, this relates only to farm subsystems.
Appropriate agro-economic planning methods are determined first by the type of whole-farm system under consideration (Section 2.2). For single-activity systems the task is to evaluate alternatives and select the best single activity. This is done using comparative budgeting (usually of gross margins, Section 4.3). Typical of such problems is selection of the best (profit-maximizing) crop activity for a mono-crop farm. However, if this single crop produces several outputs which can be used as the basis for subsequent on-farm processing/marketing activities, the question might arise as to which combination of these second-stage activities offers the greatest potential. The problem then becomes a multi-activity one (as illustrated by the coconut example of Figure 5.5).
In constructing a multi-activity system, the planning requirement is to select from all feasible alternatives the optimal combination of activities relative to the objectives of the farmer and the resources and opportunities available. Methods suitable for the planning of multi-activity farm systems are discussed in the following sections of this chapter. Focus is on the planning of small farms of Type 1 (subsistence) and Type 2 (semi-subsistence) in the context of a short-term planning horizon of up to one year. No consideration is given to planning for the longer term or under conditions of uncertainty which are, respectively, considered in Chapters 10 and 11.
Four types of economic planning may be required within a farm household's total 40-, 50-... year time horizon, viz.:
(1) short-term planning only, within each seasonal or annual phase. Here the problem is to select the best mix of short-term crop and livestock production activities in each phase. The necessary resources are either initially present or internally generated within each phase or held over from some previous phase or obtained externally by barter or purchase. Planning on the great bulk of small Asian farms is of this nature.(2) long-term planning only. This is required in selecting those production activities which have a lifespan extending over several phases, or possibly even over the household's entire time horizon, as in the case of selecting the best single or best mix of perennial tree crops having lives of 30, 40... 100 years. These are best selected by comparative activity budgeting (Chapters 10 and 11).
(3) both short- and long-term planning. This is required, e.g., when the problem is to determine the best mix of corn, citronella, cassava etc. to grow under a permanent stand of coconut palm. It is essentially the same problem as (1) except that growing/agronomic conditions (particularly shade effects and moisture requirements) for the short-term crops might change from year-to-year with changing development of the long-term crop.
(4) either short- or long-term production planning combined with long-term farm development planning. In new intensive settlement areas the planning emphasis is often on farm development rather than current production. A common objective is to produce some minimum level of cash income or food in each short-term planning phase while devoting most effort to land clearing, water supply etc. so as to create a new farm service matrix of Order Level 9, as distinct from maximizing the current output from the existing more extensive whole-farm system of Order Level 10.
These various situations provide a time dimension for whole-farm planning. They largely determine the applicability and relevance of the various planning methods discussed in this and the following two chapters.
The general objective of whole-farm system planning is to select from all feasible activities that combination which is expected to best achieve the goals of system beneficiaries (here the farm family represented by the farmer) within constraints imposed by available resources, the lack of perfect information and other limiting factors. Household goals provide specific operating objectives in formulating the plan. Planning consists essentially of a systematic search through all of the possible activity combinations for that combination which best meets the planning objective. This constitutes the optimal plan for the whole-farm system. As long as any selected plan can still be improved (by some other combination of activities), it remains sub-optimal.
As always, the first general step in this type of planning is to specify the problem. This is done by preparing a base table as exemplified by Table 9.1. This base table has the following four components:
(i) An explicit or acknowledged planning objective (e.g., maximization of net cash income or food production).(ii) A listing of all the feasible activities by which the objective might be achieved. This listing is in the form of unit activity budgets which show the inputs required per unit of each activity, i.e., the input-output coefficient for each activity standardized on a per unit of activity basis. Thus, in the simple example of Table 9.1, a unit of paddy activity is specified as requiring one unit of land, three units of water and zero units of feed. The various types of activities that may need to be considered are discussed in Section 9.3.1 below.
(iii) As part of these activity budgets, a quantification of net activity outputs in a form by which the possible contribution of each activity to achievement of the planning objective can be measured. Thus if the objective is to maximize money income, the net outputs also must be measured in money units.
(iv) A list of available resources and other factors which might constrain or limit the levels to which each of the activities can be brought into the plan. There are four main types of constraints:
Objectively based material resource constraints which typically consist of the limited amounts of available land, water, labour etc. and which, to at least a certain degree, the analyst must accept as being fixed in the short term.Objectively based non-material resource constraints such as limited access to markets, production quotas etc.
Subjectively based structural constraints which the analyst might wish to impose in order to partly pre-determine the kind of plan that will be formulated. These are discussed in Section 9.3.3 below.
Subjectively or objectively based consistency constraints which might be needed to ensure that the plan is consistent with the family's other broad goals beyond that priority goal which has been specified in terms of the immediate operating objective of (i) above. These also are discussed in Section 9.3.3 below.
TABLE 9.1 - Example showing Components of a Base Table for Whole-farm Planning
|
(i) Planning objective (e.g., maximization of net cash income) | ||||
|
|
(ii) Activity unit budgets | |||
|
(iv) Resources, constraints |
Soybeans |
Paddy |
Cows | |
|
Land |
8 units |
1 |
1 |
0 |
|
Water |
6 units |
0 |
3 |
0 |
|
Feed |
10 units |
0 |
0 |
5 |
|
(iii) Activity output ($GM) |
5 |
10 |
12 | |
9.3.1 Types of farms and activities
9.3.2 Assumed optimality of plans
9.3.3 Specification of non-resource constraints
Three relevant planning methods are available. In increasing order of their relative power, effectiveness and sophistication, but also - if done by hand - in order of their increasing clerical and tedious calculation requirements, these are allocation budgeting (AB), simplified programming (SP) and linear programming (LP). All these methods are essentially formalized budget procedures (Rickards and McConnell 1967). Unlike LP, however, AB and SP do not consider the (infinite) array of all possible budgets of activity combinations and thus may not lead to the optimal farm plan. In contrast, within the context of its assumptions and the data used, LP does lead to the optimal plan (Dillon and Hardaker 1993, Section 4.5). This is because of LP's underlying algebraic basis as shown by, e.g., Heady and Candler (1958, Ch. 3) or Doll and Orazem (1984, Ch. 9). Indeed, LP (considered here in only its simple or standard form) has been further extended in many ways and, like non-linear programming, is but one part of the general field of analysis known as mathematical programming (Hazell and Norton 1986; Winston 1991).
Before looking at AB, SP and LP, the following general points might be noted regarding their relative applicability in different planning situations.
The applicability of AB, SP and LP varies significantly depending on the type of farm to be planned and the types of activities it involves. In general, LP is much more widely applicable than AB or SP.
Types of farms
Each of the three planning methods is applicable to mixed-activity family-farm systems, i.e., to small farms of Type 1 (subsistence) or Type 2 (semi-subsistence) and to large farms of Type 5 (commercial). They are not generally applicable to the specialist family farms of Type 3 (independent) or Type 4 (dependent) or to the basically mono-crop tea, rubber, oilpalm etc. estates of Type 6 (Section 2.2.1). On these latter estates, the (presumably best) production activity has already been chosen; or if not, it is selected by comparative budgeting. However, if long-term activities are involved, such as tree crops, these will generate their returns and costs as streams extending over many years and it is necessary to first bring these (by their future nature, uncertain) income and cost streams to some common basis in time by applying the methods of Chapter 10.
One situation in which the three methods (especially LP) can be applied to mono-crop farms is when these produce or could produce a range of second-stage outputs and the problem then is to determine the best combination of such outputs. Another situation is when the problem is to select the best combination of technologies/inputs with which to produce the given mono-crop or farm-processed product: e.g., sheet or crepe rubber on a rubber estate; copra, charcoal, oil etc. on a coconut estate. Generally, however, the main planning problem on mono-crop farms is to determine the optimal levels of individual resources to apply to the selected single activity and this is best done using the methods of response analysis (Chapter 8).
Note, however, that even highly mixed farms do not automatically call for application of these planning methods. If the economic environment (prices, costs, yields) has been stable for some time and is expected to remain so, all that might be required are occasional marginal changes to the production plan rather than its complete reformulation. This is best done using partial budgeting (Section 4.5).
Types of activities and activity budgets
Activities were discussed in a general way in Chapter 4, particularly in Section 4.4.1. Here they are reviewed from the viewpoint of their use with each of the three planning methods; in doing so, some additional types of activities needed in whole-farm planning are noted.
(i) Final product-generating activities are those which produce in the current planning phase only a direct output which has value in terms of the planning objective. They generate only some final return or GM. They can be handled by AB or SP or LP.(ii) Final product + resource-generating activities produce primarily the former, but incidentally also produce some amount of resource which is to be or could be used either within the current planning phase or stored for later use. Sometimes a value can be attached to this resource (in which case this is included in the activity GM), sometimes it cannot. These activities also can be handled by AB or SP or LP.
(iii) Resource-generating activities produce only a resource for use by other activities. Typically these activities generate only a cost or negative GM and can be handled satisfactorily only by LP.
(iv) Resource + final product-generating activities are the same as (iii) except that they also produce some final product. The cost of producing the resource will be partly offset by the value of the final product and this is to be reflected in the GM of the activity. Or it might be exactly offset and result in a GM of zero. If the cost is more than offset it becomes a type (ii) activity. Usually these activities require to be handled by LP.
(v) Development activities are aimed at producing a resource for use at some time in the future beyond the current planning period. They carry only a cost, i.e., they return a negative GM in the current planning period. If such an activity is undertaken fully or partly within the current planning phase and if it is economically related to other activities in the current plan, at least part of its costs should be charged proportionately (as an activity negative GM) to the current plan phase, e.g., construction of a dam entirely or partly in the current planning phase, say Year 1, if it uses resources which could otherwise have been available to the other (production) activities in that year, should be partly charged as a negative GM in Year 1. At the same time, insofar as its resource will become available to future production activities over the next 30, 40... years, the costs of the dam should be spread over these 30, 40... years rather than charged as a (large) one-off negative GM in the current year. This requires application of the discounted cash-flow methods of Chapter 10 in order to obtain an appropriate current-year GM for the dam construction activity. These and the following activities require LP.
(vi) Development + production activities are the same as (v) except that here the activity also produces some final product. This latter can occur entirely within the current planning period or as a flow of output over some future time period. In South East Asia when jungle is cleared and land is prepared for planting rubber, the costs of this development activity, which can occur over several years, are often partly or entirely offset by the income-generating activities of selling, in the current year, logs, ratan and other forest items. Or some logs might be stockpiled for producing sawn timber or charcoal to generate activity income streams over several years. Again, as in (v), it is first necessary to bring the costs and returns streams of this type of activity to the same value basis or equivalence in time as that of the other activities.
(vii) Resource-purchase activities were discussed previously (Section 4.4.1) and are another way of obtaining resources. Oxpower, labour etc. may simply be purchased. These activities also require a budget, the GM of which is negative and equivalent to the purchase price per unit of activity. As well as a negative GM, these budgets will show activity 'requirements' (Tables 4.4 and 4.5). Usually the resource will be paid for with cash or credit; if this is in limited supply, the purchase-activity's requirements (for the farmer's limited cash/credit supply) must be shown as internal or structural coefficients in the activity's budget. If no such limits apply, there is no need to show their requirements; the activity's budget will then consist only of its negative GM or price and the amount of resource which the purchase activity obtains.
(viii) Resource-exchange activities are another way of generating resources by a farmer exchanging, e.g., some (surplus) oxpower for a neighbour's (surplus) labour (Table 4.4). Again a budget is required. If an 'even swap' has been arranged, the activity will carry a GM of zero. If the potential for exchange is limited, e.g., either by the amount of oxpower the farmer can give up or by the amount of labour the neighbour can give up, these quantities become 'requirements' in the activity budget.
(ix) Transfer activities were also discussed in Section 4.4.1. Typically they do not generate a positive GM. They usually carry a GM of zero - it costs nothing to use hay to feed cows rather than sheep. However, they might in fact incur a cost, as when a cow barn (animal storage) must be rat-proofed before it can be transferred as grain storage space for use by a wheat activity. Transfer activities then carry a negative GM.
In summary, as the above listing of activity types indicates, there is a variety of ways by which resources can be provided to final product-generating activities. In general, these rather special activities require the use of LP rather than AB or SP analysis. Their use is illustrated in the examples of LP analysis given in Sections 9.6.2 and 3.
(x) Resource-disposal activities are primarily of a technical nature and are used only in LP. They permit the non-use of resources. In a practical sense, since it usually costs nothing not to use all or some part of a resource such as farm land, water, ox days etc. as long as doing so means that an improved plan can be formulated, disposal activities usually carry a GM of zero. But there are important practical exceptions where these activities do incur a cost, thus a negative GM. Disposal activities are discussed further in Section 9.6.1.
Activity structural independence and dependence
All three planning methods can readily handle final product-generating activities and activities which are structurally independent of other activities. But only LP is really capable of handling activities which are primarily designed to provide resources internally or which are structurally dependent on other activities. As discussed later, the reason for this is that, operationally, activities are selected for inclusion in the plan according to some specified criterion such as their relative GM value. Since resource-producing activities generate directly only a cost, i.e., a negative GM, they would be excluded from the plan using AB or SP methods of analysis. (The same is true of most long-term development activities.)
The matter of structural dependence/independence between activities is illustrated schematically in Figure 9.1. Situation A shows a set of independent activity subsystems arranged for planning (as in Section A of Table 9.2 below). Since each activity carries a positive GM and is independent of the others, application of either AB or SP or LP methods is possible. In planning situation B of Figure 9.1, some activity dependence is depicted: here the cassava is both sold and used as live supports for the beans, which are thus dependent on the cassava; and the legume crop is now not sold but used to provide fertility for the corn crop which is in turn used to provide a grain resource for the dairy cows. In contrast to situation A, in situation B, according to the GM activity selection criterion using AB or SP methods, neither legumes nor corn would be considered for inclusion in the plan; and beans also would be unlikely to come into the plan because this activity, though itself carrying a high GM, first requires production of some amount of low-GM cassava. In summary, situation B is readily handled by LP, but not by AB or SP unless the beans + cassava and the cows + corn + legume activities are redefined as new composite activities. Essentially this would 'tie' a negative or low-value GM activity to a high GM one, thus permitting the former to be considered for plan inclusion. This is possible up to a point but is limited by the amount of clerical work involved and the fact that it partly predetermines the planning outcome.
Given their assumptions about the structure of the farm system and its operation, AB, SP and LP each generates an optimal plan relative to the planning criterion used and the limitations of the planning method. Such plans, however, may in reality be far from optimal due to deficiencies either in the assumptions made about farm structure or in the data used for planning.
Assumed optimality of resource use within activities
As implied by the above discussion, each planning method involves the manipulation of previously defined activities. Each method requires or assumes that the level of each resource used in each activity is at its 'best' level - e.g., that in an individual activity budget for paddy, the alleged input 'requirements' of paddy for water, fertilizer, labour etc. are economically the best amounts to provide to this activity. If this assumption cannot be made, it might be necessary first to determine the optimal input levels for activities by response analysis (Chapter 8). If such within-activity near-optimality is not ensured, the subsequent application of AB, SP or LP methods might result only in selecting the best combination of bad activities. Relatively greater gains will usually be made by devoting more attention to structuring sound activities and then applying simple planning methods than by combining 'sick' activities into a plan using sophisticated methods.
Assumed certainty in activity budgets
Another assumption in using AB or SP or standard LP is that the results (yield, production, gross margin) which are projected for the individual activities will in fact be achieved with reasonable certainty (Dillon and Hardaker 1993, Section 4.5). Even the most sophisticated of plans will be of little value if there is not a reasonable chance of them being borne out by events. Again, in such circumstances it is likely to be better to formulate a simple plan using simple budgeting methods, and then to subject this to the kind of analysis discussed in Chapter 11.
Optimality in plan formulation
While AB, SP and LP are respectively tools of increasing power and sophistication, the quality of their output is always determined by how competently the planning problem has been specified. A large subjective element enters into this. Further, because of unforeseen variations in prices and yields, very seldom will activity budgets be exactly borne out by events. Thus an 'optimal' plan is something of a misnomer. If the planning assumptions are a valid, accurate, comprehensive reflection of perceived reality, the best that can be hoped for is a plan which is proven by later events to have been near-optimal. More often it will only tend towards an optimum.
Length of the planning period
Each of the methods is most commonly used to formulate short-term plans - i.e., for a season or operating year. Only LP is readily extended to multi-stage or multi-year planning, e.g., to generate in one analysis all of the two, three, four ... annual phases of a two-, three-, four-... year plan - but only if the work is done on a computer. With the same proviso, only LP is suitable for multi-stage development planning.
Outputs of the planning process
Each of the three methods generates two types of output. The first consists of some identified combination of activities constituting the required plan. The second output is informal and consists of insights afforded into how the formal plan might still be further improved after the AB or SP or LP analysis has been concluded (Rickards and McConnell 1967). However, not infrequently analysts decline to accept these insights, preferring to crunch numbers rather than reflect on what these numbers mean in the context of practical farm management. Too, because of the effort involved in applying AB, SP or LP, analysts may sometimes be prone to attach undue credence to the plans generated.
Trial-and-error approximations
Application of any of the planning methods should proceed by trial-and-error as a series of closer or improving approximations to the final optimal plan, rather than as an arithmetical problem to be solved, as it were, with a single blow. Inevitably, as the analyst proceeds with formulation of the plan, he or she will think of possible additional or improved activities, or of the need to include additional constraints, or of possible modifications in the activity resource requirements. Even on farms with an apparently simple structure there might in fact be dozens of ways in which resources can be used or commodities produced; they will not all be apparent when the planning problem is initially specified.
Computerization
Computer programs are widely available for standard LP and other more sophisticated types of mathematical programming - see, e.g., Brooke, Kendrick and Meeraus (1992) and Schrage (1991) or Lindo Systems Inc. (1994). Similar programs could also be written for AB and SP. However, there would be no point in doing this because LP is so much the superior method in terms of scope and applicability; if a computer is to be used at all, it should be used for LP. AB and SP methods require and warrant only use of a hand calculator. Their advantage lies in their 'hands-on' nature and the direct feel for the resource-allocation problem that they give the analyst. Their disadvantage is that they can only be applied with any surety to relatively simple problems.
The advantages of carrying out LP by computer are that larger farm systems (i.e., ones with larger numbers of possible activities and constraints) can be considered, together with the ease and quickness of computation as well as the avoidance of calculation errors. The associated danger is that these features, combined with an impressive printout of results, may lead the analyst or client to attach greater credibility to the generated plans than they deserve.
A deficiency in AB and SP is that if all the activities to be considered compete for exactly the same resources, the first activity to come into the plan - unless it is otherwise restricted - will exhaust the supply of its limiting resource, thus leaving no possibility for other activities to subsequently enter the plan because they too will require this (now exhausted) resource. The generated plan will then consist of only one activity and significant amounts of the non-limiting resources may be left idle. In such cases, consideration of other possible plans involving a mix of activities can, if AB or SP are being used, only be considered on a trial-and-error basis. With LP, however, constraints relating to the farm's structure and/or to family goals may be introduced to overcome this problem.
Subjectively based structural constraints
This type of constraint was only noted in passing in Section 9.2. Briefly, in addition to specifying as constraints the material and non-material resources which are available, in most planning situations the analyst must also start with a preconceived idea of the kind of plan he or she wants to formulate - i.e., the kind of system he or she wants to construct. This amounts to predetermining some selected aspects of the plan. If the problem is one of constructing a mixed-farm system, a minimum limit would be imposed on the number of activities to enter the plan; if working with farmers who are good with livestock but not with crops, the analyst would perhaps impose a maximum limit on the area to be used for crops.
In this type of structural pre-specification, the analyst must achieve a balance. If the problem is under-specified (not enough constraints imposed), the plan might well run directly to some logical but nevertheless idiotic solution. If the problem is over-specified (too many constraints), the planning process might have only one possible outcome, in which case there would obviously be no point in executing the analysis.
Constraints to achieve consistency with broad family goals
Farm planning usually emphasizes two dimensions of performance. These are productivity and profitability measured relative to direct output either, for subsistence farms, in terms of income in kind or, for commercial farms, in terms of cash GM per unit of land, operating capital or family labour. But, as discussed in Section 6.2, there are at least six other dimensions or generally desirable properties of a whole-farm system, viz.: income stability, product diversity, flexibility, time-dispersion of income, sustainability and environmental compatibility. Operationally, these can be incorporated into the planning process as constraints. The kind of constraint which is implied in each case is briefly noted as follows:
· Income stability. This could be achieved by imposing maximum or ceiling limits on the size of those crop/animal activities whose yields/prices/costs are highly uncertain and fluctuate widely over time.· Diversity of income/food sources. The appropriate way to achieve this system property would be to set a minimum or floor limit on the total number of different activities required to be in the plan.
· Flexibility in product disposal/use. Some activities produce outputs which can be disposed of or used in a variety of different ways. (Use-flexibility is one means of achieving income diversity.) One or more of these methods of disposal or use could be forced into the plan by imposing them as minimum constraints or mandatory elements.
· Time-dispersion of production or income. This also could be achieved by imposing minimum constraints on those activities whose outputs are highly time-dispersed rather than time-concentrated. If applicable, perhaps the best way would simply be to allocate at least some specific area of the farm to the highly time-dispersed tree crops, i.e., treat them as mandatory activities.
· System sustainability. This could be facilitated or enhanced by applying maximum constraints on the erosive or fertility-depleting crops, or more general maximum limits on all crops according to the slope and/or erodability of different parcels of land. If sustainability is threatened by a rising watertable and salt, it might be possible to counter this by imposing maximum limits on the area of individual high water-using crops. Alternatively, minimum limits might be set on the areas of soil-rehabilitating crops such as pastures, trees and legumes.
· Environmental compatibility. Finally, the general desirability of formulating a plan which is compatible with the wider physical and social environment will suggest ways of achieving this by imposing maximum limits on certain activities or on the amounts of hazardous inputs to be used.
Considering these and the other types of constraints, in general, maximum constraints can be handled by any of the three planning methods; but planning situations involving more than one or two minimum constraints require the use of LP methods.
9.4.1 Operating criteria for allocation budgeting
9.4.2 Allocation budgeting using GM per unit of land
9.4.3 Allocation budgeting using GM per unit of operating capital
9.4.4 Allocation budgeting using GM per family labour day
Allocation budgeting (AB) is the simplest of the three whole-farm planning methods; it is also the easiest and cheapest to apply. Its limitations have been noted in Section 9.3 above.
AB aims at selection of the optimal mix of activities on the basis of the GM per unit of what is judged to be the most limiting or scarce resource. Most commonly, the criterion used is either:
(i) GM per unit of land;
(ii) GM per unit of operating capital; or
(iii) GM per unit of family labour.
This is the most widely used type of AB. It is the most relevant measure of resource productivity and activity performance where maximization of short-term money income is the operating objective and where land is the most limiting resource. But, as discussed in Chapter 6, some other objective such as subsistence food production may be more important for farm households not well-linked to the market. Too, not infrequently, land will not be the most limiting resource.
AB proceeds by six general steps as illustrated in Table 9.2. This relates to a Javanese mixed farm of one ha of which 0.1 ha is under a permanent mix of tree crops, dominated by coconut and used to supply some subsistence requirements, while the balance of 0.9 ha is available for short-term field crops. The six steps in AB are as follows:
1. Determine the most appropriate planning objective given the type of farm and the goals of the individual farm household. Ideally this should be done in participatory/consultative fashion with the farm family. In the example of Table 9.2, production is assumed to be constrained primarily by land and the first objective is to meet basic sustenance requirements after which the objective is to maximize money income. The planning criterion is therefore (modified) GM per land unit.2. Determine the appropriate planning period: in the example of Table 9.2, this is the coming wet season of six months.
3. Identify all of the possible feasible final product-generating and resource-generating activities (remembering that AB has only limited capacity to handle the latter). Activities considered could be those that have been operated on the subject farm in the past, or new or adjusted versions of these, or completely new activities. Depending on the Mode and Field of analysis, they might include one or more mandatory activities (e.g., mixed-farm plans formulated in support of a cassava research project would have to include some cassava).
In the present example, the possible activities are listed in a base table comprising Section A of Table 9.2. As shown there, it might sometimes be necessary to distinguish between similar activities on the basis of their intended purpose: HYV paddy is intended for cash sale while low-yielding traditional paddy is preferred for the family's own use. In the example a minimum area of this traditional paddy is considered as a mandatory family-sustenance activity. In this situation it would therefore be wrong to specify only one 'paddy' activity. The second mandatory activity is maintaining the existing area of coconut mix. This is mandatory not only because its products are needed for sustenance (food, fuel, building materials etc.) but also because these trees would be harvested and generally maintained regardless of any incidental cash GM which they might produce.
4. Quantify each activity by a unit budget as in the respective columns of the base table of Section A showing the unit size of the activity, its outputs and the value of its GM (in the present instance, from cash sales per unit of land), and its resource requirements. The unit budgets are formulated on a per unit of land basis. The land unit used here is the (Javanese) 'patok' equivalent to about 0.1 ha. Note that for resource-allocation purposes, it is not necessary to know the cash GM of any mandatory activity which is included in the plan for other than GM-generating reasons. Here, e.g., both the mandatory activities of traditional paddy and coconut mix only incidentally generate a cash GM.
5. Define and list the planning constraints as shown in the lower-left side of the base table of Section A in Table 9.2. In the present example there are nine of these constraints. They consist of eight physical resource constraints plus a market-based constraint. The latter is a production limit placed on roselle to reflect the fact that there is an assured market for only two patoks of this commodity. Note that the land constraint refers to arable land and does not include the coconut-mix area (which therefore has a zero input-output coefficient relative to the arable land constraint). (The one patok of coconut-mix land could have been included as a further constraint. However, since coconut mix is a mandatory activity and its land is not used by any other activity, this is not essential.) Note also that the labour constraints relate to family labour. There is no hired labour.
6. Formulate the farm production plan, developing Sections B and C of the AB worksheet by the following steps:
(i) First, bring into the plan one of the mandatory activities to the required level - in Table 9.2, the one patok of coconut mix is brought in. List the requirements of coconut mix in the first inner column of Section C; then subtract these from the initial stock of available resources (B-1) (as shown in the resource constraints list of Section A of Table 9.2) to obtain the new Resource Balance (B-2) as shown in Section C.(ii) Repeat this in turn for each of the remaining mandatory activities, if any (here, only one patok of traditional paddy giving the new Resource Balance (B-3) in Section C).
(iii) Maintain a list of each selected activity level and its associated GM as shown in the lower part of Section B of Table 9.2.
(iv) After all mandatory activities have been brought in, select next that non-mandatory activity having the largest GM: here roselle with a GM of $60 per patok is the first to be selected.
(v) To find the maximum level to which roselle can enter the plan, divide each element of the current Resource Balance (B-3) of Section C by the corresponding element of the roselle requirements column of Section A and enter the results as shown in Section B of Table 9.2. The maximum possible level (i.e., number of units or, in this case, patoks) of roselle is given by the smallest number appearing in this generated column of Section B; this is '2' (it is placed in parentheses for ease of reference), i.e., the most limiting constraint for roselle is its market constraint of two patoks.
(vi) Enter roselle resource requirements as shown in Section C of the worksheet. Because there are to be two patoks of roselle in the plan, these resource requirements are obtained as two times the unit resource requirements of roselle from Section A, i.e., (2) x 1 = 2 units of arable land, (2) x 20 = 40 units of cash etc. Subtract the total roselle activity requirements so obtained from the Resource Balance (B-3) to obtain the new Resource Balance (B - 4) of Section C.
(vii) Repeat steps (iv), (v) and (vi) to bring other activities into the plan on the basis of the highest GM (here only HYV paddy) to levels permitted by the (declining) available resources of Section C and enter the TGM of each selected activity in the lower part of Section B. This concludes the formal AB analysis. For the example farm of Table 9.2, as shown in the bottom part of Section B, the optimal plan based on AB using the criterion of GM per unit of land consists of one patok of coconut mix, one patok of traditional paddy, two patoks of roselle and 4.3 patoks of HYV paddy. The plan meets the mandatory activity requirements and is expected to generate a farm TGM of $384.
TABLE 9.2 - Example of AB Worksheet for Whole-farm Planning based on GM per Unit of Land
However, there still remains the important informal step of considering if and how the worksheet-based plan might be further improved. Thus, e.g., inspection of the worksheet's final Resource Balance (B-5) reveals that 1.7 patoks of land remain unused as well as 3.6 units of irrigation water. Few farmers would accept this. The analyst would now reconsider the initial planning specifications. Could other possible activities be considered? Could the resource requirements be relaxed? Could additional resources be found? Thus, would perhaps a little more HYV paddy be possible? Expansion of this activity is prevented by prior exhaustion of the farm family's planting-labour resource. Could a little more planting labour be found? But even if this proved possible, HYV paddy expansion would then be limited to only 0.5 additional patoks by irrigation water (i.e., 3.6/8 = 0.5 patoks). The same limit and maximum possible additional level of 0.5 patoks would apply if an expansion of traditional paddy was attempted (this additional area, over and above family food requirements which have already been met, could now be regarded as a cash crop). Perhaps maize is a possibility. Dividing Resource Balance (B-5) by the requirements for maize, the maximum possible area of maize is limited to zero by the lack of planting labour and next would be set by irrigation supply at 3.6/2 = 1.8 patoks. Thus there would be more than enough water to permit using the remaining 1.7 patoks of land for maize as long as a few additional days of planting labour (1.7 x 5 = 8.5 days) could somehow be obtained. At this point the initial problem specifications in Section A of Table 9.2 regarding available resources, particularly planting labour, would be checked. The farmer who has provided the information on his or her constraints might concede that, even though the supply of planting labour is tight, he or she could nevertheless possibly obtain the necessary nine additional days of labour by exchanging, say, 18 of his or her surplus growing-labour days with a neighbour. If so, 1.7 patoks of maize would then be possible and the final plan would be as shown in Table 9.3. This plan gives an expected gain in farm TGM of $43 over the initial plan of Table 9.2. However, some unused resources still remain. The analyst might continue to look for ways - other activities - to use them up. But since land and water are now exhausted, such other activities (if they can be found) could not be field crops but only some intensive activity - such as stall-fed livestock or a fish pond - which uses only cash and labour.
TABLE 9.3 - Final Whole-farm Plan based on GM per Unit of Land for the AB Worksheet Example Farm of Table 9.2
|
Production Activity |
Level (patoks) |
TGM ($) |
Unused Resources |
|
|
Resource |
Amount |
|||
|
Coconut mixa |
1 |
40 |
Cash ($) |
28.0 |
|
Traditional paddya |
1 |
30 |
Growing labour (days) |
22.0b |
|
Roselle |
2 |
120 |
Harvest labour (days) |
8.8 |
|
HYV paddy |
4.3 |
194 |
May oxpower (days) |
8.7 |
|
Maize |
1.7 |
43 |
Irrigation water (units) |
0.2 |
|
Farm TGM |
|
427 |
|
|
a Mandatory activity.b 51.9 days from Resource Balance B-4 of Table 9.2, less 11.9 days for the 1.7 patoks of maize now brought into the plan, less 18 days exchanged with neighbours for nine days of planting labour for the maize.
Calculating net farm income
In the above AB and the following SP and LP analyses, the activity budgets account for only their respective direct costs; they do not account for those farm costs which are not activity-specific. The expected cash return from the plan of Table 9.3 is measured as a farm TGM of $427. If the level of farm net cash return is needed, it is obtained as farm TGM less any farm fixed costs: e.g., if whole-farm fixed costs are $100, farm net cash return for the plan of Table 9.3 is $(427 - 100) = $327.
There is one possible hazard. The cost of some existing capital item, e.g., a maize shelter, might have been attached to some specific activity, e.g., growing maize, at the budget preparation stage. If then at the analysis stage maize does not come into the plan, the fixed costs of the sheller will not have been accounted for and must now be included as a part of whole-farm fixed cost in calculating net farm cash income.
This planning criterion is based on the assumption that operating capital (cash and access to credit) is the most limiting resource. The assumption can be a valid one on farms in both the developed and developing world. The large sheep, cattle and wheat farms of Australia have historically been more short of capital than of land; and the same is true, e.g., of many farms on the geographical fringes of development in Kalimantan, Bhutan and West Irian.
As exemplified by the AB worksheet of Table 9.4, the problem is again specified by construction of the base table of Section A. However, while the activity unit budgets are again on a per unit of land basis, the base table now includes the new selection criterion of GM per unit of operating capital. Operating capital is defined as cash plus available credit or, if appropriate, as cash and available credit plus the cash value of resources in store which have required a past cash outlay (e.g., such as an on-farm store of fertilizer). In the example of Table 9.4, operating capital consists of only cash. It is also assumed that traditional paddy is now only a marketable crop and not mandatory. The only mandatory activity is the existing one patok of coconut mix. Having Section A of the worksheet, the procedure to develop the farm plan is the same as in the previous example of Table 9.2 but with priority for the entrance of activities being determined by their GM per unit of operating capital. Thus the first activity to enter the plan after the mandatory coconut mix is maize. The full plan based on the uncompleted worksheet of Table 9.4 is given in Table 9.5 along with a listing of its associated unused resources. This plan has an expected farm TGM of $418. As with the plan of Table 9.2, further partial budgeting may lead to a marginally better plan.
The criterion of GM per family labour day is probably the most relevant planning criterion for farmers who have no shortage of land but also no real potential for usefully employing more operating capital, even if it became available. The bulk of subsistence-oriented (i.e., Type 1) farms in geographically isolated areas fall into this category. Often the only significant resource of these families is their own labour supplemented with a hoe, a shovel and an axe. Indeed, as farms tend further towards the subsistence end of the farm-type scale (Figure 6.1), it might even be necessary to specify activity outputs in terms of their food/energy content. In extreme cases it might be appropriate to reduce all activity outputs to whatever the local basis of exchange happens to be - maunds of paddy, 'tins' of maize, bottles of butter oil etc.
Once the base table has been prepared, the steps in selecting activities to enter the plan using the criterion of GM per unit of family labour are the same as outlined above for the criteria based on land and operating capital. The procedure is illustrated by the uncompleted worksheet of Table 9.6. For the present example, this leads to exactly the same plan as that based on GM per unit of operating capital (Table 9.5). Because there is little difference between the TGM of each plan generated by AB on the basis of GM per unit of land, operating capital and family labour, it can be concluded that these three resources are, for all practical purposes, equally constraining to the example farm.
Simplified programming (SP) is used for the same purpose as AB. However, it proceeds by successive reference to two criteria rather than only one as in AB and thus requires a good deal more clerical work. In this it is held to be more sophisticated than AB; but it is subject to the same limitations.
An example of SP is shown in the worksheet of Table 9.7 with its five sections A, B, C, D and E. As with AB, the first step in SP is to define or specify the planning problem in terms of a base budget table as given by Section A. These budgets are here expressed on a per unit of land basis. The second step is to develop two intermediate working tables, Sections B and C. The analysis then proceeds through the operations shown in Sections D and E.
TABLE 9.5 - Whole-farm Plan based on GM per Unit of Operating Capital for the AB Worksheet Example Farm of Table 9.4
|
Production activity |
Level (patoks) |
TGM ($) |
Unused Resources |
|
|
Resource |
Amount |
|||
|
Coconut mixa |
1 |
40 |
Arable land (patoks) |
0.6 |
|
Maize |
3 |
105 |
Operating capital ($) |
52 |
|
Roselle |
2 |
120 |
Growing labour (days) |
44 |
|
HYV paddy |
3.4 |
153 |
Harvest labour (days) |
21 |
|
|
|
|
May oxpower (days) |
12 |
|
Farm TGM |
|
418 |
Irrigation water (units) |
13 |
a Mandatory activity.
The elements of Section B, maximum possible activity levels, are obtained by dividing each element of the initial resource constraints column (B-1) of Section A by the corresponding coefficient in the respective activity requirements column of the unit budgets' table of Section A. Thus the paddy activity column for Section B of Table 9.7 is obtained as good land 6/1 = 6 units, rough land (suitable for fodder and sesame but not paddy) 3/0 = ¥ (i.e., non-constraining and therefore ignored), cash 200/20 = 10 etc. The lowest value obtained in each of these derived B columns is then bracketed. This bracketed number indicates the maximum possible level to which the respective activity could enter the plan with the given set of constraints, e.g., in the case of paddy, the supply of water would limit paddy to a maximum of 2.9 units before any other constraint became operative.
The bottom row of Section B of Table 9.7 is then developed by multiplying the bracketed (activity limiting) values of the B columns by the per unit cash GM values of the same respective activities as recorded at the foot of the base table of Section A. The derived activity TGM values in Section B now show the total possible maximum contributions which each activity could make to the whole-farm plan. This row of maximum possible activity TGM values in Section B is later used as the first basis for activity selection; these TGM values provide criterion (i) as detailed below.
Section C is next developed to obtain the activity GM per unit of each resource if it were to be used in the production of each activity. The coefficients of the columns of Section C are found by dividing (a) each (per unit) activity GM of Section A by (b) the per unit resource requirements (coefficients) of the same activity, also found in Section A. For example the paddy column of Section C is found as good land $50/1 = $50, rough land $50/0 = ¥ (ignored), cash $50/20 = 2.5, planting labour $50/10 = 5 etc. These derived coefficients of Section C are later used as the second criterion in activity selection, criterion (ii).
TABLE 9.6 - Example of AB Worksheet for Whole-farm Planning based on GM per Family Labour Day
TABLE 9.7 - Example of SP Worksheet for Whole-farm Planning
Having the base table of Section A of Table 9.7 and Sections B and C derived from it, the farm plan is now formulated by applying successively the two SP criteria. The operating steps are as follows.
(1) Apply criterion (i): Select in Section B that activity which would give the highest activity TGM. It is maize with a TGM of $240. Now identify the constraint in the maize column of Section B which would limit maize. It is 'good land'. Maize is tentatively selected to enter the plan.(2) Now apply criterion (ii): Go to Section C, inspect the maize column and compare the value of the limiting constraint from Section B for good land with the value of good land if it was used for any other activity. If it is equal to or greater than any other value in the good-land row of Section C, select maize to finally come into the plan. If it is less than any other value/coefficient in this good-land row of Section C, drop maize, return to Section B and select for consideration that activity in Section B which has the next highest TGM after maize. In the example of Table 9.7, the value ($40) of good land for maize in Section C is exceeded by the values of good land for both roselle and paddy ($75 and $50, respectively); therefore drop maize from the plan at this stage.
(3) Return to Section B. By criterion (i), the next highest possible activity TGM would be $180 from sesame. It would be limited by rough land to three units.
(4) Again apply criterion (ii). Go to Section C; compare the value of the rough-land coefficient for sesame, $60, with the value of this same resource if it were to be used for any other activity. It is higher than any other coefficient in this rough-land row (only fodder with a rough-land coefficient value of $30). Therefore select sesame to enter the plan.
(5) As previously with AB, obtain now the sesame column of Section D by dividing the per-unit-of-activity requirements of sesame (of Section A) into the corresponding elements of the current Resource Balance (B-1) of Section A. Then bracket the smallest coefficient found in this new sesame column of Section D. This shows the resource/constraint which now limits the level to which sesame can come into the plan (i.e., rough land) and the maximum possible level of sesame permitted by this limiting resource, three units.
(6) Again as previously with AB, begin to develop Section E by listing the resource requirements for three units of sesame in the innermost column of Section E. Subtract these from the previous Resource Balance (B-1) to obtain the new Resource Balance (B-2).
(7) Using criterion (i) select in Section B the next activity to (tentatively) enter the plan. Again it is maize with an activity TGM of $240. Again it is limited in Section B by good land. Again apply criterion (ii) by moving to Section C and comparing the GM per unit of good land for maize with the other values in the good-land row. It is still less than the other values of $75 and $50, so again drop maize.
(8) Return to Section B. Using criterion (i), select the next best activity. This is roselle with a maximum possible activity TGM of $150. The limiting constraint is the market limit set on roselle of two units. Apply criterion (ii) by considering this constraint in Section C. In no other activity is the value of this constraint in Section C greater than its value for roselle, $75, so bring roselle into the plan.
(9) Form a roselle column in Section D; form the column for total roselle requirements (for two units of roselle) in Section E and subtract from Resource Balance (B-2) to obtain the new Resource Balance (B-3) available after the introduction of roselle.
(10) Return to Section B and identify the activity with the next highest TGM. It is still maize. When the second criterion is again applied in Section C, maize is still prevented from entering the plan by the higher good-land coefficient for paddy. (It is also higher for roselle, but since roselle is already in the plan, its coefficients in Section C are now inoperative.)
(11) Return to Section B. Again applying criterion (i), select paddy, noting that the limiting resource is water. Go to Section C and apply criterion (ii). The value of water if used for paddy, $7.1, is greatest. So bring paddy into the plan at the feasible level of two units generating a paddy TGM of $100. Complete the paddy columns of Sections D and E.
(12) Repeat the procedure. Maize now enters the final plan at a level of two units generating a maize TGM of $80.
(13) Obtain the new Resource Balance (B-5), i.e., $110 of cash and 16 units of planting labour. There remains only one activity which has not been brought into the plan and which might possibly use these resources. This is the fodder and goats activity. However, comparison of the (B-5) resource-supply column and the fodder + goats resource-requirements column of Section A indicates that this activity would not be feasible because of the prior exhaustion of rough (fodder) land.
This concludes the formal part of the SP analysis. As previously with AB, a running total of plan or farm TGM is maintained at the bottom of Section D of the worksheet of Table 9.7. The final plan is as shown in Table 9.8.
TABLE 9.8 - Final Whole-farm Plan for the SP Worksheet Example of Table 9.7
|
Production activity |
Level (patoks) |
TGM ($) |
Unused Resources |
|
|
Resource |
Amount |
|||
|
Sesame |
3 |
180 |
Cash ($) |
110 |
|
Roselle |
2 |
150 |
Planting labour (days) |
16 |
|
Paddy |
2 |
100 |
|
|
|
Maize |
2 |
80 |
|
|
|
Farm TGM |
|
510 |
|
|
Extensions to SP by partial budgeting
As with AB, it will usually be possible to further improve the formal SP worksheet plan by relaxing one or more of the constraints (especially if these were subjectively based), or by adjusting the initial assumptions regarding activity requirements, or by thinking of additional possible or improved activities. In the example of Table 9.7, the analyst might now look for activities which could productively use the idle cash balance. There are no land or irrigation resources left so any new production possibility obviously could not be a crop activity. On the other hand, an activity such as stall-fed goats which uses a fair amount of cash and very little else might offer possibilities in contrast to the budgeted goat activity which is based on fodder cropping and thus needs land. Could perhaps a second type of goat activity be considered? One which consists of housed goats fed on crop residues from the maize, paddy and sesame? If so, this might result in worthwhile improvement to farm TGM. One would explore the possibility with a little side budgeting. Likewise, a fish pond for carp or tilapia or silver barb might be a possibility.
9.6.1 Linear programming of systems consisting of only final product-generating activities
9.6.2 Linear programming of Type 2 farms: systems with internally-generated resources
9.6.3 Linear programming of Type 1 farms: subsistence-oriented systems
9.6.4 Relevance of LP
In setting up a base table for AB or SP, the analyst will also have taken the most important and difficult step in linear programming (LP), keeping in mind that more complex activities - especially resource-generating activities - can now be included in the analysis. On the other hand, the amount of tedious arithmetic calculation required in LP is greater than in AB or SP. For this reason, if the problem is a relatively simple one involving no more than five or six activities and constraints, and when resource- or cost-generating activities are not a significant part of the problem, it will probably be best handled using one of the simpler methods (especially AB). As the number of activities or constraints becomes large or activities become complex (mutually dependent), or resource- or cost-generating activities become important, LP offers the only feasible method of analysis - but only if it is done on a computer using such software programs as, e.g., GAMS (Brooke, Kendrick and Meeraus 1992) or What'sBest!ä (Lindo Systems Inc. 1994; Schrage 1991).
The objective in this section is limited to consideration of (1) how the base table in which a problem is specified needs to be extended to make it suitable for standard LP application; (2) the mechanical steps in standard LP analysis; and (3) how the main types of problems which arise in planning of Type 1 and Type 2 whole-farm systems can be handled by standard LP. More comprehensive treatment of the application of LP to agricultural problems is to be found in, e.g., Hazell and Norton (1986), Dent, Harrison and Woodford (1986), Rae (1977, Chs 7 and 8) and Rae (1994, Chs 5 and 6). As well as other types of mathematical programming, Hazell and Norton (1986) and Winston (1991, Chs 3, 4 and 5) outline many of the extensions to LP beyond the standard form considered here.
Based on Heady and Candler (1958, Ch. 3), an example of LP analysis is shown in the worksheet of Table 9.9. This worksheet uses what is known as the simplex method of LP analysis (Mao 1969, Ch.3). The example involves only type (i) activities (i.e., activities generating only a final product) (Section 9.3.1); it does not include any resource-generating activities. As previously, a base table is prepared in which the problem is specified. As shown in iteration or part I of Table 9.9, the base table of the LP worksheet consists first of a set of unit activity budgets including the GM of each which, following LP convention, is now termed the activity 'price' and denoted by p; each has exactly the same meaning as a GM and they are listed as a row of p values at the top of the base table. The possible farm activities to be considered are referred to as real activities. The base table also contains a list of constraints (here, for simplicity, only the supply of resources available - days of labour, $ of working capital and units of irrigation water - and no other types of constraints) which might limit the real activities. The base table then begins to differ from the worksheet format for AB and SP, viz.:
(i) In addition to real activities, unit disposal activities are specified, one for each resource/constraint. Each permits the respective resource to be disposed of, i.e., not used, by the real activities. Since in most cases (as here) the non-use of a resource costs nothing and earns nothing, the price (p or GM) attached to each of these disposal activities is $0. Each disposal-activity column consists of a coefficient of unity in the resource row to which it refers and zeros in the other cells. Note, however, unused resources can sometimes incur an operating cost. If some land is left idle it might rapidly run to weeds, subsequently increasing cultivation costs by some amount per ha the next time the land is used. If some water which is supplied to a farm is left unused, it might lie as a public health hazard and the farmer might be charged for this at $5, $10... per unit of such unused water.(ii) The 'resource' column B now has a more inclusive function than formerly. In the initial specification of the problem, part I of the worksheet, it shows the amount of each resource which is available to the activities; but in those subsequent parts or iterations II, III ... which are developed as the programming analysis proceeds, this B column also includes those activities which have previously been brought into and currently remain in the plan. In effect, insofar as already selected activities can be taken out again, if by doing so the plan can be further improved, each of these activities is a quasi-resource. (In fact something like this happens in AB and SP when a worksheet-derived plan is marginally adjusted by side budgeting to permit the partial or full substitution of one selected activity by another if it is thought that such a change will increase farm TGM.) In short, the B column at any stage (iteration I, II, III ...) of the LP planning process shows resources not yet used (and therefore still available for formulation of the next plan or iteration) as well as activities which are in the plan at that current stage.
(iii) A work column K is needed at the right-hand side of the table in which is indicated the limit to which any incoming activity can in fact enter the plan and the identity of the limiting resource or constraint in the B column. (This is obtained in the same way and serves the same purpose as did Section B of the AB worksheet of Table 9.2.)
(iv) A column p is needed at the left of the LP table in which the unit price (GM) of each item currently in the B column (resource or other constraint or activity) is entered. As relevant, these prices are taken as needed from the activity price row (p values) at the top of the base table.
(v) An addition to the base table as its last two rows respectively are a set of Z and Z - p values. The specification of these is detailed below.
Iteration and plan I
Programming consists of moving from an initial iteration and plan I to successively better plans, through iterations II, III, IV ..., according to a specified operating criterion (detailed below). In the example LP of Table 9.9, the first three rows of the B column of iteration I constitute the first 'plan'. The B column at any stage identifies those activities/resources which are in the plan at that stage and their levels. Under B in iteration I, those activities in the plan are the disposal or non-use activities for the initial resources of labour, capital and water; they are 'in' the plan to the levels shown under B: 100 units of labour, 100 units of capital and 80 units of water (i.e., all of these resources are disposed of, not yet used).
The TGM of this or any later plan is found as the sum of the products of each of the activity/resource levels currently in the plan (shown in the B column) times its respective price p, given in the left-side p column of Table 9.9. TGM under plan I is therefore (100)($0) + (100)($0) + (80)($0) = $0. This is shown in the Z row of the B column of iteration I.
a Based on heady and Candler (1958, Ch. 3).
The Z coefficients or values for the other (activity) columns in iteration 1 are now obtained in the same way by summing the results of multiplying each coefficient of each activity column by the corresponding price shown in the left-hand p column. Thus the Z coefficient for roselle is (1)($0) + (0)($0) + (1)($0) = $0; the Z coefficient for cows is (1)($0) + (1)($0) + (0)($0) = $0 etc. These Z coefficients for the various activities show the opportunity cost of bringing one unit of a real or disposal activity into the plan. This is in terms of the income which would be lost by any necessary forcing of other activities out of the plan. Thus, in iteration I, paddy has a Z value of $0 because, if it were brought into the plan at this stage, it would not be at the expense of any other activity and thus would have no opportunity cost. The main purpose in obtaining these Z coefficients for the activity columns is to now use them in forming the Z - p operating-criterion row.
The p part of the Z - p criterion coefficient is obtained from the p row at the top of the table. Thus, in iteration I, the Z - p coefficient for roselle is $0 - $30 = -$30, for cows 0 - 10 = -10, for paddy 0 - 40 = -40, for sesame 0 - 12 = -12; and since the prices p of the disposal activities are all zero, the Z - p value for disposing of labour (denoted by DL) is 0 - 0 = 0, for disposal of capital (DC) is 0 - 0 = 0 and for disposal of water (DW) is 0 - 0 = 0.
This concludes iteration I. The LP now proceeds by asking and answering three questions:
(i) Is it possible to improve on the existing plan?
(ii) If so, which activities should be brought in, and in what order?
(iii) To what level can such activities be brought in?
The just-obtained Z - p coefficients are used to answer the first two of these questions. This is because these Z - p values indicate whether the opportunity cost (Z) of including a unit of the activity in the plan is greater or less than the net return (p) obtainable by having one more unit of the activity. Thus if Z > p, i.e., Z - p is positive, the activity should not be included because its net return or GM measured by p would not cover the opportunity cost of its inclusion. If Z < p, i.e., Z - p is negative, it will pay to include the activity in the plan because its p value is larger than the opportunity cost of its inclusion. Moreover, the best activity to enter the plan is that with the largest negative Z - p value. Thus, in answer to questions (i) and (ii) above:
(i) Yes, it is possible to improve the existing plan (of iteration I) since there are negative Z - p coefficients below the real-activity columns in iteration I of Table 9.9; and(ii) That activity having the highest negative Z - p coefficient is the one to bring into the next iteration. In the Z - p row of iteration I this is paddy which has a Z - p coefficient of minus $40.
Iteration and plan II
In iteration II, paddy is brought in but, as in the case of SP, this inclusion is only tentative: it might later be driven out by some superior activity.
The third question is now addressed: To what maximum level can the incoming activity, i.e., paddy, enter the plan? The procedure for determining this maximum is the same as before: divide the resource-requirements column of the incoming activity into the current-resource column B; record the result in column K; bracket the lowest of these recorded values. This simultaneously identifies both the maximum possible level of the incoming activity and the outgoing resource (or activity) from the B column. (For every such incoming activity there will be at least one outgoing resource or previously selected activity.) In the example, the paddy activity will come in to a level of 40 units and, as indicated by the left-side arrow from B in iteration I, the outgoing resource will be the 80 units of water.
The first step in iteration II for obtaining the second plan is to enter there the row of relevant coefficients for the incoming activity, paddy (marked now by an incoming arrow on the left-side of B). Construction of this and of the other new rows of coefficients in iteration II requires a substantial amount of arithmetic; clerical error is common and for large problems with many activities the use of a computer is almost mandatory. First we derive the new row of coefficients for paddy.
Coefficients in the incoming-activity (paddy) row of iteration II are found by dividing (a) the corresponding coefficients in the outgoing row of iteration I (i.e., the water row) by (b) the requirement of the incoming activity (paddy) for the outgoing (water) resource, i.e., by the coefficient in iteration I at the intersection of the outgoing (water) row and the incoming (paddy) activity. This pivotal value at the row-column intersection for water and paddy of iteration I has, in the present example, a value of two; it is bracketed for easy reference. These operations to find the coefficients for the incoming row (paddy) in iteration II are also performed on the B column. The new coefficients for the incoming (paddy) row in iteration II are thus found as follows:
|
|
B |
R |
C |
P |
S |
DL |
DC |
DW |
|
(a) |
80 |
1 |
0 |
2 |
0 |
0 |
0 |
1 |
|
(b) |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
|
(a)+(b) = |
40 |
0.5 |
0 |
1 |
0 |
0 |
0 |
0.5 |
While it is convenient to bring the incoming row (paddy) in to occupy the same row position as was occupied by the outgoing row in iteration I (i.e., to occupy the third row of iteration II), this is not essential.
After the coefficients for the incoming (paddy) row in iteration II are found, the coefficients for the other rows in iteration II are obtained. Starting with the top or labour row, as illustrated below, each of the coefficients for this in iteration II is found as follows:
(a) record the column coefficient of the same row (labour) in iteration I, then(b) calculate the product of the coefficient of the same column in the incoming row (paddy) in iteration II and the labour input-output coefficient for the incoming activity (paddy) for this resource/row (labour) in iteration I. (This input-output coefficient is the paddy resource-requirement coefficient for labour from the unit budget for paddy.)
(c) subtract the value obtained in (b) from the value in (a) to obtain the corresponding coefficient in the labour row of iteration II.
For the example worksheet of Table 9.9, these calculations are:
(a) the row coefficients for labour in iteration I were:
|
B |
R |
C |
P |
S |
DL |
DC |
DW |
|
100 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
(b) the coefficients of the incoming paddy row in iteration II are:
|
B |
R |
C |
P |
S |
DL |
DC |
DW |
|
40 |
0.5 |
0 |
1 |
0 |
0 |
0 |
0.5 |
The input-output coefficient of paddy for labour in iteration I was one. Thus the set of values to be subtracted in step (c) from the elements in (a) are:
|
B |
R |
C |
P |
S |
DL |
DC |
DW |
|
40(1) |
0.5(1) |
0(1) |
1(1) |
0(1) |
0(1) |
0(1) |
0.5(1) |
(c) Subtracting the final values in (b) from those in (a), the coefficients for the labour row in iteration II are thus:
|
B |
R |
C |
P |
S |
DL |
DC |
DW |
|
60 |
0.5 |
1 |
0 |
1 |
1 |
0 |
-0.5 |
The new coefficients for the remaining rows in iteration II (only capital) are found in the same way.
As in iteration I, the next step is to form the row of Z coefficients for iteration II, including the Z value for this current plan. The Z coefficient for B is now (60)($0) + (100)($0) + (40)($40) = $1 600. The other Z coefficients for the activities are found in the same way, i.e., as the sum of the products of the elements in each activity column of iteration II by their corresponding p value in the left-side p column of iteration II. Thus the Z value for roselle in iteration II is (0.5)($0) + (0)($0) + (0.5)($40) = $20. The final step in the iteration is to obtain the Z - p coefficients by the procedure outlined previously for iteration I, i.e., by subtracting each activity's p value given at the top of the table from its Z value. Thus the Z - p value for roselle is ($20 - $30) = -$10. Inspecting these activity Z - p values as the criterion for possibly bringing further activities into the plan, the largest negative coefficient is now -$12 for sesame. Sesame is therefore tentatively brought into the plan in the next iteration.
Subsequent iterations and plans
In iteration III, as determined in the K column of iteration II, sesame comes into the plan at a level of 60 units as constrained by the available supply of labour. Further, iteration III results in roselle having the highest (and only) negative Z - p value. Roselle should therefore be brought into the plan of iteration IV. The logic of this is that according to the Z coefficients of iteration III, the marginal cost of a unit of roselle (in terms of income reduction by driving other crops from the plan) is $26, or $4 less than the marginal income of $30 from roselle. Therefore it will pay to bring roselle in even though it will force some other activity out. This activity substitution occurs in iteration IV where roselle replaces paddy because the paddy row of iteration III has the lowest value in the K column. In iteration III no other activity except roselle could come in without either leading to an income decrease (of $2 per unit in the case of cows) or leading to no improvement in income in the case of (more) paddy or (more) sesame.
At the end of iteration IV there are no negative coefficients in the Z - p row; thus no activity is present which could increase plan income still further if it were brought in or substituted for any activity already in the plan. The positive Z - p coefficients of iteration IV warn that if the unutilized cows activity were to be forced into the plan, it would actually reduce total plan income at the rate of $2 per unit of cows brought in. Similarly if paddy was to be forced back into the plan, having left the plan at the end of iteration III, this would reduce plan income by $8 per unit of paddy. As shown in the B column of iteration IV (the final iteration in the example of Table 9.9), the final (and thus optimal) plan specified by LP has an expected income in farm TGM terms of $2 640 based on 20 units of sesame and 80 units of roselle; $90 of capital is left unused. It will be recalled that this plan TGM of $2 640 has not accounted for farm fixed costs. If required, these would now be deducted from the plan TGM to obtain net farm income.
Value of resources
In addition to formulation of an optimal plan, LP analysis also provides useful management information relating to the marginal value or shadow price that can be placed on the resources used by the plan. This value is based on their actual contribution at the margin to the achievement of plan income. In the last iteration of Table 9.9, the labour, capital and water disposal activities are shown to have a Z - p value of $12, $0 and $18 respectively. The interpretation is that if, e.g., one unit of labour were to be forced into non-use (or the amount of labour which is actually employed in executing plan IV is reduced by one unit), this would reduce plan income by $12. Thus, to this particular farmer executing this particular plan under the agro-economic conditions specified in the base table, the value to him or her of one unit of labour less or more is $12. For similar reasons the marginal value or shadow price of water is $18 per unit. On the other hand, because - unlike labour and water - working capital is not fully used, its marginal value to the farmer is zero. Of course, other farmers executing different plans with different activities and/or different input-output coefficients would have different shadow prices placed on their resources if an LP analysis were to be done for their farms. The usefulness of this information will be obvious. From iteration IV, the subject farmer could afford to pay up to $12 per unit but not more for a little extra labour, and up to $18 per unit but not more for a little extra water.
Such shadow prices are marginal productivity-based resource values. A method of finding average productivity-based resource values was discussed in Section 7.2. Clearly these LP-based marginal productivity resource values are more helpful to farmer decision making than are average productivity values. This is because of their marginal orientation combined with the fact of their holistic derivation in that they take into account the system effects of all the resources being used.
The structural characteristics which distinguish farm systems of Types 1 and 2 from other types (Section 2.2) are that they generate most of their own resources and have a generally subsistence rather than commercial orientation. However, the difference between Type 1 and Type 2 farms is one of degree of emphasis placed on these respective characteristics and thus on the type of activities by which they are structured.
On Type 2 farms the internally-generated resources (with possibly substantial externally-sourced resources) are intended primarily to support cash-generating activities, as well as some direct subsistence activities. On Type 1 farms the internally-generated resources (with very few external resources) are intended primarily to support direct subsistence activities - but since complete self-sufficiency is now rare, these Type 1 farms must also generate a little cash. There is also a difference in planning focus. On Type 2 farms the focus is somewhat more on optimizing output of the farm component; on Type 1 farms it is on meeting the subsistence requirements of the farm household.
These distinctions cannot be pushed too far: both types of farms merge into each other (McConnell 1992; Prabowo and McConnell 1993). But they are of sufficient magnitude to require that a somewhat different technical approach be taken in formulating production plans for each farm type. This section relates specifically to small farms of Type 2. The more complex more heavily subsistence-oriented small farms of Type 1 are discussed below in Section 9.6.3.
Resource generation and activity interdependence
As noted, Type 2 farms generate most of their own resources; there is a high degree of integration of activities and thus of structural dependence. This was implied in the definition of various activity subsystems in Section 9.3.1. When reduced to LP format for the purpose of determining the profit-maximizing combination of activities, their unit budgets might appear as shown in Table 9.10. Structurally, the difference between this base table and the base table of iteration I of the LP example of Table 9.9 is that one of the activities, growing a legume crop, is now specifically intended to generate resources (and thus carries a negative GM or p value equivalent to its direct costs), while the other activities of feeding cows and growing maize, each primarily a final product or cash-generating activity, also incidentally generate resources.
As previously, in the unit budgets of Table 9.10 the requirement of an activity for a resource is indicated by a positive input-output coefficient shown against the particular resource; e.g., one unit of maize crop requires one unit of land. If, on the other hand, an activity generates a resource, the coefficient for such resource is preceded by a minus sign. Thus while cows need cow feed, they also provide fertility via their manure; while the legume activity needs land and water, it also provides cow feed; and while the maize activity needs land, water and fertility, it also provides cow feed. This differs from the system of Table 9.9 in that some of the resources might not be present at the initial planning moment: the system must generate them. (It might also be possible to obtain them by purchase or barter.)
TABLE 9.10 - Example of Base Table with Resource Generation and Activity Interdependence
|
Activity: |
|
Cows |
Legume |
Maize | |
|
Activity unit: |
|
per head |
per ha |
per ha | |
|
Activity GM/unit ($): |
|
+30 |
-20 |
+60 | |
|
Resources |
B |
Input-output coefficients | |||
|
|
Land |
10 |
0 |
1 |
1 |
|
|
Water |
10 |
0 |
1 |
2 |
|
|
Cow feed |
0 |
1 |
-1 |
-1 |
|
|
Fertility |
0 |
-1 |
0 |
1 |
The planning objective remains the same, i.e., to maximize farm cash TGM, but here it is subject to the technical dependence conditions that: (a) high-profit maize needs soil fertility (but there is not yet a 'supply' of this in the resource pool B); (b) such fertility could be provided by cows, but cows need feed (and there is initially no feed in B); (c) such feed could be obtained from legumes and/or maize but, from above, maize is not yet possible. Therefore, the only way to achieve the TGM objective is to grow some legume (at a negative GM) for the cows; then obtain fertility from the cows for the maize which, incidentally, would provide yet more feed for the cows to produce more fertility for the maize etc. until some critical resource (land, water, labour) is exhausted.
A more realistic planning situation for a Type 2 farm is shown in the LP base table of Table 9.11. Features pertinent to or exemplified by the worksheet example of this table are outlined below. The example used is a small Javanese farm which well displays the resource-generating activities characteristic of Type 2 farms.
Planning period
The assumed planning horizon for the LP analysis of the example farm of Table 9.11 is one year, corresponding to an operating year which consists of two six-month phases: a wet-season followed by a dry-season. Some of the Phase I (wet-season) activities generate cash outputs which become available as cash inputs to (dry-season) activities in the following Phase II. Of course, if the system was being planned for a longer period of 2, 3, 4... years, then outputs of any Phase II would be available as inputs to Phase I of the next annual cycle.
Agronomic conditions as the basis for system phases and activities
In areas such as the Solo Valley of Java, high rainfall supplemented by seasonal irrigation permits production of a large range of short-term crops in the wet season (Phase I) of the annual cycle; these crops are planted in February to be harvested in June (Prabowo and McConnell 1993). In the (Phase II) dry season of July-December, lack of water restricts cropping to crops which can be grown on the dwindling supply of residual soil moisture from Phase I crops, supplemented by the little remaining water in the public irrigation system. Further, because soil moisture is rapidly decreasing, the time which would be required for normal land preparation for Phase II crops is in fact not available, so that possible Phase II crops are only those which can be planted quickly by 'gejik', i.e., by placing seeds in small shallow holes made with a pointed stick. This is done immediately after the Phase I crop has been removed and without further land preparation. In practice, since maximum residual soil moisture is built up under a previous wet-season paddy crop, dry-season Phase II crops consist mainly of soybeans and peanuts which are 'gejik'-planted on ex-paddy land.
Time dimension of activities and resources
In contrast to the situation depicted in Table 9.9, some of the activities of Table 9.11 now have a time dimension, or are time-specific in terms of some of their resource requirements. As shown in the table, the farm's activities fall into four groups: five wet-season activities which need Phase I resources; two dry-season activities which need Phase II resources; a third group of six activities which continue through most of the annual cycle and require both Phase I and II resources; and a fourth group of three barter or transfer activities whose time relationships vary.
The activities
All the activities of Table 9.11 are optional. These activities are now briefly noted as per the listing of activity types (i) to (x) given in Section 9.3.1. There is only one type (i) activity - growing chillies for sale. There are four type (ii) activities: beans, paddy, soybeans, peanuts. These are primarily intended to produce a final output but also incidentally produce resources - all produce roughage by-products for cow feeding and (except for paddy) also contribute to the degree shown to maintaining base field fertility (for use by the fertility-extractive activities of maize, paddy, cassava and chilli). Thus one unit (patok) of beans, as well as contributing $40 to farm cash TGM from sales, generates 0.4 tonnes of cowfeed roughage and 0.2 units of fertility to the field.
Growing maize and keeping cows are structured as type (iii) activities, producing only intermediate outputs/resources. The GM of maize of -$4 is the direct cost of producing one unit (patok) of maize. As Table 9.11 shows, the cows require no external inputs/costs; they need only household labour (20 per cent of 'February' and 'other' household labour) and internally-generated feed (maize and roughage from maize, beans, paddy, soybeans, peanuts and cassava) and thus have a GM of $0. But it is possible to specify these activities in other ways: e.g., if half the maize output is intended for direct sale while the remainder is to be used as resource for subsequent maize-using activities such as chips or cow feed, those direct sales could well offset or more than offset the $4 maize production cost (and so give this maize-growing activity a unit GM or p value of say -$3 or $0 or $10).
Kitchen processing of maize chips for sale in the village market and processing/selling milk, butter, cheese are second-stage type (i) activities. In general, when there is a possibility of using a farm-produced output in several ways, it is useful to view this as forming a resource 'pool'. Thus, in the example of Table 9.11, maize grain flows into the 'maize pool' (at the rate of 0.3 tonnes of grain per patok of maize) as a result of the maize-growing activity; it would then be withdrawn from the pool by the activities of chip processing or feeding cows (at the rate of 1 tonne per tonne of chips and 0.7 tonnes per cow, respectively). These withdrawals will occur in the LP analysis according to the relative total economic benefits to the whole system of using the resource for either purpose of chip processing or feeding cows.
Regarding cows, this activity could be specified as 'keeping a cow and selling her milk' but this would predetermine that this is the best use for the milk. It is better to set up a 'milk pool' in the B column and let the analysis decide if and to what extent the most profitable use of the intermediate resource is to sell it or to make butter, ghee, cheese or feed skim milk to animals etc., each of these activities having a different GM and other resource requirements. Because only LP can consider and evaluate all of these possibilities, only this planning method is really suitable in formulating 'optimal' plans of the required degree of complexity for Type 2 farms.
There are no activities of type (iv) (resource + final product-generating) or type (v) (development) or type (vi) (development + production) in the example of Table 9.11. There is only one type (vii) activity; this consists of the simple purchase of green manure (the leaves of leguminous trees, litter scraped up off the ground in the public forests). (These traditional methods of maintaining base soil structure and fertility are still common in parts of Java and elsewhere in South Asia.)
Resources may also be obtained by barter - a type (viii) activity. In the example of Table 9.11, milk can be bartered for (probably) scarce February field labour at the rate of 200 labour days per tonne of milk - or, in more realistic terms, five litres of milk per day of labour. Therefore, one indirect limit on February labour supply (and thus on the levels of crops using this labour, mainly maize and paddy) would be the relative economics of those other activities of the system which also compete for milk, i.e., production of cheese and butter.
Using household labour (additional to the available field labour) for field operations in the busy February planting month is a typical transfer activity of type (ix). From Section 3.3.4, a farm's family labour force is typically differentiated on the basis of the type of work each person is able or expected or willing to do. Normally the housewife, older children and aged people look after the livestock and kitchen processing/marketing activities (in addition to purely domestic chores) but they might also be needed in the field at planting/harvesting times. Thus this transfer activity simply states that if one such member of the household of four persons - which, in this example, excludes adult males who are routinely occupied with only crops - is needed for field work, this will require the reduction of household labour supply in February by 25 per cent and yield 28 additional days of field labour in that month.
Disposal activities
As previously, one disposal activity is required for each resource/constraint row. These consist of a diagonal line of '1' coefficients and carry a price of $0; they are not shown in Table 9.11 or discussed further.
Double counting of the output of activities
The last activity on the right side of Table 9.11 is of a technical nature. As shown in the row labelled 'Cash income available for use in Phase II', the cash income generated by Phase I activities, and half the income generated by the year-round dairy activities, is assumed to become available for meeting the establishment and operating costs of Phase II activities. This technical activity specified in the final column of the base table is a mechanism for ensuring that the income from other activities is not counted twice, once as direct activity income (GM) and again if/when this income, as savings, enables a second GM to be generated by some other activity.
The resources
The resources/constraints of Table 9.11 are largely self-explanatory. They are grouped into four categories according to the period to which they refer. Some are initially present (at the start of Phases I and II); some such as maize grain and milk must be generated; some such as field fertility must be maintained (system sustainability, Section 6.2.7). Cash income and store-type resources can be transferred forward through time from Phase I to Phase II. Flow-type resources (e.g., labour) must in general be used as they become available, or go into disposal or non-use (but some of these can sometimes also be transferred forward by structuring activities to allow sale and later repurchase of their resource outputs, or by barter of a resource now for a similar resource in the future). Also, it might be necessary to differentiate in resource use on the basis of quality, custom or tradition. Thus, in the example of Table 9.11, household labour is specified as normally being available and required only for keeping cows and dairy processing activities but, as need be, it could be specified as transferable to some other uses (as is done in Table 9.11 for February household labour which, like 'other household labour', has its input-output coefficients specified here in terms of the percentage of the total (fixed) amount available).
As shown by the respective coefficients of '1' and '-1' in the cash-transfer activity column of Table 9.11, cash for establishing and operating Phase II activities is generated by Phase I activities (being careful to avoid double counting). Finally, the land resource must be precisely defined in terms of time, quality and purpose. In the example of Table 9.11, 'land' means successively wet-season (Phase I) land, dry-season (Phase II) land, year-round land and, specific to Phase II, land immediately after a wet-season paddy crop has been removed from it.
Analysis and solution
Though the base table of Table 9.11 is much more elaborate than that of Table 9.9. it would be processed in exactly the same way - first adding a p column, disposal activities and a K column, then forming Z and Z - p rows, then selecting the most negative Z - p value etc. Too, in a real situation the system would probably be given a longer assumed life and the program run over a planning horizon of several annual cycles to determine the optimal plan after the system had stabilized; as noted above, this would require rows/columns allowing the flow-on of resources to successive phases and cycles. Solving such problems by hand is extremely tedious. However, they are readily solved by computer using such software packages as GAMS (GAMS Development Corporation 1997) and What'sBest!ä (Lindo Systems Inc. 1994). The more difficult and important task is to ensure that the farm is modelled adequately, in particular that its activities are structured appropriately and that its constraints are specified correctly.
Summary
Table 9.11 is probably a reasonable representation of production opportunities and the variety of activities involved on highly mixed small farms. But it still does not reflect the second structural characteristic of these farms - their subsistence orientation. This is discussed in the following section.
All the activities of Table 9.11 were optional: they might or might not enter the final plan, depending on their relative contribution to farm cash TGM. However, the characteristic purpose of Type 1 farms is to seek subsistence self-sufficiency directly by the production of household food and household/farm materials as commodities rather than through the medium of cash-generating activities. Thus the focus now shifts to the household; the planning objective is to meet its food and material needs. In consequence, the system is now dominated by mandatory subsistence food- and material-producing activities.
The activities
The production activities on a Type 1 farm fall into seven groups. Five of these are household oriented and two are farm oriented.
Household-oriented activities consist of producing food, including beverages and condiments, and non-food materials for direct use by the household component of the system as distinct from its farm component (although it is often difficult to distinguish between materials intended for household use and those intended as farm resources). Food-producing activities are often of a mandatory nature and fall into four groups according to the types of commodities they produce (which of course differ according to the physical environment, family preferences and custom):
(1) bulk staples/carbohydrates: e.g., grains, root crops, breadfruit, jackfruit.(2) vegetable and animal proteins: e.g., beans, peas, meat, fish.
(3) vegetable and animal oils and fats: e.g., sesame, mustard, coconut, peanut, soybean, maize, palm, butter, ghee.
(4) vitamins/minerals/taste: e.g., chilli, pepper, vegetables, paan.
As noted in Section 2.2.1 relative to the extraordinary product diversity found on many Type 1 and Type 2 farms, a variety of non-food materials are produced for household and farm use as subsistence items. Common examples are:
(5) bamboo (for construction timber, water pipes, furniture, flooring); coconut, kitul, aren and areca palms (for fibre, twine, containers, tools); and stems of cassava, cotton, roselle (for fuel and trellising).
Farm-oriented activities are of the same various types as those discussed previously in Section 9.6.2 relative to Type 2 farms. Thus:
(6) final-product activities are intended to generate extra-subsistence income by sale or barter.(7) resource-generating activities are intended to support all or some of the above activities (1) to (6).
As indicated by the example of Table 9.11, most field and livestock activities will in fact generate both final products and resources. Usually both these categories (6) and (7) will consist of sets of optional activities.
General vs specific requirements
There are two ways of handling mandatory subsistence-oriented activities. If appropriate, the requirements of such an activity might simply be subtracted from the initial stock of resources, then the planning analysis is directed at finding the best mix of optional activities for the remaining resources. This common-sense approach is adequate if the mandatory activity is predetermined - if, e.g., the family must have 0.25 ha of paddy; exactly or at least 0.1 ha of beans; at least one patok of sesame etc.
But from (1) to (4) above, there are many possible crops/activities/ways of meeting the household's general requirements for each of the four food groups. Although meeting each of these general requirements (carbohydrates, protein etc.) is mandatory, the specific activities for achieving this are themselves optional. In theory there are so many ways of meeting, e.g., a household's carbohydrate requirements that determination of the least-cost combination of crops/activities for achieving this would itself require a large LP analysis. The same is true for the other food groups. However, in practice - because of household preferences, tastes, custom as well as actual resource constraints - the household will predetermine only some of the requirements in terms of specific crops, while leaving its options open as to how the other general requirements can best be met.
As an example the household might specify the following conditions as the basis for formulating its production plan:
· at least 0.5 ha of country paddy.· at least 0.2 ha of pulses (but these can be from any crop/species/variety).
· at least 200 litres of vegetable oil (but this can be pressed from any oil source).
· at least 0.2 ha of chillies interplanted with leafy vegetables, but no more than 0.5 ha.
· maintenance of the existing grove of bamboo (for fuel, building timber, twine, fences, water pipes).
· any crops at all which will generate maximum net cash income (to meet household and farm needs not met by the above items).
· any activities at all to generate the resources needed by the above items.
Example
This type of subsistence-oriented farm planning problem is set up for LP as was the problem of Table 9.9, but with certain modifications. An example is shown in Table 9.12. The steps are summarized as follows:
(i) Distinguish clearly between maximum and minimum planning constraints or requirements. (Table 9.9 dealt only with maximum requirements.)(ii) For the (real) potential production activities:
· in section B of the worksheet, define the available resources and other constraints which would limit production or expansion of the several real activities;· construct a unit budget/requirements column for each of these real activities and enter the GM of each in the top p row; and
· again as previously, construct a disposal column/activity for each of the resources/constraints of B and attach prices to them which will be $0 unless the non-use of a resource actually bears a cost (as is the case with water in the present example of Table 9.12).
Now, as illustrated in Table 9.12, the modifications begin:
(iii) For each minimum requirement of the plan:· include this requirement as a planning constraint Q in the B column. Enter one Q row for each minimum requirement of the plan, Q1, Q2 ... ;· regard this minimum requirement also as an artificial activity and construct an activity column for it. Designate this activity column Q1, Q2... to correspond with the minimum requirements already designated as Q1, Q2... in the previous step;
· these artificial Q1, Q2... activity columns will consist only of a '1' coefficient at the intersection of each Q row and its corresponding Q activity column;
· in the p row, attach a very high negative p value to each artificial Q activity; denote this notional value by -M where this is unquantified in terms of money value but is understood to be higher than the money price of any real (i.e., non-artificial) activity. Having done this, any Q activity carrying such a very high and negative price -M is always the least profitable activity to have in the plan; it will therefore be driven out in the subsequent LP iterations where the operational objective is to replace low-value activities with relatively better ones (Section 9.6.1);
· as with the real production activities of (ii), construct a disposal activity column for each minimum plan requirement Q and attach to this a price of $0 in the p row. Specify the unit coefficient of each of these disposal columns at its intersection with the corresponding Q row as '-1' rather than as '1' (which latter was the practice with the disposal activities/columns for real non-Q resources).
The activities
On the example farm of Table 9.12 there are six possible production activities - cotton, paddy, chilli, sesame, mustard and bamboo - to first meet household requirements and, if there are any resources left over, to generate the maximum amount of net cash income. Typical requirements were discussed above. In this example they are specified as:
· at least 0.5 ha of grain, but only paddy is acceptable and any paddy in excess of 0.5 ha can be sold.· at least 200 litres of oil which might be obtained from 0.2 ha of either sesame or mustard; but while any amount of sesame oil in excess of household requirements can be sold, there is in this village no market for mustard oil; its sale price is $0.
· at least 0.2 ha of chillies for household consumption, but because the market for chillies is uncertain the farmer will not take the risk of producing more than 0.5 ha; chillies thus have both a minimum and a maximum limit.
· cotton to any amount as purely a cash crop.
· the present area of bamboo must be maintained.
As previously noted, the best way of handling any of these mandatory activities which involve no alternative supply activities is simply to deduct their resource requirements from the initial stock of resources on the farm. Thus, applying this to bamboo, total net available resources for entry into the B section of Table 9.12 are calculated as follows:
|
|
Land |
Cash |
Water |
|
Initial resources: |
3.3 ha |
$250 |
250 units |
|
Bamboo requirements: |
0.3 |
50 |
0 |
|
Net resources (B values): |
3.0 |
200 |
250 |
Table 9.12 is largely self-explanatory; only two points might be noted. First, on this example farm the disposal or non-use of irrigation water carries a cost of $10. This is based on the fact that, if the farmer does not use her or his full quota of water in any season, it will be reduced by this amount in the next season and she or he must then buy it back or pay a fine of $10 for each unused unit. The other disposal activities bear no such cost. Second, for each minimum requirement specified in the B section, there will be a disposal activity which carries a zero price, and an artificial activity which carries a very high negative price of -M. Finally, given this base table specified so as to accommodate mandatory activities, the operating steps to determine the LP-based optimal farm plan are the same as in previous examples: the Z and Z - p rows are obtained and the analysis proceeds as in Table 9.9. While such analysis is clearly tedious (and prone to error) if done by hand, it is easily carried out on a personal computer using available LP software such as, e.g., GAMS (Brooke, Kendrick and Meeraus 1992) or What'sBest!ä (Lindo Systems Inc. 1994). The skill and artistry involved reside in formulating the base table so as to adequately reflect or model the reality and objectives of the farm being programmed.
As Sections 9.6.2 and 3 evidence, the application of LP to Type 1 and Type 2 farms can be quite complicated - not in terms of calculation (which is easily done using available computer software) but in terms of specifying the base table with its various types of activities and their unit budgets. Such specification requires skill if not artistry and can be quite demanding of the analyst's time. Obviously, the question must be asked as to whether the benefit gained is worth the cost involved. In general, the answer to this relative to one-off analyses of small farms will be negative. However, there are two situations for which the benefit may exceed the cost involved. The first is when the analyst is concerned (either for farm advisory, development or government policy purposes) with a recommendation domain consisting of a significant number of relatively homogeneous small farms. LP analysis of a representative farm may then provide broad guidelines or insights relevant to all the farms of the recommendation domain. The second situation is when the analyst may wish to have a better professional understanding of the operation of various small-farm systems of concern. Modelling of these systems by developing at least the LP base table (if not full LP analysis) of a number of distinctive case-study farms may then greatly enhance his or her understanding of such farm systems.
While there is no doubt that LP can enhance an analyst's understanding of a farm system, he or she should beware of taking the LP-based optimal farm plan at full face value. In particular, any significant difference between what a farmer is actually doing and what LP analysis suggests he or she should be doing should not necessarily be attributed to farmer irrationality, ignorance or inefficiency. Rather, such differences should be seen as a reason to review and possibly respecify the LP analysis. Thus, in general, LP analysis should be seen as a starting point or guideline input to the choice of a final plan; it should not be seen as the final arbiter to choice of a plan. Obvious reasons for such caution are (i) the possibility that the LP base table does not properly specify the objectives, activities and constraints pertinent to the farm system, (ii) the possibility that the input-output data used in the LP analysis are not error-free and (iii) the reality that the real world of the farm system involves both non-linear input-output relationships (particularly diminishing returns) and risk arising from uncertainty about, in particular, yields and prices. The first of these deficiencies - misspecification of the base table - may be lightened by dialogue with the farmer in developing the LP base table; the second - errors in the input-output data - by the use of sensitivity analysis via parametric LP (Hazell and Norton 1986, pp. 125-131; Rae 1994, pp. 109-114); and the third - non-linear relations and risk - may be lessened by using more advanced forms of mathematical programming, in particular risk programming as outlined in Chapter 11 and by Hardaker, Huirne and Anderson (1997, Ch. 9).
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