PLANT LOCATION ANALYSIS USING DISCRETE STOCHASTIC PROGRAMMING1*

A plant location model with two major aspects is outlined. First, discrete stochastic programming is used to handle variability in supplies and demands. Second, the cost structure of plants is modelled in more detail and with more realism than is usual. Results from applying the model to the Queensland cattle slaughtering industry demonstrate the inappropriateness of using traditional deterministic plant location models to analyse problems with major stochastic elements. Deterministic models yield plant locations, sizes, throughputs, commodity flows and implications which differ markedly from those generated by stochastic models in which plant sizes and locations are optimally matched to variable fat cattle supplies. In addition, the traditional deterministic long-run model overestimates the normative gains of industry rationalisation.     

THE ECONOMIC OPTIMISATION OF SOW REPLACEMENT DECISIONS BY STOCHASTIC DYNAMIC PROGRAMMING

A stochastic dynamic programming model is designed to determine the economic optimal replacement policy in swine breeding herds. This optimal policy maximises the present value of net revenues from sows present in the herd and from subsequent replacement gilts over a given planning horizon. The model also calculates the total extra profit to be expected from trying to retain an individual sow until her optimal lifespan and not replacing her immediately. This total extra profit is an economic index which makes it possible to rank sows within the herd on future profitability and, therefore, can be used as a management guide in culling decisions. For typical Dutch values the optimal replacement decisions result in an average herd life of 3.43 parities. The maximum economic life of sows of average productivity turns out to be 10 parities. All data can easily be adjusted to represent a specific herd or a different region of the world.     

A DYNAMIC PROGRAMMING MODEL OF EARLY POTATO HARVESTING

A vegetable producer often faces complex harvest decisions where yield increases through time and varies across crop area, price is determined in erratic seasonal markets, and harvest rate is constrained. In this paper, a simplified two-period potato harvest problem is developed to define a set of marginal conditions for an optimum. The model is then extended to the multi-period case and numerical solutions are generated for a representative farm in South Wales using dynamic programming. The model provides a general framework for analysing crop harvesting systems and prescribing marginal changes, such as adjustments in the harvest capacity, which improve profitability over myopic harvest patterns.     

DERIVATION OF OPTIMAL LIVESTOCK RATIONS USING QUADRATIC PROGRAMMING

Linear programming has been used extensively as a procedure for formulating least-cost livestock rations. More recently attention has heen focused on the incorporation of information on animal performance into the linear programming derivation of optimum livestock rations. Where the production is a quadratic function of nutrient inputs and where there are a large number of possible ration ingredients, parametric quadratic programming is shown to be an efficient computational technique for the derivation of “expansion path” rations. The region of economic interest along the expansion path is identified for the liveweight gain interval described by the production function. The rise of information contained in programming solutions to evaluate the economic significance of nutrient requirements and to aid in the search for possible ration ingredients is briefly discussed.     

USING REGRESSION ANALYSIS TO REDUCE AGGREGATION BIAS IN LINEAR PROGRAMMING SUPPLY MODELS*

Because methods of eliminating aggregation bias are impracticable, an alternative method is suggested for reducing aggregation bias which uses regression estimates of farm resonrce availabilities as functions of farm size. The estimates are incorporated in a parametric run of the LP problem in which size is parameterized. The method is applied to a case study problem, and the results compared with other methods of demarcating representative farms.     

LINEAR PROGRAMMING ANALYSIS OF CONSTRAINTS UPON HUMAN DIETS

This paper applies linear programming cost-minimisation models to the analysis of human diets. The models incorporate considerations of nutritional and non-nutritional factors in diet choice in order to assess the impact of adopting dietary guidelines upon the cost of nutrition-only and palatable diets. The dual prices yielded by the models are used to estimate the total cost of meeting requirements for separate nutrients in diets for different population groups. Sensitivity analysis is then used to derive marginal cost curves for changes in the supply of nutrients covered by the dietary guidelines. The cost and composition of ‘healthy’ human diets contrast markedly with the results of past studies and indicate that economic constraints upon dietary guideline adoption are limited.     

THE INTEGRATED USE OF SIMULATION AND STOCHASTIC PROGRAMMING FOR WHOLE FARM PLANNING UNDER RISK*

Methods of whole-farm planning under risk are briefly reviewed, noting especially associated operational problems. A planning problem relating to spatial diversification of beef production in the Clarence region of N.S.W. is investigated using a model comprising both simulation and linear programming components. It is concluded that such composite models are valuable for the analysis of sequential stochastic decision processes not presently amenable to solution by stochastic programming alone.     

OPTIMAL FEEDING POLICIES FOR BROILER PRODUCTION: AN APPLICATION OF DYNAMIC PROGRAMMING*

The determination of an optimal feeding and selling strategy for broiler production given a space constraint is formulated as a dynamic programming problem. Production equations derived from trial data are used to obtain an optimal sequence of rations in which energy density changes through time. The stability of the plan is explored and the implications of the results for production research and commercial practice are considered.     

AN ALTERNATIVE SOLUTION TO LINEAR PROGRAMMING PROBLEMS WITH STOCHASTIC INPUT-OUTPUT COEFFICIENTS

Deriving acceptable farm plans where input-output coefficients are stochastic is a complex problem. Previous formulations have required many simplifying assumptions about the stochastic variables in the analysis. This paper presents an alternative approach based on the mean absolute deviation, which permits solution by a conventional linear programming algorithm whilst avoiding some of those assumptions previously required. The formulation also incorporates a stochastic objective function. Examples are provided using the situation of stochastic feed supply with reference to representative sheep-grain farms on the Northern Tablelands of New South Wales. Results from these suggest that this alternative approach is a distinct improvement on earlier stochastic formulations which utilize linear programming algorithms.     

IMPLICATIONS OF AGGREGATION BIAS FOR THE CONSTRUCTION OF STATIC AND DYNAMIC LINEAR PROGRAMMING SUPPLY MODELS*

Aggregation bias is acknowledged to be one of the more serious problems confronting the Linear Programming approach to supply analysis. Whilst the literature abounds with theoretical solutions to the problem there is a notable lack of ideas on how these solutions might be made operational. This conclusion holds a fortiori for the dynamic case. This paper discusses a practical methodology for the classification of farms in order to minimise aggregation bias, and also the implications of avoiding bias for the specification of dynamic linear models.     

CONTROLLING STRAW BURNING: FARM MANAGEMENT MODELLING OF THE POLICY OPTIONS USING LINEAR PROGRAMMING

Autumn-sown cereals place pressure on post-harvest operations, particularly straw disposal. Burning is often a private solution but imposes external costs on others. Policy options to control burning include an outright ban, standard regulations, pollution taxes and transferable discharge rights. The effects of such options on farm income are assessed for an East of England cereals farm using a Linear Programming model. Results are sensitive to assumed straw yields, the market price of straw, and incorporation costs. Transferable discharge rights offer a flexible and efficient instrument to regulate straw burning at a non-zero level.     

DYNAMIC PROGRAMMING: A TOOL FOR FARM FIRM GROWTH RESEARCH

This paper is concerned with dynamic programming as a tool for studying the process of farm firm growth. Studies of growth are restricted by characteristics of the analytical tools used. Dynamic programming provides a method for including added realism in conceptual and analytical growth models. This paper illustrates the formulation of a firm growth problem in a dynamic programming framework and discusses advantages and disadvantages of such models. The type of results obtained from dynamic programming is contrasted with that normally obtained from dynamic linear programming formulations.     

A GRAPHICAL ANALYSIS OF SPOT PRICE STABILIZATION USING FUTURES*

This paper presents a graphical analysis of stabilizing commodity prices via intervention in the futures market. It uses a two-period analysis. The paper identifies some of the major parameters which seem likely to influence the success of such a scheme, but it is without empirical content.
Cet article présente une analyse graphique de la stabilisation des prix des biens au moyen a"interventions sur le marché des cotations en utilisant une analyse en deux phases. Ce document identifie quelques uns des principaux paramètres qui semblamt vraisemblablement influencer le succès d'un tel projet, mais sans fondement empirique.     

A DYNAMIC ANALYSIS OF US EXPORT WHEAT PRICING AND MARKET SHARES

The economics of a higher loan rate to support US wheat prices is analysed. Utilising optimal control theory, a dynamic wheat trade model is developed. The basic premise underlying the model is that the United States finds itself having transient monopoly power in the wheat market. An expression for the optimal pricing policy which maximises the present value of expected profits over the indefinite future is derived. Results from both the theoretical and empirical models demonstrate that the US wheat pricing strategy depends on its costs relative to competitors' costs, the discount rate and the competitors' response function. The main policy implication of the analysis is for the dominant wheat exporting country constantly to seek to lower costs relative to competitors and to maintain a price exceeding unit cost without encouraging competitors' expansion.     

THE USE OF A DECISION MAKER'S UTILITY FUNCTION IN A LINEAR PROGRAMMING ANALYSIS OF AGRICULTURAL POLICY*

A decision theoretic approach to agricultural policy decision making is examined to discover whether a utility function of an Australian Wool Corporation decision maker can be established and, if so, whether this can be used to improve the policy analysing performance of an agricultural sector linear programming model. After discussing the theoretical requirements of the utility function elicitation and the elicitation procedures, the characteristics of the resulting functions are examined. A means for its inclusion in a linear programming framework is described and some analysis of policy is carried out. The general conclusions are that the relevance of the agricultural sector analysis is enhanced by the use of such a utility function.