ON THE ANALYSIS OF A SIMPLEX LINEAR PROGRAMMING SOLUTION TABLEAU-WITH REFERENCE TO NET REVENUE STABILITY LIMITS

An assumption in a conventional net revenue stability analysis of a linear programming solution tableau is that net revenues are independent. For many activities this assumption is violated in that changes in a particular activity's net revenue may nell be associated with changes in other activities' net revenues. The significance of the independence assumption is examined for an example problem, and a method of calculating the range over which a particular activity's net revenue can vary without giving rise to a sub-optimal solution where activity net revenues are correlated is developed.     

A LINEAR PROGRAMMING SOLUTION TO SOME MARKET ALLOCATION PROBLEMS

Certain market allocation problems involving linear average net revenue functions can be solved by linear programming. The technique can be applied to an objective function derived from linear marginal net revenue functions, the objective being to force each marginal net revenue as near to zero as possible given the constraint set. If a particular problem is suited to a linear programming solution, researchers may prefer to use this technique rather than more sophisticated optimization methods.     

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 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.     

THE INFLUENCE OF WORKING CAPITAL ON FARM ORGANIZATION — HOW APPROPRIATE IS A LINEAR PROGRAMMING ANALYSIS?*

Effective limitations on farm working capital are not easily identified but behaviour consistent with such limitations is observed. Using a linear programming analysis, the results of having limited working capital are shown. It is also shown that the value of the working capital resource is so high that farmers make every endeavour to keep it free from limitation.     

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.     

THE LOCATION OF MAINCROP POTATO PRODUCTION IN BRITATN-AN APPLICATION OF LINEAR PROGRAMMING

In any dynamic economy the allocation of resources, particularly land, is in need of continual reappraisal in order to reduce their misallocation. For some years now linear programming and similar operational research techniques have been applied to solving problems of this nature within the agricultural economy. In this paper interregional competition within the potato industry is analysed using the framework of the transportation algorithm. Problems of specification and data compilation are discussed. Three models are then formulated, their solutions illustrated, and comparisons made with the present distribution of production in order to arrive at conclusions as to possible areas of adjustment. Finally, some of the strengths and weaknesses of the methodology used are outlitled.     

解决西北地区干旱、沙漠化问题的对策

在分析我国西北地区沙漠化严峻形势的基础上,提出了治理沙漠化的根本在于节流与开源相结合以增加水资源,并就东水西调提出个人看法。     

A LINEAR PROGRAMMING STUDY OF FAMILY-RUN DAIRY FARMS IN NORTHERN IRELAND

The paper presents the results of a study in which multiperiod linear programming models were used to examine the probable responses of small and medium sized dairy farms in Northern Ireland to various policy, farm indebtedness and development options and to project consequent structural change in the dairy sector. The introduction of quotas has curtailed the considerable potential for expansion of output on these farms while having a less detrimental effect on farm profits and the survival of the smaller dairy herd than the price cut necessary to produce the same reduction in output.     

SHORT-AND LONG-RUN FARM PLANNING UNDER UNCERTAINTY; INTEGRATION OF LINEAR PROGRAMMING AND DECISION TREE ANALYSIS

The paper presents an approach to an integrated long-run and short-run farm planning under uncertainty, based on a decomposition of the problem into (i) a series of short-run plans, and (ii) a master long-run plan. The series of the short-run plans are parametrically solved by linear programming "variable right hand" techniques and are later integrated into a long-run program using a (computerized) decision tree analysis. The attitude towards risk of the farm operator is expressed in the willingness to maximize the expected value of the income stream over the planning horizon subject to the restriction that alternatives which may lead to lack of liquidity must be eliminated.
Ce travail présenle une approche tentative ďintégrer, sous conditions incertaines, une planification de ferme à court et long terme. La planification est basée sur la partition du problème en (i) série de courte durée et (ii) de tongue durée. Les séries de courte durée sont résolues àľaide dun programme linéaire, et intégreés ensuite dans un programme à long terme àľaide de ľanalyse de "décision arbre."ľattitude envers les risques de ľentrepreneur est exprimée par la volonté-de maxiliser la valeur de revenu prévu au delá de la planification sous resérve de la restriction que des alternatives qui peuvent conduire à un manque de moyens liquides, doivent être éliminees.     

A MIXED INTEGER LINEAR PROGRAMMING EVALUATION OF SALINITY AND WATERLOGGING CONTROL OPTIONS IN THE MURRAY-DARLING BASIN OF AUSTRALIA

Pollution of the River Murray by salt imposes costs on domestic and industrial users in Adelaide and to irrigators on the River Murray. Salt enters the Murray-Darling system through saline ground water aquifers and from irrigation and drainage of saline land. Irrigation and drainage generate benefits from improved agricultural productivity and impose costs through increased salt loads to the Murray-Darling system. The salinity of the River Murray can be reduced by pumping highly saline ground water into evaporation basins before it enters the River Murray. This paper presents a mixed integer linear programming model which is used to determine the mix of ground water interception schemes and land improvement schemes that minimises the net present value (over a time horizon of 30 years) of total Murray-Darling Basin costs due to salinity and waterlogging. By varying a target salinity level, the mix of works that yields various salinity targets in the River Murray at minimum cost is obtained. The sensitivity of the optimal solution to prescribed changes in costs and benefits of projects and to a longer planning horizon is examined.     

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.     

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.