Multi-period Linear Programming Research Articles

Economic comparison of nutritional management strategies for Venezuelan dual-purpose cattle systems

Objectives of this study were to compare three nutritional management strategies for dual-purpose herds in Venezuela in 1987 using a deterministic, multiperiod linear programming model of a representative farm. The model maximized discounted net margin (total revenues minus variable costs) from the herd for a 3-yr cow replacement cycle partitioned into six periods. The periods accounted for seasonal variation in forage availability and quality, and the model provided information about optimal animal inventories, animal sales, land in forage, and feed supplements. We compared current nutritional management practices and alternatives allowing optimal supplementation with commercial concentrate, molasses, cassava root, and urea. Iteration between the programming model and results from the Cornell Net Carbohydrate and Protein System assured technical coefficients consistent with predicted animal performance. Compared with management practices relying on commercial concentrate, optimal use of molasses and urea permitted increases in the stocking rate. Productivity and profit were restricted primarily by energy intake, which was constrained by intakes of NDF and DM. Alternative management strategies changed the relative importance of nutrient requirements and feed intake constraints. Thus, optimal interventions to alleviate nutritional constraints will vary with current management. Mobilizing adipose and protein tissues during lactation was optimal for most strategies. Supplementing with molasses and urea instead of commercial concentrate was the most profitable strategy, increasing herd net margin by 16% compared to the predominant feeding strategy in the late 1980s.

An optimization model of the dual-purpose cattle production system in the humid lowlands of Venezuela

We developed a deterministic, multi-period linear programming (LP) model of the dual-purpose (milk-beef) cattle production system in the Sur del Lago region of Venezuela. The LP model selected animal, forage, and purchased feed activities subject to nutritional, land, and herd composition constraints to maximize discounted herd net margin. A cattle nutrition model provided original coefficients for feeds and animal nutrient requirements. Revised coefficients resulted from an iterative procedure to avoid errors from the interaction between diet and requirements. Model applications demonstrated that alternatives to traditional feeding practices are profitable and nutritionally feasible. However, the benefits of alternative nutritional management depend on labor availability. Our simulation of price policy changes in the late 1980s indicated that dual-purpose producers may experience increased relative incentives for milk production under the new input and output prices. The model is adaptable to dual-purpose production systems elsewhere in Latin America.

The economics of biomass energy: A case study from Hawaii

Abstract The thesis that the cost-effective conversion of Hawaii's biomass sources to electricity can be best accomplished by a central power plant is developed and empirically tested using a multiperiod linear programming model. The results also suggest that it is cheaper to produce electric power from a biomass-fueled plant than from a fuel oil-based facility.

Analysis of some forest management strategies in Côte d'Ivoire: a regional case study

Extensive forest harvesting in Côte d'Ivoire has raised concern over the long-term timber supply from the country's national forests. To alleviate anticipated timber shortages in the future, the Ivorien government is shifting its management emphasis to reforestation. This paper examines existing and alternative forest management scenarios using a multiperiod linear programming model. Three issues addressed by the model are: economic returns, timber removal, and timber inventory. Emphasis is given to individual firms and their financial capability to conduct reforestation. A regional case study consisting of six forest companies and eleven primary timber species is presented and examined.

Vector forecasting and dynamic portfolio selection: Empirical efficiency of recursive multiperiod strategies

In the paper we present a dynamic portfolio selection system. The system combines recent results from the domains of time series analysis, portfolio theory and multiperiod linear programming under uncertainty. The performance of the decision support system is tested empirically against a dynamic super criterion defined in the study. We demonstrate that suitable combination of ex ante and ex post information with initial balances for the planning horizon yields better portfolio efficiency through time than a strategy relying purely on ex ante information. The system was programmed on Åbo Academy's vax 8800 computer, mainly in fortran, with access to the imsl library and ifps/optimum.

Planning harvesting and marketing activities for integrated fishing firms under an enterprise allocation scheme

This paper focuses on the tactical planning problem for integrated fishing enterprises operating in Canada's Atlantic Groundfish industry. A firm with a fleet of trawlers, a number of processing plants, quasi-property rights to fish in the sea, and market requirements, must coordinate harvesting and marketing strategies which will allow it to maximize potential revenue. To achieve this, we outline a large-scale linear programming model which maximizes net revenue from product sales less fleet operating costs, subject to marketing and fleet operating constraints. The output of the multi-period linear program suggest what products and their respective volumes should be marketed, and how raw fish should be caught in order to satisfy marketing requirements. We demonstrate the planning and diagnostic potential of the linear program by solving an example problem based on data obtained from a large Atlantic seafood company.

REVERSE COMMUTATION IN A MONOCENTRIC CITY*

ABSTRACT. A general equilibrium multiperiod linear programming model of urban land use is used to identify reverse commutation as a rational response to economic change. Information about future economic conditions is complete, and capital is replaceable at finite cost. Export mixes are defined exogenously, and temporal shifts between activities of different land intensities are shown to induce reverse commutes as one way of avoiding the cost of land use change.

Organic viticulture in West Germany

We present results from a survey of organic grape operations in the three most important grape-producing areas in West Germany. Data on expenses for fertilizers, pesticides, machinery and buildings, on labor requirements, on the quantity and quality of yields, and on marketing channels and price premiums are compared to data on conventional grape operations from statistical sources. Based on these data, multi-period linear programming models were constructed to assess the economic implications of a transition to organic grape growing for different types of operations. Model results indicate that the grape production quota implemented in West Germany in 1989-90 favors organic methods. However, with direct marketing of wine, the effect of the quota depends on the effect that the expected rise in the price of conventional wine has on the price of organic wine. Premium prices for organically produced wine currently can be achieved only by farms that sell their wine directly to the consumer, which means that direct marketing is necessary for a profitable organic grape operation under current market conditions.

On the Use of Pseudo Shadow Prices in a Multiperiod Formulation of the Production Planning Problem

A multiperiod linear programming model of the production planning problem is used to argue for a different costing, profit and resource-evaluation procedure in manufacturing. This procedure is based on the concept of ‘pseudo shadow prices’, and it avoids many of the pitfalls associated with the more traditional accounting methodologies. Conclusions are drawn which question the profit objectives used by many firms, as well as by those in academia.

A primary/secondary memory implementation of a forward network simplex algorithm for multiperiod network flow problems

The minimum cost, multiperiod network flow problem is an optimization model that is frequently used to assist decision makers in the areas of resource planning, scheduling and distribution. This model describes network structured decision making problems over time. Important problems in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, economic systems, etc. can be described by this model. Usually, standard network codes are used to solve such problems because of their availability and perceived efficiency. To date, few researchers have considered the multiperiod structure in devising efficient solution methods. The forward network simplex algorithm of Aronson and Chen is one such method. It is a forward algorithm that exploits the natural decomposition of the problem by limiting its pivoting activity to later time periods. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for the multiperiod linear programming problem, some of its specializations and generalizations and a large number of specially structured models. The forward network simplex algorithm solves multiperiod network flow problems efficiently. Encouraging computational results indicate that the forward network simplex implementation is significantly more efficient than standard network optimization codes that do not exploit the multiperiod structure. Even though the forward network simplex method is efficient, there are still limitations to the size of problems that can be solved in-core. In this paper, we discuss a primary/secondary storage implementation of the forward network simplex method and report computational results. This implementation is capable of solving much larger problems than the in-core code and is more efficient than standard codes. Problems having 700 time periods for a total of 3500 nodes and 9095 arcs were solved in less than one third the time of the standard code on which the forward network implementation is based. Furthermore, problems up to about double this size, which the standard code could not solve, were solved by the primary/secondary implementation.

Optimal bank asset and liability management with financial futures

AbstractThis paper presents a model for optimal bank asset and liability management with financial futures. This model is a multiperiod linear programming model based on Markowitz portfolio theory. Given the bank's initial position, its economic forecasts, and the constraints under which it operates, the model can help a bank's senior executives determine the current and expected future balance sheet composition and financial futures position which will minimize the bank's operating risks and which will meet the bank's expected profits goal with the minimum possible profits risk. By parametrically varying the expected profits goal, the model will generate the set of risk‐return efficient decisions. Bankers need then examine only the set of efficient decisions to choose their optimal solution.A simplified example is used to illustrate the application of our model and to demonstrate that banks that use financial futures in asset and liability management can obtain better results than banks that do not use financial futures.

Chance‐Constrained Financing as a Response to Financial Risk

AbstractThe results of a recent survey suggest that many decision makers view financial risk in a safety‐first context. Imposing safety‐first chance constraints on potential financial ratios or flows can be difficult with traditional methods. This is particularly true with financial ratios when both the numerator and denominator are random and are affected by endogenous decisions. A model and numerical example are presented which enforce probabilistic or chance constraints upon potential debt/asset ratios in a multiperiod linear program. The model can be easily modified to probabilistically constrain alternative financial performance measures such as current ratios, working ratios, or cash flows.

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.

Analyzing Equity Capital Programs of Banks for Cooperatives

AbstractCharacteristics of Banks for Cooperatives term loan and equity capital programs contribute toward complex intermittent exchanges of positive and negative cash flows between the cooperative lender and borrower and complicate the analysis of the net present value and effective interest of the financing project. A multiperiod linear program was developed to analyze the effect of variations in equity capital program components on the present value of the financing project. Furthermore, the concept of a “mixed financing project” was used to analyze the effective interest rate associated with such projects.

Energy-economy interactions in Mexico: A multiperiod general equilibrium model

A multisector, multiperiod linear programming model is constructed to analyze the interactions of energy and economic policy issues in Mexico. Using piece-wise linear approximations, the model embodies non-linear substitution possibilities between alternative technologies within sectors, between foreign borrowing in successive time periods, between the rate of oil extraction and reserve depletion and in consumption and trade patterns. Complete intertemporal efficiency is achieved as compared to the temporally myopic feature of conventional computable general equilibrium models. Alternative solutions suggest that production restraint to help stabilize oil prices may have had significant costs to Mexico and that imposition of a debt ceiling could create infeasible conditions, without significant changes in behavioural relations.

Discount rate for technology assessment: An application to the energy sector

When comparing the relative merits of technologies in the energy sector, analysis of a long time span is frequently required. Discounting of costs and benefits is usual in such analysis, and the choice of an appropriate discount rate can be vital. The available empirical evidence suggests that the appropriate real discount rate could vary widely depending on which concept it is based. For Australia, a value reflecting the social time preference rate could be as low as 2%, while one based on the social opportunity cost of capital would be considerably higher, probably 7–10%. A multiperiod linear programming model, MARKAL, suitable for energy technology assessment, was used to analyse the effect on the optimal long-term energy strategy for Australia, of using discount rates over the range 2–10%. The results indicate that capital-intensive technologies such as coal liquefaction and solar water heaters are disadvantaged when using high discount rates. This could result in energy strategies being pursued in which the level of oil imports is much

Optimum loading for GT/MRP manufacturing systems

A hierarchical planning procedure to utilize the potential advantages of coexistence of Group Technology (GT) and Material Requirement Planning (MRP) systems is presented. In addition, a multi-period linear programming model is proposed to determine the minimum cost loading schedule of manufacturing cells used in batch production environment. The proposed model provides the optimum work force for each cell over the planning horizon.

Identification and selection of technology for a specific agricultural region: A case study of sheep husbandry and dryland farming in the northern Negev of Israel

The chances that innovative technology will succeed in a given agricultural region are difficult to determine in advance. Information that would point to the likely or optimum course of development would be very useful for development planning and applied agricultural research administration. An approach is presented whereby the diffusion of new technology can be analysed in the context of a developing region. The development of sheep husbandry and wheat cultivation systems in a semi-arid agropastoral region in the northern Negev of Israel is used as a case study. The approach employed involves defining the input/output relations of a set of technologies based on wheat cultivation and on an increasingly intensive range of sheep production systems. The region is defined by its borders, land classes, physical and financial capital, available labour, plant and animal genetic stock and climatic conditions. An optimum mix of technologies over a development period is determined by using a multiperiod linear programming routine. The technology assessment is then conducted by varying the future socio-economic scenarios of the region and analysing the response of the model. The results indicated that the most fertile sheep breed, the Finn cross, would be selected only if labour were plentiful and cheap. It would also be selected whenever the demand for sheep created high shadow prices—especially at the beginning of a development period. The local, relatively extensive, breed of sheep (Awassi) is maintained over a long period even when meat: grain price ratios are high. Eventually, it tends to phase out in favour of a more intensive breed, the German Mutton Merino. The high price ratio did not result in massive transfer to confined, intensive husbandry but increased the use of improved pasture on cultivable land.

Energy modelling for technology assessment: the MARKAL approach

The primary objective of energy policy in many countries is to change the structure of their energy systems so as to reduce the dependence on imported oil. A large amount of funds is spent on energy research and development. The technologies competing for such funds have widely varying characteristics. These relate to costs and benefits, technical performance, environmental effects, the requirements for land, water and materials and the impact on employment. It is necessary to analyse these effects in some detail before decisions on technology programmes can be made. A complete assessment of the possible value of a particular technology cannot be made on an individual basis. It is necessary to consider many technologies simultaneously, competing against each other for various shares of the energy market. However, analysing the behaviour of the entire energy system requires the handling of an extensive amount of data and can only be done effectively with the help of a computerised system. The model, MARKAL, described in this paper is a multi-period linear programming model which has been developed and applied by 15 OECD countries for the purpose of energy technology research and development planning. Examples of the use of the model for this purpose are given both for the group as a whole and for individual countries. The model is structured so that an exogenously specified set of end-use demands must be satisfied given available technologies and energy supplies. The model allows for substitution possibilities in both the energy supply and demand sectors. A feature of the model is the use of varying objective functions such as minimum discounted costs, oil imports, or environmental effluents. These can be used individually or in combination in trade-off situations. The broader question of the use of energy modelling for technology assessment, including its limitations, is also discussed with particular reference to the insights that can be gained from the MARKAL model. Information from the MARKAL model has been used by the International Energy Agency to assist it in formulating a strategy for energy research development and demonstration.

A Dynamic Model for Technical and Economic Analysis of Fertilizer Recommendations1

AbstractThe rationale of this study was to jointly estimate response functions for N, P, and K for wheat and soybean cropping in southern Brazil and carryover functions for residual fertility. The two sets of functions were then combined in a dynamic model having general applicability for optimizing fertilizer recommendations. The model is composed of (a) a yield‐nutrient response function incorporating Liebig's Law of the Minimum and Mitscherlich's relative yield theory, (b) fertility carryover functions for P and K, and (c) a multiperiod economic programming model which combines crop yield response and carryover functions with crop and fertilizer prices. Important implications are that (a) the Law of the Minimum assume no nutrient substitution, (b) the relative yield theory allows pooling response data from different experiments, and (c) the fertilization problem is treated as a dynamic process that utilizes revised measures of soil fertility as they become available through soil tests. The crop response was specified as a piecewise linear and plateau function while the fertility carryover was postulated as a first order difference equation, incorporating an exponentially declining process of soil fertility. The solution of the overall dynamic model took the form of a multiperiod linear programming problem.The N, P, and K response functions for wheat (Triticum aestivum L.) and soybean (Glycine max L.) yields were generated from 38 fertilizer field experiments conducted at Rio Grande do sul and Santa Catarina states in southern Brazil between 1968 and 1976. The seven experiments that were repeated for 4 years provided the information for estimating the carryover effects of P and K fertilization.The results indicate that the optimal target levels of soil fertility are in accordance with those recommended locally. The maintenance applications recommended, however, are substantially different than the optimal quantities determined by the dynamic model presented here. The model calls for a reduction of the current maintenance application for both N and P of 10 kg/ha and an increase for K of 12 kg/ha. This would result in a U.S. dollars saving of $27/ha 1 year.