Simple Linear Programming Model Research Articles

Approaches to Multiple Attribute Decision Making with Intuitionistic Fuzzy Preference Information

Abstract The fuzzy multiple attribute decision making problems are investigated, in which the attribute values are given as intuitionistic fuzzy numbers and the preference information on alternatives can be provided by decision maker. For the situations where the preference information on alternatives is expressed in intuitionistic judgment matrix and the information on attribute weights is incomplete, the concepts of additive consistent intuitionistic judgment matrix, multiplicative consistent intuitionistic judgment matrix and score matrix of intuitionistic fuzzy decision matrix are defined. On the basis of the score matrix and intuitionistic judgment matrix, some simple linear programming models are established by using two transformation functions, from which the attribute weights can be derived. Then two approaches to multiple attribute decision making with intuitionistic fuzzy preference information are proposed. Finally, a practical example is used to show the processes of calculation of the developed approaches and to verify their effectiveness.

Lumber Manufacturing, Log Exports, and Timber Availability in Western Washington

Abstract We analyzed historical data on timber use and projected timber availability to 2045 to examine whether timber volumes would be available to meet the harvest requirements of existing or expanding lumber manufacturing and log export sectors in western Washington. Biennial mill surveys from the Washington Department of Natural Resources were used to describe past timber demand by the sawmilling and log exporting sectors. A simple linear programming model was used to project timber availability into the future. Our analysis revealed that current harvest levels could continue into the future, under some restricting assumptions, and can provide adequate timber volume to maintain the current lumber manufacturing sector. The projection also suggested that sawmilling capacity could expand if log exports should continue to decline. The projections are further analyzed with respect to historical distributions by species.

Improving adoptability of farm forestry in the Philippine uplands: a linear programming model

In the Philippines, smallholder farmers have become major timber producers. But the systems of timber production practiced have several limitations. In intercropping systems, the practice of severe branch and/or root pruning reduces tree-crop competition and increases annual crop yields, but is detrimental to tree growth and incompatible with commercial timber production. In even-aged woodlots, lack of regular income and poor tree growth, resulting from farmers’ reluctance to thin their plantations, are major constraints to adoption and profitable tree farming. In the municipality of Claveria, Misamis Oriental, the recent practice of planting trees on widely spaced (6–8 m) contour grass strips established for soil conservation suggests ways to improve the adoptability (i.e., profitability, feasibility and acceptability) of timber-based agroforestry systems. Assuming that financial benefits are the main objective of timber tree farmers, we develop a simple linear programming (LP) model for the optimal allocation of land to monocropping and tree intercropping that maximizes the net present value of an infinite number of rotations and satisfies farmers’ resource constraints and regular income requirements. The application of the LP model to an average farmer in Claveria showed that cumulative additions of widely spaced tree hedgerows provides higher returns to land, and reduce the risk of agroforestry adoption by spreading over the years labour and capital investment costs and the economic benefits accruing to farmers from trees. Therefore, incremental planting of widely spaced tree hedgerows can make farm forestry more adoptable and thus benefit a larger number of resource-constrained farmers in their evolution towards more diverse and productive agroforestry systems.

Quasi-Bayesian Analysis Using Imprecise Probability Assessments And The Generalized Bayes’ Rule

The generalized Bayes’ rule (GBR) can be used to conduct ‘quasi-Bayesian’ analyses when prior beliefs are represented by imprecise probability models. We describe a procedure for deriving coherent imprecise probability models when the event space consists of a finite set of mutually exclusive and exhaustive events. The procedure is based on Walley’s theory of upper and lower prevision and employs simple linear programming models. We then describe how these models can be updated using Cozman’s linear programming formulation of the GBR. Examples are provided to demonstrate how the GBR can be applied in practice. These examples also illustrate the effects of prior imprecision and prior-data conflict on the precision of the posterior probability distribution.

Energy optimization model for a CCHP system with available gas turbines

This paper deals with the problem of optimal energy management of cogeneration system for combined cooling, heating and power production (CCHP). The energy system consists of a gas turbine, an absorption chiller and a heat recovery boiler. A simple linear programming model is presented to determine the optimal strategies that minimize the overall cost of energy for the CCHP system. It is shown that the optimal operation of this system is dependent upon load conditions to be satisfied. In view of energy cost, it is shown that sometimes it may not be optimal to operate the turbine. This is the case when the electric-to-gas cost ratio is very low.

소유역에서 홍수조절용 펌프 및 유수지 규모의 결정에 관한 연구

내배수시설계획시 최대저류비에 의한 유수지 규모의 결정 방법은 이전 연구자에 의하여 제시된 바 있다. 본 연구에서는 동두천시 11개 소규모 내배수시설을 선정하여 분석한 결과, 배수면적이 작고 펌프기능이 강화된 내배수 시설에서는 강우지속기간별 우수지의 저류비의 차이는 미미하므로 최대저류비에 의한 조정지 규모의 결정은 무리가 있음을 알 수 있었다. 또한 최대저류비에 의하여 결정된 조정지 용량을 펌프에 의하여 배제되는 시간은 펌프의 허용시동간격보다 짧은 경우도 있어 펌프의 빈번한 작동을 초래한다. 그러므로 조정지는 펌프의 빈번한 작동에 의한 펌프 고장의 가능성을 피할 수 있는 규모로 결정되어야 한다. 다양한 펌프용량을 적용하여 분석한 결과, 소유역에서도 조정지의 기능이 강화된 내수배제시설에서는 최대저류비를 기준으로 한 조정지 용량의 결정은 펌프운영 측면에서 타당함을 알 수 있었다. 따라서 본 연구에서는 소규모 배수구역에서 조정지용량의 결정시 펌프의 계획배수량과 유수지의 용량에 따른 펌프의 시동빈도를 반영하여 기존의 최대저류비에 의한 방법을 개선한 방안을 제시하였다. 또한 유수지 규모와 펌프용량의 관계를 간단한 선형계획모형으로 분석한 결과, 종래의 유수지 홍수추적에 의한 유수지 용량 결정은 도시지역의 내배수시설 계획에만 타당함을 알 수 있었다. The concept of the effective storage ratio has been suggested to determine the size of detention pond by the previous researchers. The 11 pump - pond facilities in Dongdu-chun city were selected to analyze the critical duration for design rainfall and the storage ratio for each rainfall duration in this study It has been then found that the criteria of the maximum storage ratio is not reasonable for determining the size of detention pond because the difference of storage ratio with respect to each rainfall duration is too small. Moreover, since the size of pond compared with the pump capacity is not always big enough, the pump should be frequently operated, which may result in pump failure. Thus, the pond should be sufficiently sized to prevent the possibility of the pump failure due to frequent operation. According to the analyses for changing pump capacity, it has been found that if the function of the pond compared with the pump is concentrated, determining the size of pond based on the storage ratio is operationally feasible for even small basin. Thus, an improved procedure based on the storage ratio for determining the size of detention pond in small basin has been suggested. The results by the proposed procedure considering pump switching frequency may lead to reasonable pump operation. A simple linear programming model has been also adopted to figure out the relationship between pump capacity and pond size. It has been shown that the determination lot the size of detention pond based on conventional hydrologic flood routing in pond is feasible for only urban districts not rural areas.

The dynamics and sustainable use of high-value tree species of the coastal Pondoland forests of the Eastern Cape Province, South Africa

We investigate the ecological status of the standing crop of high-value tree species in coastal scarp forest of the Eastern Cape Province of South Africa. We compare resource availability, distribution and use in several forests that are under state and community management. Species suitable for harvesting were identified using a simple linear-programming model based on the frequency and scale of regeneration (grain) of the tree species. Twenty high-value tree species were widely used. Nine species were apparently over-exploited and absent from community forests. Tree densities were higher in state forests than community forest. Size-class distribution profiles for all species, except Harpephyllum caffrum and Heywoodia lucens, displayed the characteristic inverse J-shaped distribution that generally indicates stable populations. Tree species varied in their spatial scale of recruitment, but were mostly intermediate- to coarse-grained. Two fine-grained species in state forest ( Englerophytum natalense and Millettia grandis) and only one species in community forest ( E. natalense) had densities that could potentially sustain current levels of exploitation. The prevailing tenurial system (i.e. state or community forest), the tree species and category of stem size (dbh) used, all affected tree harvesting off-take levels. Trees in the 10–20 cm diameter size-class (poles) were most harvested. Harvesting levels of pole-sized stems were more influenced by tree size than species, were significantly greater in community than state forests, and could be explained by the closer proximity of households to community ( x ̄ =1.5 km) than state forests ( x ̄ =3.2 km). Given the willingness of communities distant from forests to plant multipurpose indigenous trees, there is the potential for strengthening community forestry, and thus rural development, via forestry interventions such as agroforestry. However, the survival of these forests depends on the establishment of suitable integrated community-based institutions and management practices.

Planning and managing manufacturing capacity when demand is subject to diffusion effects

When launching a new product, the manufacturing and marketing functions of a firm are required to jointly take critical decisions concerning the amount of manufacturing capacity to be acquired, and to elaborate policies for managing it over the product's life cycle. The time-varying demand profile caused by new-product diffusion phenomena, together with learning effects, cause the emergence of critical trade-off decisions among the options of increasing production capacity, delaying launch, increasing backlog or accepting a significant amount of lost sales. In this paper these trade-offs are studied by developing a simple Mixed-Integer Linear Programming model and by experimenting upon it with realistic data representing different scenarios. Optimal policies arising from the experiments are then compared and discussed.

Labor Shortages on Small Landholdings in Malawi: Implications for Policy Reforms

A simple linear programming model of representative smallholder households is used to investigate the sources of relative scarcity of labor and land in Malawi. The paradox of on-farm labor shortages on small landholdings can be explained by the multiple constraints smallholders face. These multiple constraints, including lack of finance, concerns for food security, and others, lead to suboptimal allocations of household resources. In turn, the low returns to labor and land, contribute to household food insecurity and a vicious cycle of poverty. The findings of the paper provide a clear signal to policymakers and research and extension institutions that these constraints are all linked, and addressing one cannot be effective without addressing the others.

Planning Home Assistance for AIDS Patients in the City of Rome, Italy

In allocating resources to health-care services, the main difficulties derive from uncertainty concerning the number of patients who need the service and the level of care required by each patient who is entitled to receive it. I deal with the problem of allocating resources to the home-care service provided to AIDS patients in the city of Rome, Italy, which include medical assistance provided by nurses and doctors and social assistance and accompaniment of patients provided by social workers. A simple linear programming model solves the problem for single organizations, which provide assistance within a given budget, and for public-health authorities, which have to evaluate the results of tentative budgets assigned to home care.

AN OPTIMIZATION MODEL FOR ENERGY SUPPLY TO RICE MILLS IN INDIA

A simple linear programming model for the determination of the least cost energy supply mix for rice mills in India has been developed. Several scenarios involving the variation of both availability and prices of energy resources have been considered. The results for some likely scenarios are presented and briefly discussed. © 1997 by John Wiley & Sons, Ltd.

An algorithm based on a new sufficient condition of optimality in dynamic lot size model

This paper presents a sufficient condition of optimality in the production scheduling of a single item with deterministic time-varying demand, setup and variable costs, in the backlog and no backlog cases. A simple linear programming model is developed for the dynamic lot size problem, along with an algorithm which checks the problem's optimality conditions. The sparseness of the table in this lot sizing problem allows a given production policy to be improved and eventually an optimal solution to be obtained. This algorithm results in significant computational efficiency as tested extensively against well-known methods.

Regulating Afforestation for Water Conservation in South Africa

SYNOPSIS It is necessary to regulate afforestation in South Africa because of the high demand exotic forest plantations make on the scarce water resources of the country. The present procedure and information base for the regulation of afforestation with exotic plantations in South Africa are useful, but rely on a large degree of subjectivity and exclude recent research information from the procedure. The problem of regulating afforestation can also be dealt with as a simple linear programming model. Solution of the linear programming model requires quantitative and qualitative information obtained by using different methods. The use of the Analytic Hierarchy Procedure (Saaty, 1983) as a qualitative method to determine a preference rating for the water demand of five user categories, i.e. terrestrial ecosystems, river ecosystems, industry, irrigation and dam storage, is demonstrated. Quantitative relationships between afforestation and annual water yield are updated. We suggest the use of this new procedure in preference to the present one. Suggestions are made for incorporating hydrological aspects such as spatial variation of evapotranspiration in catchments, critical low flow constraints and the influence of rotation age on water use. The need for accurate determination of evapotranspiration, not only of exotic plantation, but also of natural vegetation being replaced by the plantations, is emphasised.

Allocating work between an FMS and a conventional jobshop: A case study

This paper discusses a real-life production planning problem in a Flexible Manufacturing System (FMS) environment. The problem is to decide which products and in what quantities to produce on the FMS. The remainder of the production requirements can be produced in a conventional jobshop. It is shown how a rather simple linear programming model on microcomputer can be a valuable decision tool. It allows for easy evaluation of various objective functions and decision alternatives. Insights gathered using the LP model have led to the introduction of new part routings which have increased FMS throughout considerably. It is also shown how the LP model is used as a screening device to select strategies to be tested in a detailed simulation of the system.

Some possibilities in the economic development of Liberia through the forestry sector

Some possible contributions that could be made to the development of the Liberian economy through the forestry sector are investigated. Emphasis is placed on the establishment of integrated wood-processing facilities comprising sawmilling, veneer and plywood manufacturing and particleboard production. Data for 1974 are used to formulate a simple illustrative linear programming model for determining the minimum investment needs for achieving specified levels of value-added.

Vegetable Crops Acreage Comparisons Under Resource Alternatives

ABSTRACT A simple linear programming model was formulated to examine the impact of resource alternatives on vegetable cropping patterns. The planning objective was to maximize the total vegetable crop net returns. Florida conditions were used to illustrate techniques. The 1973-74 season was chosen as a base period. The reductions in available resources were simulated by the parametric linear programming technique, and their effects on the changes of cropping patterns were obtained. The effects of curtailed resource supplies on crop acreage were varied. Crops which required large amounts of energy were sensitive to reductions in energy. When subject to water reduction only, the response showed a relatively balanced cropping pattern. Crop acreages generally declined when both energy and water levels were reduced. Crops with medium resource requirements were not as adversely affected by reduced inputs; crops with low resource inputs showed marked increases in acreage when resources were limited.

A simple linear programming model of the heckscher-ohlin theory of international trade

The linear programming model of the classical Ricardian theory of comparative costs has been analyzed in Dorfman, Samuelson and Solow's famous book, entitled Linear Programming and Economic Analysis (1958, pp. 31–45). We analyze here the Heckscher-Ohlin theory of international trade by using a simple linear programming model. The basic dual relationship of the Rybczynski theorem and the Stolper-Samuelson tariff theorem can be most clearly stated by means of our model. The simple set-up helps to investigate, rather easily, the implications of the theorems in cases like specialization and redundancy of one factor.

A Model for Bond Portfolio Improvement

The problem of bond portfolio selection may be viewed as consisting of two parts. The first is concerned with the maturity profile of the total cash flows (the after-tax coupons and principal repayments) which the investor requires; in general there will be many portfolios of bonds which provide the desired cash flow profile. Accordingly, the second problem is the choice of a particular portfolio of bonds which provides these cash flows in some optimal fashion. If bonds are default free, future taxes are known, and differences in marketability and callability among issues can be ignored, then price is the only relevant criterion in choosing among alternative portfolios. This paper describes a simple linear programming model for this last problem of selecting the portfolio which provides a given pattern of cash flows at minimum cost. This provides a method for improving any initial portfolio, where such improvement is possible, by increasing its yield without reducing any future after-tax cash flows.

Urban improvement programming models

This paper explores the potential application of mathematical programming in the evaluation of alternative urban plans and improvement programs. After a brief review of past modeling efforts of this type, an examination of the problems likely to be encountered in identifying and measuring specific objectives and programs is presented. The Model Cities Program is used as an example. A simple linear programming model is subsequently developed, built around a matrix of relative effectiveness coefficients, a set of performance standards, and appropriate program budgets. Supporting analytic techniques and information systems also are discussed. Finally, potential applications of the model are surveyed, and examples of its use in testing and evaluating basic Model Cities programs and objectives presented.Examples of the linear programming model are programmed and run for a hypothetical model neighborhood, using real and assumed data from Chicago. The model allocates dollars among various Model Cities program alternatives, either minimizing the total budget spent or maximizing the achievement of specific Model Cities objectives. Objectives are expressed in terms of standardized percentage impacts upon various socio-economic conditions within a model neighborhood. The purpose of the model is to show how a specific operations research technique might be applied to systematically improve our plan evaluation methodologies. Emphasis is placed upon properly structuring the Model Cities evaluation context, rather than upon refining the mathematical technique itself.Much work remains to be done before viable urban improvement programming models can actually be developed. This exploratory study attempts to draw several basic guidelines for continuing research effort. First, the need for consistency and comparability in the selection of quantitative measures or indices of goal achievement is examined. Second, the need to express alternative programs and policies in terms of three essential characteristics—the objectives to which they are related, the impact or effectiveness which they will have in achieving each objective, and the costs associated with varying levels of effectiveness—is illustrated. Third, in order to permit comparisons and trade-offs among different programs and groups of programs, it is essential that a common measure of goal achievement be developed. One way to define such a common measure of goal achievement is to develop a programs-objectives matrix in which each coefficient represent the percentage of objective j which can be achieved by each dollar invested in program i. Fourth, it must be understood that programs-objectives effectiveness matrices of this type will require a prodigious amount of supporting research and analysis in order to predict the individual impacts of alternative programs and policies. Finally the sensitivity analysis of all variables and parameters—standards, budgets, or programs—within a mathematical programming problem can provide a good deal of information on relative costs, effectiveness and trade-offs.

The Application Potential of Integer Programming

Linear programming has received much attention as a tool for managerial decision making in business and government. It provides the decision maker with a precise and simple framework for defining his problem and a quick and simple means of obtaining an optimal solution to that problem. In addition, linear programming has the advantages of being applicable to a wide range of managerial problems, being able to consider simultaneously each of the multiple goals and relationships which may be represented by a complex problem, and providing information about the relative significance of each constraint with respect to the objective (shadow prices). However, because of the simplicity inherent in the linear programming model, there are many managerial problems to which it cannot readily be applied. Such problems may be too complex for a modeling approach, or may contain relationships which cannot be represented by linear functions, or may be characterized by probabilistic relationships or perhaps relationships which change over time. Most managers could probably cite which the simple linear programming model would be unable to consider if applied to problems in their area of authority. To cope with complexities of this sort, several variations and extensions of linear programming have been developed. Quadratic programming and integer programming have been developed to attack problems of nonlinearity of functional relationships. Stochastic programming deals with problems containing probabilistic relationships. Dynamic programming can be adapted to problems in which time or the sequence of events is an important consideration. However, it can be stated that, in general, what these techniques contribute in terms of more accurate representation of actual problems is often sacrificed in the form of great difficulty in reaching an optimal solution. This paper concentrates upon a particular class of extensions of the traditional linear programming model-those problems containing integer variables which are restricted to a value of either zero or one. These variables are referred to as variables, and the formulation and solution of problems containing such variables is referred to as programming. Dichotomous-integer variables generally indicate discrete changes in objective or constraint functions, or the presence or absence of some condition or decision. Several well-known linear and integer programming problems are presented in this paper and then extended by means of adding dichotomousinteger variables representing additional considerations or complicating factors which are typical of many real world problems. The purpose of the paper is to demonstrate that integer programming, particularly dichotomous-integer programming, provides a powerful means of * Assistant professor of accounting at the College of Business Administration, University of Texas at Austin.