Goal programming solutions to transportation problems with variable supply and demand requirements

This article deals with goal programming as an aid to resolving transportation problems. The objective of this study is to demonstrate the use of goal programming as an approach to reducing total cost in transportation problems that possess variable supply and demand requirements. A generalized goal programming model is formulated and applied to a series of transportation problem situations based on the empirical data provided by a medium-size trucking firm. Comparison of the results demonstrates the cost advantage of using the goal programming model in place of the transportation method and integer interval linear programming.     

Planning in an uncertain environment: Stochastic goal programming using the versatility criterion

This article presents a planning model that applies the versatility criterion to goal programming problems with uncertainty about the constraints which define the set of feasible decisions. Some of the constraint parameters are assumed to be stochastic variables with a joint normal distribution. The solution sought maximizes the probability of satisfying all the constraints. A nonlinear programming model is set out which can be solved by using numerical integration at every step. An illustrative example is provided which shows the possible application of the versatility model to land-use planning.     

The application of goal programming techniques to the CPM problem

This paper demonstrates how goal programming (GP) can be used to incorporate considerations other than project completion time and total project cost into the typical CPM problem. In particular, factors such as share of the market, completion time of individual jobs, contractual agreements, and scarcity of resources such as men, materials and machines are taken into consideration. An example is provided to illustrate the use of the GP approach in a CPM problem.     

An application of goal programming to the desegregration busing problem

This paper develops a goal programming model for obtaining solutions to the desegregation busing problem. The model is compared with the linear programming approach and is applied to 31 schools serving over 14,000 students. Solutions result in potential cost savings of over one-half million dollars.     

A goal programming model for achieving racial balance in public schools

This paper develops a goal programming model for achieving racial balance in segregated public schools. The model is illustrated and offered as an improvement upon linear programming, a model previously applied in the literature which allows a single objective function only and, in comparison with goal programming, requires more variables and constraints. Goal programming, a member of the general multiple objective linear programming (MOLP) model, improves upon these among other disadvantages thereby emerging as a more efficient tool for student assignment problems.     

A polynomial goal programming approach to a class of quality control problems

The traditional quality control approach based on statistical tools has been very useful and effective when output and input qualities can be denned in terms of a single characteristic. However, in process industries such as paper, the output quality is denned in terms of two or more distinct characteristics; hence, reducing the deviation of one output characteristic from its permissible limits could result in forcing other output and/or input characteristics to deviate from their respective limits. Compounding this phenomenon is the fact that most of these industries produce substantial amounts of pollutants whose characteristics are a function of the input and output characteristics. Thus, with increasing costs of waste treatment and stringent pollution standards, there arises a notion of a trade-off between attaining market specified output characteristics and meeting federally regulated pollution standards.In this article a general process quality control problem has been formulated that reflects the above trade-off both in terms of a linear and a polynomial goal programming problem. Major advantages and differences between the two formulations are highlighted and illustrated with a practical example drawn from the paper industry.Three separate cases each with different priorities assigned to the output, pollutant and input characteristics are developed and solved under both formulations. Based on the analysis it is observed that the different solutions that result are contingent on the assumptions concerning the priorities associated with each goal and the manner by which one chooses to incorporate tradeoffs between goals in the objective function. Additionally, it is found that the solutions obtained under polynomial goal programming formulation are more conducive for implementation in practical quality control contexts.     

A goal programming approach to public investment decisions: A case study of rural roads in Indonesia

The development planner must often face complex problems with multiple, conflicting objectives. Goal programming provides a general methodology for solving such problems. The tool is applied here to aid in the selection of rural road projects in the Indonesian Rural Works Program. Selection criteria are formalized into a set of nineteen goals which form the basis for a goal programming model. Changes in priority levels of goals and weights are used to analyze the respective effects upon the spatial distribution of investments. The approach is applicable to a wide range of problems and a variety of sensitivity analyses. Despite clear advantages, several drawbacks must be noted. First, the application of the methodology, given its degree of sophistication, is limited to a central decision making unit which has access to appropriate software. Second, the technique assumes that the planner has the ability to formulate alternative actions and consequences in a quantifiable expression.     

Multi-objective programming models: New ways in regional decision-making

The article focuses on the use of multiple objective functions in regional decision-making. After a survey of various multi-objective programming models an interactive procedure for determining a best-compromise solution is discussed. The method is illustrated by means of an empirical application in the field of regional industrialization policy.     

Discussion of dynamic programming and linear programming approaches to stochastic control and optimal stopping in continuous time

This paper seeks to highlight two approaches to the solution of stochastic control and optimal stopping problems in continuous time. Each approach transforms the stochastic problem into a deterministic problem. Dynamic programming is a well-established technique that obtains a partial/ordinary differential equation, variational or quasi-variational inequality depending on the type of problem; the solution provides the value of the problem as a function of the initial position (the value function). The other method recasts the problems as linear programs over a space of feasible measures. Both approaches use Dynkin’s formula in essential but different ways. The aim of this paper is to present the main ideas underlying these approaches with only passing attention paid to the important and necessary technical details.     

A goal programming model for readiness and the optimal redeployment of resources

Organizations such as the military and those involved with disaster relief are vitally concerned with their ability to redeploy resources between various geographical locations in response to cataclysmic events. Measuring the effectiveness of a redeployment plan involves multiple objectives and differing priorities. The primary objective of redeployment is meeting requirements at affected locations with a secondary concern for transportation costs. In order to reflect these features, the problem is formulated as a goal programming model. Several variations of the model are investigated that can enhance its value. An example redeployment problem is formulated and solved to illustrate the approach.     

Global supplier selection using fuzzy analytic hierarchy process and fuzzy goal programming

Global supplier selection is a multi-goal multi-criteria problem which needs to consider both qualitative and quantitative factors. Which suppliers are the best and how much should be purchased from the selected suppliers is an important purchasing issue for manufacturers. Traditionally, decision makers can determine the best supplier from evaluating few suppliers with qualitative supplier selection criteria by using fuzzy analytic hierarchy process (FAHP), but evaluate dozens of global suppliers simultaneously or determine the order quantity from them will be complex and difficult. Meanwhile, decision makers can determine the order quantity form the suitable suppliers by using fuzzy goal programming (FGP); however, it is not easy to decide weights for each goal of global supplier selection with different supply chain strategies. This study integrated the FAHP and FGP (FAHP-FGP) method to be a new approach for global supplier selection in considering the manufacturer’s supply chain strategies. With FAHP-FGP method, the manufacturer can consistently integrate multi-manager’ opinions in determining weights of each goal and obtain the order quantities for suitable suppliers based on manufacturer’s strategies. To demonstrate the usefulness of the proposed method, a real-world case of a digital consumer products manufacturer is presented.     

A satisficing method for fuzzy goal programming problems with different importance and priorities

For treating multiple objectives decision making problems with fuzzy goals and different importance, various kinds of fuzzy goal programming (FGP) models have been developed in the past three decades. Among them, two most widely used methods are: (1) weighted FGP, where the importance of the objectives is represented by weights (2) preemptive priority (also known as “Lexicographic”) FGP, where the priority levels of the goals are set in advance, and the trade-offs among goals placed at different priority levels are implemented strictly. This article presents a satisficing method based on FGP model, which holds that a more important objective has to be achieved as much as possible. The relaxed preemptive priority requirement in the proposed model provides a more efficient, flexible and practicable decision support compared to the weighted and the lexicographic models. In addition, the trade-off between optimization and importance requirement can be realized by the regulation parameter in the presented method. The performance of this method is evaluated by comparing its result with those of the six existing models in the literature.     

Bus transportation crews planning by goal programming

In the present paper, an integer goal programming model formulation is presented for the bus transportation crews planning to find an optimal schedule in which each crew is assigned two days off (consecutive or non-consecutive) per week and several goals like upper and lower limits on the total number of crews having consecutive and/or non-consecutive days off on each day, lower limit on the number of crews having consecutive days off on the particular pairs of consecutive days, and minimization of the number of crews having non-consecutive days off, are taken into consideration. The model is demonstrated by a numerical example.     

Regional economic models and continuous programming

This paper is concerned with an optimal investment allocation problem in a simple N-regional economic model. The problem is described as a class of optimal control problem, and formulated into a continuous linear programming problem. Both the primal and dual problems are considered. The procedure finds an optimal regional allocation of investment derived in terms of continuous programming.     

Indefinite quadratic fractional functional programming

The present paper suggests a finite iteration technique for findinglocal minimum of a special type quasi-concave quadratic fractional functional subject to linear inequalities. The procedure adopted is exactly similar to “Simplex Technique” in linear programming and the problem has been attacked directly starting with a basic feasible solution and finding conditions under which the solution can be subjected to improvement. A numerical example has been given to illustrate the procedure.     

A chance-constrained multiobjective model for mental health services planning.

Mental health services planning, and particularly the planning for deinstitutionalization, is a very complex problem. This paper suggests a chance-constrained goal programming (CCGP) approach to mental health services planning. The CCGP approach is based on the sequential solution of a linear programming formulation, allowing efficient solution of large-scale planning problems using commercially available linear programming computer codes. The procedure is demonstrated with a case example and implementation of the approach is discussed.     

Scilab as an econometric programming system

This article reviews Scilab, a free MATLAB‐like programming system. Scilab can be used for data analysis and applied numerical work in both research and teaching. Scilab is an interesting alternative to some commercial programming environments. Copyright © 2001 John Wiley & Sons, Ltd.     

Using goal programming to determine interest group disutility for public policy choices

Within this paper a framework is developed for incorporating into the process of social choice both interest group preferences for social goals and the efficient allocation of limited resources. The social welfare function is adopted as the foundation for the framework and the goal programming algorithm is used to approximate the utility of the interest groups for their optimal policy choice. A function is defined which measures the disutility experienced by a social unit when a policy other than its optimal choice is selected. A surrogate measure of this disutility involving imposed preference weight changes for social goals is determined and its implications for use in developing the social welfare function are examined.     

Linear programming and locational equilibrium: The Herbert-Stevens model revisited

The paper reviews the early work of Herbert-Stevens in which linear programming was used to find a competitive equilibrium to an urban land market. First, it is demonstrated that a solution to the Herbert-Stevens model does not meet well-established criteria for an equilibrium. Secondly, a new linear programming model is suggested which is proven to achieve equilibrium if certain conditions are met. An iterative procedure for meeting these conditions is suggested, and an operational version of the model exhibits no problem in obtaining convergence. The revised model represents a feasible way of simulating urban land markets.     

Improving perishable product inventory management using goal programming

The multiple objectives of perishable product inventory management are examined in this paper. These objectives include: (1) satisfying demand by carrying sufficient inventories, (2) holding down inventory carrying costs, (3) keeping the amount of product spoilage (outdating) at an acceptable level, and (4) maintaining quality by using the product while it is still fresh, and (5) keeping the cost of rotation low. Some of the above objectives are in conflict. Thus, certain redistribution policies may help attain one or more of these objectives to a greater extent. Redistribution involves the transfer of the product from outlets where demand is low to outlets where demand is high. A goal programming model for solving redistribution problems is presented. An example is provided and sensitivity analysis is performed in order to determine when redistribution is advantageous. Applicability of the model is discussed.