A goal programming model for facility location planning

The paper presents a goal programming model for facility location planning. Often the location-decision is coupled with multiple objectives, at times conflicting among themselves. Specifically the model considers the four major objectives: (i) necessary locations, (ii) maximum number of locations, (iii) capacity restrictions and (iv) transportation cost/walking distance minimization, simultaneously and proposes optimal locations in conjunction with the existing facilities in the region. The model developed has been illustrated with an example considering the location of community storage facilities in a specified region.     

An alternative solution method for goal programming problems: The lexicographic goal programming case

This article provides an example of the use of an alternative goal programming solution procedure. The solution procedure is applied to solve a lexicographic goal programming problem. In the process of illustrating the problem, a number of unique technical problems and their solution procedures are discussed. This study provides a flowchart as a procedural guide to aid in its use. This article also provides a comparative analysis of GP algorithms. The results demonstrate the tableau element reduction capabilities of the proposed alternative goal programming solution procedure.     

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 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.     

Allocation of teaching personnel: A goal programming model

This paper is concerned with the development of a model structure for allocating the teaching resources of a high school in an effective and efficient manner. In allocating these resources the multiple and often conflicting goals of the school system administrators will be considered, as well as the various operating and financial constraints of the school system.     

A goal programming model for the siting of multilevel EMS systems.

Facility siting models known as location covering techniques have proven to be useful particularly for emergency medical services (EMS) planning, given the importance of ambulances responding to demand within some maximum time constraint. These models represent a set of methods which focus the health planner's attention on the access of people to health care, since they attempt to “cover” people in need of service within some specified time standard.This research develops a technique for the locational planning of sophisticated EMS systems, characterized by multiple levels of emergency health services. Specifically, a two-tiered system with “basic life support” and “advanced life support” capabilities is modeled as a goal program.By applying location covering techniques within a goal programming framework, this study develops a method for the siting of multilevel EMS systems so that (1) each service level maximizes coverage of its own demand population, and (2) “back-up” coordination between levels is assured. The usefulness of this goal program as a health planning tool is evidenced in the model's explicit articulation of EMS policy objectives and its ability to link system levels in terms of “goal-directed behavior”. The working of this multilevel covering model is demonstrated by reference to EMS planning scenarios and related numerical examples.     

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.     

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.     

A parametric simplex-like algorithm for a fractional programming problem

A few theoretical results are given for the fractional programming problem where the objective function is the product of an affine function and a linear fractional function and where the feasible region is a polytope. Moreover, a simplex-like algorithm is proposed to solve the same problem when the feasible region is bounded. The algorithm is based on the exploration of a set of suitably defined optimal level solutions.

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Riassunto Nel lavoro vengono esposti alcuni risultati teorici per un problema di programmazione frazionaria nel quale la funzione oggetto è data dal prodotto tra una funzione affine e una funzione lineare definita su una regione ammissibile poliedrica. Viene inoltre formulato un algoritmo di tipo simplesso che consente la risoluzione del problema qualora la regione ammissibile sia limitata. Tale algoritmo è basato sulla esplorazione di un insieme opportunamente definito di soluzioni ottime di livello.

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This research was partially supported by MURST.     

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.     

A fixed sample size selection procedure for negative binomial populations

Summary A fixed sample size procedure for selecting the ‘best’ ofk negative binomial populations is developed. Selection is made in such a way that the probability of correct selection is at leastP* whenever the distance between the probabilities of success is at leastδ*. The exponentr is assumed to be known and the same for all populations. Extensive computer calculations* were employed to obtain the exact least favorable configuration. The smallest sample sizes needed to meet specifications (P*,δ*) are tabulated forr=1 (1)5;δ*=0.05 (0.05) 0.55 andP*=0.75, 0.80, 0.90, 0.95, 0.98, 0.99 involvingk=3 (1) 6, 8, 10 populations. All the computations were carried out on the Alabama Supercomputer. Part of this work was completed when the authors were at the Department of Statistics, Oklahoma State University, Stillwater, OK 74078.     

Integer goal programming for multistage lot sizing: Experimentation and implementation

This article considers the issues involved in implementing a large-scale multistage lot sizing model in a pharmaceutical manufacturing environment, and reports on a series of sensitivity experiments that subsequently examined the critical impacts of system capacity and inventory policy on the specification of a multistage schedule. The model was initially developed as an aggregate scheduling aid for a class of tablet pharmaceuticals. The manufacture of tablet products is a serial-type process characterized by batch flow. The model placed multiple resource capacity restrictions on various stages of the multistage system to ensure the feasibility of the resultant schedules. Difficulties in estimating penalty costs for shortages were circumvented by employing a multi-objective formulation of the lot-sizing problem.Various obstacles encountered during the implementation process are discussed. Model implementation encompassed the development of an approximation algorithm for efficiently solving the large-scale problem. The performance of the algorithm was evaluated by examining the closeness to optimality of the solutions obtained using the procedure. Performance statistics are presented for the sensitivity experiments discussed herein. Another essential aspect of implementation involved the timely revision of model input parameters. This facet of implementation proved to be at least as important to management as the efficient provision of a “good” solution.Model experimentation centered on variations in the capacities of bottleneck resources and changes in target inventory parameters whose values are predetermined by company policy. The first set of experiments was designed to demonstrate the importance of system capacity to the lot-sizing process and to illustrate that the location of a system bottleneck can vary over time as a function of both internal and external factors. The results indicated that lot-sizing procedures that fail to incorporate capacity information or that focus on a single bottleneck production stage in order to schedule production are severely limited with respect to practical and/or long-term applicability.The final set of inventory-related experiments indicated that the specification of target ending inventory levels was a crucial factor in the lot-sizing process. The determination of appropriate target levels must reflect the inherent trade-off between the objective of minimizing shortages and the desire to avoid excessive inventory accumulations. The generation of usable model information was found to be contingent upon the realistic definition of target level parameters.     

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.     

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.     

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.     

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.     

A statistical procedure for testing social reciprocity at group,dyadic and individual levels

This paper examines statistical analysis of social reciprocity, that is, the balance between addressing and receiving behaviour in social interactions. Specifically, it focuses on the measurement of social reciprocity by means of directionality and skew-symmetry statistics at different levels. Two statistics have been used as overall measures of social reciprocity at group level: the directional consistency and the skew-symmetry statistics. Furthermore, the skew-symmetry statistic allows social researchers to obtain complementary information at dyadic and individual levels. However, having computed these measures, social researchers may be interested in testing statistical hypotheses regarding social reciprocity. For this reason, it has been developed a statistical procedure, based on Monte Carlo sampling, in order to allow social researchers to describe groups and make statistical decisions.     

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 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.