Showing papers on "Goal programming published in 1984"

Two-Level Linear Programming

Abstract: Decentralized planning has long been recognized as an important decision making problem. Many approaches based on the concepts of large-scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which often exist in practice. Multilevel programming models partition control over decision variables among ordered levels within a hierarchical planning structure. A planner at one level of the hierarchy may have his objective function and set of feasible decisions determined, in part, by other levels. However, his control instruments may allow him to influence the policies at other levels and thereby improve his own objective function. This paper examines the special case of the two-level linear programming problem. Geometric characterizations and algorithms are presented with some examples. The goal is to demonstrate the tractability of such problems and motivate a wider interest in their study.

An Overview of Techniques for Solving Multiobjective Mathematical Programs

Abstract: Multiobjective mathematical programming has been one of the fastest growing areas of OR/MS during the last 15 years. This paper presents: some reasons for the rapidly growing increase in interest in multiobjective mathematical programming, a discussion of the advantages and disadvantages of the three general approaches (articulation of the decision maker's preference structure over the multiple objectives prior to, during, or after the optimization) towards multiobjective mathematical programming, a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming, and a discussion of important areas for further research. The overview concentrates on those techniques which require an articulation of the decision maker's preference structure either during or after the optimization, since these are the areas where most of the recent research has been conducted. It differs from previous overviews in that, in addition to the timing of the elicited preference informa...

Real‐Time Reservoir Operations by Goal Programming

Abstract: Preemptive goal programming is applied to the real-time, daily operation of multiple-purpose, multiple-reservoir systems. A significant advantage of the goal programming approach is that it may be based on physical operating criteria. It does not require the penalty-benefit functions that may be difficult to define but are essential to other real-time operating models. Therefore it is easier to implement. The goal programming model is applied to the Green River Basin (GRB) system comprising four multipurpose reservoirs. The GRB system operations resulting from use of the goal programming model are compared to operations resulting from another optimization model which is more data intensive and which was designed specifically for the GRB system. Both sets of operations are comparable in their effectiveness, although in some cases, the goal programming operations are better.

Scheduling Nurses Using Goal-Programming Techniques

Abstract: This paper presents a single-phase goal programming algorithm for scheduling nurses in one unit of the hospital. The goals represent the scheduling policies of the hospital and nurses' preferences for weekends on and off. An application to one unit of the hospital with 11 nurses resulted in satisfactory schedules. The computer time to solve the problem using a goal programming algorithm was very reasonable.

Multiobjective optimization in structural design with uncertain parameters and stochastic processes

Abstract: The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

Introductory management science

Abstract: (NOTE: At the End of Each Chapter is a Video Case.) 1. Introduction: Models and Modeling. I: DETERMINISTIC MODELS. 2. Linear Programming: Formal and Spreadsheet Models. 3. Linear Programming: Geometric Representations and Graphical Solutions. 4. Analysis of LP Models: The Graphical Approach. 5. Linear Programs: Computer Analysis, Interpreting Sensitivity Output, and the Dual Problem. 6. Linear Programming: The Simplex Method. 7. Linear Programming: Special Applications. 8. Integer and Quadratic Programming. 9. Network Models. 10. Inventory Control with Known Demand. 11. Heuristics, Multiple Objectives, and Goal Programming. 12. Calculus-Based Optimization and an Introduction to Nonlinear Programming. II: PROBABILISTIC MODELS. 13. Simulation. 14. Decision Theory and Decision Trees. 15. Project Management: PERT and CPM. 16. Inventory Models with Probabilistic Demand. 17. Queuing Models. 18. Forecasting. Answers to Odd-Numbered Problems. Appendix A: Basic Concepts in Probability. Using LINDO. Index.

Goal programming and multiple criteria decision‐making in farm planning: an expository analysis

Abstract: Several paradigms can be used to analyse multiple-criteria decision-making problems. Of these goal programming is probably the most widely used one, at least in management science. Goal programming seems to offer considerable potential for application to multiple-criteria problems in farm planning. However, its applications in agricultural economics have been few and far between. Even these attempts seem to suffer from some serious misconceptions. In this paper an effort is made to explain the structure of a goal programming model by deriving it from the familiar paradigm of linear programming. This is done to put the potential usefulness of goal programming and its relationship to linear programming in perspective, and to encourage further applications to multiple-criteria decision-making in farm planning.

Aggregate production planning using chance-constrained goal programming

Abstract: Multiple objective models have frequently been proposed to assist in solving aggregate production planning problems. Although such models are an improvement over those with single objectives, demand is usually considered deterministic. For this reason, previous attempts at solving production problems have often lacked realism and could not be successfully applied in many real decision environments. This paper suggests a chance-constrained goal programming (CCGP) approach to production planning which allows the decision maker to specify both probabilistic product demands and production line operating characteristics more in keeping with actual situations. The CCGP approach is based on the sequential solution of a linear programming formulation, allowing efficient solution of large-scale real-world problems using commercially available LP codes. The procedure is demonstrated with a hypothetical example, and proper interpretation of goal achievement is discussed. The findings in the paper are applicable whet...

Assessing Scenario Probabilities Via Interactive Goal Programming

Abstract: An interactive goal programming approach for assessing scenario probabilities used in long-range forecasting and decision analysis is developed and illustrated using a small numerical example. The method only requires marginal event probability and ordinal or interval first-order conditional probability assessments of a limited number of events constituting the scenarios and guarantees the consistency of the assessments in terms of the laws of probability calculus.

Goal Programming Approaches to Solving Linear Decision Rule Based Aggregate Production Planning Models

Abstract: This paper reviews several goal programming extensions to the Linear Decision Rule Formulation of the Aggregate Production Planning Problem, and presents an extension using Polynomial Goal Programming. Employing a well known problem as a point of reference, the solution of the various model formulations is illustrated using commercially available mathematical programming software.

Goal Programming and Allocating Children to Secondary Schools in Reading

Abstract: The secondary allocation scheme proposed for Reading by Berkshire County Council (B.C.C.) in 1978 has been investigated under the Race Relations Act. After reviewing previous programming studies of devising school catchment areas, this paper uses the technique of goal programming to analyze the problem of proposing catchment areas for the secondary schools in Greater Reading. Six goals are identified: distance, difficulty of journey, racial balance, reading-age retarded balance, sex balance and capacity utilization. The problem is solved for 10 alternative sets of goal weights, and it is shown that most of these dominate the B.C.C. solution.

Proposal of Satisficing Trade-Off Method for Multiobjective Programming

Abstract: In recent years, many kinds of interactive methods for solving multiobjective decision problems have been developed. Many of them require high degree of judgment to decision makers, for example, marginal rate of substitution or ordering among a set of alternatives, and a number of auxiliary scalar optimizations. These features make their application to practical problems difficult. In this paper, a new type of interactive method, called satisficing trade-off method, will be proposed. The method is very simple and easy to carry out, and therefore is expected to be applied to many practical fields. Keyword: multiple criteria decision making, interactive multiobjective programming method, satisficing trade-off method

Interactive Fuzzy Decision Making for Multiobjective Nonlinear Programming Problems

Abstract: An application of fuzzy approach to multiobjective linear programming (MOLP) problems was first presented by Zimmermann (1978) and further studied by Leberling (1981) and Hannan (1981). Following the maximizing decision proposed by Bellman and Zadeh (1970) together with linear, hyperbolic or piecewise linear membership functions, they proved that there exists an equivalent linear programming problem.

Goal Programming and Financial Planning Models for Highway Rehabilitation

Abstract: This paper examines the problem of capital budgeting in the area of highway maintenance. Emphasis is placed on specific, real-world user concerns relating to standard capital budgeting models, and suggestions are made for improving planning in this area. A two-phase approach to capital budgeting is suggested as a mechanism for resolving some of these concerns. In phase 1 a financial planning model is used as a means of determining appropriate budget levels. In phase 2 a goal programming model for achieving desired levels of service is given. A brief description is given of such a two-phase system currently being implemented in a Canadian transport ministry.

Comparison of Four Goal Programming Algorithms

Abstract: A major limitation in the use of goal programming has been the lack of an efficient algorithm for model solution. Schniederjans and Kwak recently published a proposal for more efficient solution of goal programming models utilizing dual simplex procedures. A goal programming algorithm based upon that method has been coded, as well as a revised, simplex-based algorithm. These algorithms are compared in terms of accuracy and time requirements with algorithms previously presented by Lee and by Arthur and Ravindran. Solution times for a series of 12 goal programming models are presented. The dual simplex method appears to have superior computational times for models with a large proportion of positive deviational variables in the solution. The revised simplex algorithm appears more consistent in time and accuracy for general goal programming models.

A Goal Programming Example in Public Health Resource Allocation

Abstract: A model developed to aid a state-level resource allocation process in the United States Department of Agriculture Special Supplement Food Program for Women, Infants, and Children WIC is presented. The model is formulated as a linear integer goal program, utilizing service levels for six categories of WIC participants as goals. The model employs a methodical, consistent approach to the allocation process, yet allows ample flexibility for consideration of state-specific issues. By allowing the user to adjust the relative importance of each goal, the model can incorporate subjective attitudes of state-level WIC administrators. This is extremely important as these attitudes are the result of the administrators' familiarity with the WIC program in their states, and the significance of input of this nature should not be neglected. An application of the model to the Indiana WIC program is presented. Sensitivity of the model to changes in the objective function weights and in the target values for the goals is explored. Although orginally developed to allocate budget increases, the model may be used in allocating budget cuts as well; this form of the model is also presented. The model can be extended hierarchically to incorporate resource allocation at the federal level. This modeling approach should be useful in all public sector programs characterized by multiple objective and hierarchical decisionmaking.

Nonlinear Integer Goal Programming Applied to Optimal System Reliability

Abstract: Few studies have been done on techniques to solve multiple objective nonlinear integer problems. This paper formulates an algorithm for nonlinear integer goal programming using a branch-and-bound method and Hwang & Masud's nonlinear goal programming method. The application of this algorithm is demonstrated by solving reliability problems with single and multiple objectives. The single objective nonlinear integer problem is solved by the nonlinear integer goal programming taking the constraints at priority level one and the objective at priority level two. One interesting feature in this algorithm is that the problem is solved by traditional nonlinear search techniques, such as Hooke and Jeeves pattern search, that are originally intended for solving the ``unconstrained'' problem. However, there is no way to guarantee finding the global optimum for a given problem. This means that the investigator must usually be satisfied with a local optimum or a set of local optima.

A Note on Diet Planning in the Third World by Linear and Goal Programming

Abstract: This note sets out to counter the view that goal programming applied to diet planning offers little improvement over conventional linear programming techniques.

A survey and critique of multiobjective power plant siting decision rules

Abstract: This paper reviews the use of multiobjective decision rules for solving power plant siting problems. After a discussion of exclusionary site screening methods for bounding the decision space, classes of multiobjective and goal programming desicion rules are discussedin the context of final site selection. Advances and limitations of these methods are highlighted. Although multiobjective decision rules have seen numerous applications to power plant siting in the literature, few electric utility companies have used these methods in practice. A review of the use of multiobjective methods in actual power plant siting decisions is also presented, and reasons for the paucity of real-world applications are suggested.

A Generalized Goal Programming Approach to the Minimal Interference, Multicriteria N × 1 Scheduling Problem

Abstract: The conventional approach to the modeling and solution of most scheduling problems involves the development of a mathematical model which (1) employs discrete variables (e.g., linear integer programs), and (2) includes only a single objective to be maximized or minimized (e.g., minimization of makespan). Unfortunately, models involving discrete variables are inherently combinatorially explosive (i.e., methods such as branch-and-bound will exhibit computation times which grow exponentially with problem size). Further, scheduling problems encountered in the real world invariably involve multiple conflicting objectives, and thus using a single-objective representation can lead to gross oversimplification. In this paper we address a specific class of scheduling problem encountered in several real-world applications that may be efficiently addressed as a linear multiobjective model having only continuous variables. The model and its solution are compared with those of a highly acclaimed recent approac...

Fuzzy programming and imprecise data

Abstract: The parameters of mathematical programming models for many civil engineering problems can only be stated imprecisely and this leads to the formulation of fuzzy programs. Considerable progress has been made recently in the solution of such programs. The fundamental problem in a Bayesian decision analysis is the evaluation of least-biased estimates of the prior probabilities. If the prior statistical knowledge is stated crisply then the problem reduces to one of nonlinear programming. Where the prior knowledge is itself imprecise, the problem becomes one of fuzzy nonlinear programming. This leads to a general extremum principle which contains the Jaynes-Shannon formalism as a special case.

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

Abstract: 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.