Showing papers on "Goal programming published in 1987"

A linear approximation for chance-constrained programming

Abstract: Decision environments involve the need to solve problems with varying degrees of uncertainty as well as multiple, potentially conflicting objectives. Chance constraints consider the uncertainty encountered. Codes incorporating chance constraints into a mathematical programming model are not available on a widespread basis owing to the non-linear form of the chance constraints. Therefore, accurate linear approximations would be useful to analyse this class of problems with efficient linear codes. This paper presents an approximation formula for chance constraints which can be used in either the single- or multiple-objective case. The approximation presented will place a bound on the chance constraint at least as tight as the true non-linear form, thus overachieving the chance constraint at the expense of other constraints or objectives.

Forest management and economics

Abstract: This volume provides a survey of quantitative methods, guiding the reader through formulation and analysis of models that address forest management problems. The authors use simple mathematics, graphics, and short computer programs to explain each method. Emphasizing applications, they discuss linear, integer, dynamic, and goal programming; simulation; network modeling; and econometrics, as these relate to problems of determining economic harvest schedules in even-aged and uneven-aged forests, the evaluation of forest policies, multiple-objective decision making, and more.

Quantitative Methods: Applications to Managerial Decision Making

Abstract: Probability Concepts Probability Distribution Decision and Utility Theory Forecasting Introduction to Linear Programming and Model Formulation Graphical Solution of Linear Programming Problems The Simplex Method Postoptimality Analysis Goal Programming Transportation, Transshipment and Assignment Problems Network Models PERT/CPM Integer Programming Models Inventory Analysis: Deterministic Models Inventory Analysis: Probabilistic Models Waiting Line Models Computer Simulation Other Quantitative Models Implementation and Integration of Management Science Techniques in the Decision Framework Appendixes Index.

Knightian Decision Theory, Part II. Intertemporal Problems

Abstract: The theory of choice proposed in "Knightian Decision Theory, Part I" is here applied to intertemporal problems. An analogue of dynamic programming called maxmin programming is developed. Also, it is shown that detailed contingent planning may not be needed in order to achieve maximality, a program being maximal if no other program is preferred to it. In certain circumstances, a maximal program can be achieved by making a finite calculation in each period. This calculation ignores distant future states and could also ignore unlikely contingencies. A decision maker making such calculations would behave much like a satisficer.

A multiple criteria decision support system for global financial planning

Abstract: :This paper presents a goal programming (gp) model-based multiple criteria decision support system (dss) for global financial planning of a multinational corporation (mnc) The GP model-based DSS provides a major technological breakthrough for presenting solutions for the critical issues in global financial planning and provides substantial improvement over existing approaches The strategic dss allows the financial managers of an MNC to choose an appropriate global financing strategy to satisfice the multiple, and often conflicting, management goals and to effectively analyze the trade-offs among costs, foreign exchange risks, political risks, and managerial motivation goals

A zero-one goal programming algorithm using partitioning and constraint aggregation

Abstract: This paper offers a new approach to the solution of zero-one goal-programming problems. The number of non-zero variables required to satisfy a constraint completely is used to identify the priority levels that can be completely achieved, and also determine redundant constraints and invariant decision-variables. The priority levels that are so identified form the basis for a subprogramme of completely achievable constraints. These constraints are aggregated to form a single constraint, and a set of necessary and sufficient conditions are developed to generate the optimal solution. The algorithm has been coded in Pascal and compared with the Lee and Morris algorithm. The virtual CPU time required to solve those problems tested was less than 10 per cent of that required by the Lee and Morris algorithm. The algorithm may also be useful in solving other types of zero-one formulations.

Goal programming formulations and extensions: an overview and analysis

Abstract: This paper provides an overview and expository analysis of goal programming (GP) formulations and extentions. The paper surveys both the traditional and recent GP methodologies. Moreover, it also discusses some of the issues, implications, and criticisms about the technique, such as (i) use of preemptive priorities, (ii) use of weights or scaling factors among noncommensurable goals, (iii) nondominance in GP solutions, (iv) efficient target levels, (v) alternative optima and unbounded solutions, and (vi) GP as a satisficing or optimizing technique.

A goal programming model for allocating operating budgets of academic units

Abstract: The purpose of this paper is to develop a model for reducing operating budgets of the academic units of a small private university, while reflecting the diverse goals of the university. A zero-one goal programming approach is used to design and implement the model for budgetary decision making.

Compromise: an effective approach for solving multiobjective thermal design problems

Abstract: In this paper, the application of the compromise Decision Support Problem Technique to the design of a Rankine power cycle to be used in a solar powered irrigation system is described. The system consists of a solar collector cycle coupled with a simple Rankine cycle. The uniqueness or the present approach lies in the interfacing of the thermal system simulation routines with a multi-objective optimization algorithm1.2, as opposed to the traditional iterative design procedure. The problem, though simple in a mathematical sense, is complete in that it is representative of the complexities associated with the design or thermal systems dealing with thermodynamic property changes.

An Interactive Satisficing Method For Multiobjective Nonlinear Programming Problems With Fuzzy Parameters

Abstract: This paper presents a new interactive satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. The fuzzy parameters in the objective functions and the constraints are characterized by fuzzy numbers. The concept of α-Pareto optimality is introduced in which the ordinary Pareto optimality is extended based on the α-level sets of the fuzzy numbers. In our interactive satisficing method if the decision maker (DM) specifies the degree a of the a-level sets and the reference objective values, the augmented minimax problem is solved and the DM is supplied with the corresponding a-Pareto optimal solution together with the trade-off rates among the values of the objective functions and the degree a. Then by considering the current values of the objective functions and a as well as the trade-off rates, the DM responds by updating his reference objective values and/or the degree a. In this way the satisficing solution for the DM can be derived efficiently from among an a-Pareto optimal solution set. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the computer outputs.

A nonlinear goal programming model for the loading problem in a flexible manufacturing system

Abstract: A nonlinear goal programming model is developed for the loading problem in a flexible maunfacturing system. A sequential search approach is used to obtain the solution. An example is presented to illustrate the application of the model proposed.

Resolving multiple goal conflicts with interactive goal programming

Abstract: A two-phase interactive goal programming procedure is described, which is potentially useful for resolving multiple-use conflicts where multiple and conflicting objectives exist. In the analytical phase, the procedure locates efficient solutions that are proportionally equidistant from the established goal targets. In the decision phase, these results are presented to the decision maker who either accepts the compromise solution provided by the analyst or revises the goal targets and enters into another iteration. The important features of the procedure are (i) the decision maker is not required to explicitly specify any weights or utility function to express preference among objectives; (ii) the results of each iteration are presented to the decision maker graphically, using value paths to allow easy visualization of the extent of compatibility or conflict among the different objectives; and (iii) the analyst explores efficient basic as well as nonbasic solutions in search of the best compromise solution...

Multiobjective decision making approach for determining alternate routing in a flexible manufacturing system

Abstract: In a Flexible Manufacturing System a particular operation on a job can be performed at several machines because of inherent capability of the machines to load multiple tools. There is a choice in the system as to which workstation each operation should be performed. Any entering workpiece therefore has the choice of several different routes. In such a complex scenario productivity could be improved by selecting an efficient routing under computer control. This paper formulates the problem as a Coal Programming model which provides a way of striving towards several objectives simultaneously. Thus the goals to be considered are - (i) to satisfy the forecasted demand, (ii) to minimize the material movements and (iii) to minimize the workload imbalance on all the machines. The solutions obtained on solving this model specify the efficient routing to be implemented. Non-preemptive penalty values are considered for comparing the goal programming formulation with prevailing single criterion objective formulations. Appropriate reasoning for the determined penalty values for the deviations from each goals are given. An illustrative example is considered to study alternate routing under multiple criteria. Lastly, utilization of the goal programming tool lies in evaluating the different layouts and determining the best layout. The layout with minimum workload imbalance and comparatively less material movement is recommended to be the best layout.

Linear Programming Models

Abstract: Publisher Summary This chapter describes the linear programming models. Linear programming is a technique for the mathematical solution of a constrained optimization problem. As such, it has been used in educational planning by formulating an objective function to be maximized or minimized subject to a set of resource constraints. Linear programming applied to education has been formulated in dynamic form or in a static form depending on whether the solution refers to a series of years over the period of the plan, or to a single year, respectively. Linear programming models applied to education have remained mostly academic rather than being used in the actual planning of school systems. The main reason for this being so is the lack of data required for formulating the relationships in the model. Linear programming uses a set of assumptions that might not correspond to the real world. Linear programming may be a good technique at the level of the firm, for example, to define a sales strategy that would maximize profits. However, when applied to education wide or even economy wide problems, data acquisitions and specification, if nothing else, become exceedingly difficult tasks. Linear programming models provide a rare case in which a social welfare function is actually quantified. Linear programming models applied to education have remained mostly academic rather than being used in the actual planning of school systems. The main reason for this being so is the lack of data required for formulating the relationships in the model.

Conditional post-solution analysis of multiobjective compromise decision support problems

Abstract: Design of systems involes Huljking a series of decision Decision Support is needed for improving the effectiveness of the designer. Decision support is provided using the Decision Support Problem Technique. It involves solving Decision Support Problems ( DSPs) and oerformind cost-solution analysis. There are four types of DSPs. This paper deals with the post-solution analysis of the compromise DSPs only. Post-solution analysis deals with interpreting, and performing parametric and sensitivity analysis for the solution of the compromise DSPs. The purpose of performing post-solution analysis is to transform information about the solution to knowledge about the DSP. The method of conditional post-solution analysis for linear, multi objective compromise DSPs, and its extension to nonlinear problems, is discussed here. This approach is suitable for implementation of an expert system on the computer in conjunction with the existing solution software for compromise DSPs. The technique is illustrated using the Tw...

Emergence of a Dominant Course of Action in a General Feedback Loop When Goal Uncertainty is Present.

Abstract: A decision maker is confronted with a finite set of possible courses of action, each of which can generate one of several possible outcomes. The decision maker must make a (possibly infinite) sequence of such decisions, the consequence of each decision being fed back to him so that the estimated averages can be updated before the next course of action is selected. Furthermore, suppose that initially the decision maker is uncertain of precisely how to assess the utilities associated with each action-outcome pair (goal uncertainty), but that as he proceeds through the decision-information feedback loop he is gradually able to sharpen his perception of these utilities (goal shaping). In this article a mathematical model of a decision maker subject to goal uncertainty is given. Conditions are established which guarantee that the decision maker's ranges of expected utilities stabilize as he cycles through the decision-feedback loop. It is also shown that a single dominant course of action will always emerge. A specific example involving a decision maker functioning in the type of environment described above provides insight as to how this procedure works in practice. © 1987 John Wiley & Sons, Inc.

Goal Programming, Method of Weighted Residuals, and Optimal Control Problems

Abstract: The feasibility of utilizing goal programming, a management science originated technique, in solving optimal control problems is investigated. The basic idea is to recast the problem in a pre-emptive goal programming model via the use of hard and soft constraints (or stiff and weak springs) in linear programming (or mechanics). It is found that the goal programming technique for solving the optimal control problem is fundamentally more general than the method of weighted residuals. An example is included to illustrate the methodology.

Air Refueling Tanker Scheduling

Abstract: : This thesis determined a way to schedule Strategic Air Command's air refueling tanker fleet to perform, if necessary, more than one refueling mission during a flight. A preemptive goal programming approach was adopted using three priority levels. The basic formulation was that of the generalized assignment problem. Three objectives had to be considered when performing the task, maximize the number tanker requests satisfied, maximize the number of category B requests satisfied, and minimize the total flight time to perform all of the missions. A preprocessor was developed to transform the inputs from the tanker and receiver scheduling units into a usable format to be executed by the mixed integer programming package. This preprocessor determined all of the possible refuelings that could take place, computed the flight times of the missions, and determined all of the variables to be used in the constraints and objective functions. Keywords: KC-135 and KC-10 aircraft.

A Multi-Attribute Assignment Goal-Programming Model with Incentives

Abstract: A multi-attribute assignment goal-programming model is developed in this paper for the selection and assignment of transfer personnel. Attributes and incentives are used to select the correct type of people from surplus personnel and assign them to vacant positions. The model is illustrated in a simple, exemplary case problem, and the results are interpreted. The model is solved by using a sequential linear goal-programming algorithm and a mixed-integer programming subroutine.

Interpreting Dual Variables for Optimization with Nonmonetary Objectives

Abstract: An approach to the interpretation of dual variables for mathematical programs with nonmonetary objectives is described. The approach is general, and in particular may be applied to problems of goal programming, expected utility maximization, intertemporal utility maximization and risk minimization subject to minimum income constraints. The technique is designed to transform shadow prices, expressed in marginal increases in the objective per unit of resource, into easily interpreted units, such as dollars per unit of resource.

Comments on “An Algorithm for Solving the Linear Goal-Programming Problem by Solving Its Dual”

Abstract: Goal Programming within a pre-emptive priority structure has been one of the most widely used multi-objective mathematical model formulations. By considering its dual problem, Ignizio has shown that a very efficient computational procedure for solving linear goal-programming problems can be problems can be implemented with any conventional large-scale simplex system. This note gives an overview of Ignizio's dual formulation, and identifies when a certain dual variable must be incorporated in the model to preserve the pre-emptive priority structure.

A New Approach to Decision Making in Multiple‐Objective Linear Programming (MOLP) Problems

Abstract: It is well known that the set of nondominated solutions (NS) (also known as efficient, or pareto-optimal) for MOLP is obtained by solving equation 2. The weight coefficients, X i , are parameters that are varied to locate NS points. The space of weights is represented by a regular simplex. The representative subset of NS may be obtained by means of a simplex lattice (SL) design.s Points A' = (A;, A:, . . . , A:), . . . , A' = (A;, A:, , . . , A:) of SL4r5 are considered and corresponding t LP problems (equation 2) are solved. Let us consider a matrix of objective function values for these solutions; let us call it { Z } . The rows of this matrix represent solutions, while the columns of this matrix represent objectives. The basic strategy of the approach is as follows: It is expected that the final solution can be chosen by the decision maker (DM) after analysis of the zone of compromise solutions. Such a zone as a simplex in the space of weights is considered. This zone is constructed by means of a S L design and a system of polynomial equations is obtained. j 1