Linear Goal Programming Model Research Articles

A method for group decision making with multi-granularity linguistic assessment information

This paper proposes a method to solve the group decision making (GDM) problems with multi-granularity linguistic assessment information. In the method, the multi-granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers. In order to make the collective opinion close to each expert’s opinion, a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation. Then, a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers. By applying a non-dominance choice degree to this fuzzy preference relation, the ranking of alternatives is determined and the most desirable alternative(s) is selected. An example is used to illustrate the applicability of the proposed method and its advantages.

A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations

This paper proposes a goal programming approach to solve group decision-making (GDM) problems where the preference information on alternatives provided by decision makers is represented in two different formats, i.e. multiplicative preference relations and fuzzy preference relations. In order to narrow the gap between the collective opinion and each decision maker’s opinion, a linear goal programming model is constructed to integrate the two different formats of preference relations and to compute the collective ranking values of the alternatives. Thus, the ranking of alternatives or selection of the most desirable alternative(s) is obtained directly from the computed collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.

Um modelo de programação matemática para otimizar a composição de lotes de minério de ferro da mina Cauê da CVRD

Esse trabalho tem seu enfoque no problema de blendagem de produtos de minério de ferro, estocados nos pátios da mina Cauê, da Companhia Vale do Rio Doce, em Itabira, Minas Gerais, para a composição de lotes. Propõe-se um modelo de programação linear por metas que visa a determinar os locais de retomada dos produtos estocados, de tal forma que a mistura atenda aos limites de especificações de qualidade e quantidade preestabelecidos pelo cliente e satisfaça as restrições operacionais dos pátios. O modelo de programação matemática desenvolvido foi implementado no modelador e otimizador LINGO 9.0, interfaceando com planilhas do EXCEL 2000, possibilitando a utilização e exportação de dados em um ambiente familiar à empresa de mineração. O sistema desenvolvido foi validado comparando-se os resultados obtidos com os produzidos manualmente pela empresa. Os resultados computacionais apresentados comprovaram que é possível prover uma melhora na composição dos lotes através do modelo proposto.

A stochastic linear goal programming approach to multistage portfolio management based on scenario generation via linear programming

A stochastic linear goal programming model for multistage portfolio management is proposed. The model takes into account both the investment goal and risk control at each stage. A scenario generation method is proposed that acts as the basis of the portfolio management model. In particular, by matching the moments and fitting the descriptive features of the asset returns, a linear programming model is used to generate the single-stage scenarios. Scenarios for multistage portfolio management are generated by incorporating this single-stage method with the time-series model for the asset returns. Meanwhile, no arbitrage opportunity exists in the proposed method. A real case is solved via the goal programming model and the scenario generation approach which demonstrates the effectiveness of the model. We also comment on some practical issues of the approach.

APPLICATION OF CRISP AND FUZZY GOAL PROGRAMMING MODELS FOR OPTIMIZATION OF CROPPING PATTERN IN HARAZ SUB-BASIN IN IRAN

All of past mathematical programming methodologies are outcome of two and multi value logic. These methods want quan-titative crisp information. Human senses (linguistic variable) and vague information do not exist in past mathematical models. In the year 1965 professor Zadeh oriented theory of fuzzy sets. In its origin fuzzy theory with the help of classic mathematics and standard indexes is able to give mathematical shape to the process of human being identification, which in the most cases is identified. This new theory improved the simple models in sense that it abolished their simplifying approach and hence giving them more consistency with the real world. With the invention of fuzzy theory one of the dead ends planning models was opened. In this way, the budget human is not an absolute human being, instead he/she is a fuzzy human being which thinks fuzzy and makes decision on the basis of fuzzy data. This paper notice to theory and application of fuzzy linear goal programming model in optimization cropping pattern. In order to, sum total membership all fuzzy goals are maximized in this model. Versus crisp goal programming model in this method to decision maker is permitted to determinate about membership function and its importance. Also this method is able to create consistent membership function according to expects decision maker. Technical coefficient in this model is not crisp, and changes in the limited area. This paper with analysis theory fuzzy linear goal programming, indicate application of it in optimization cropping pattern in irrigation land of Haraz sub-basian in Iran. Results indicate with create flexible RHS in model, resource allocation is bettered and land surface cropping is developed.

A method for multiple attribute decision-making with the fuzzy preference relation on alternatives

This paper investigates the multiple attribute decision-making (MADM) problem with preference information on alternatives. A new method is proposed to solve the MADM problem, where the decision maker (DM) gives his/her preference on alternatives in a fuzzy relation. To reflect the DM's subjective preference information, a linear goal programming model is constructed to determine the weight vector of attributes and then to rank the alternatives. Finally, a numerical example is used to illustrate the use of the proposed method.

Allocating production batches to subcontractors by fuzzy goal programming

Allocating production batches to subcontractors arises frequently in industry. When subcontractors operate different equipment, batch assignment is a complex decision that must take into account both throughput and quality of finished goods. In this paper, a Mixed Integer Linear Goal Programming Model, where productivity uncertainty is taken into account through Fuzzy Set Theory, is developed. Our study was motivated by a real‐world application arising in an Italian textile company. Computational results show that this method outperforms the hand‐made solutions put to use by the management so far.

A goal programming approach to strategic resource allocation in acute care hospitals

This paper describes a methodology for allocating resources in hospitals. The methodology uses two linear goal-programming models. One model sets case mix and volume for physicians, while holding service costs fixed; the other translates case mix decisions into a commensurate set of practice changes for physicians. The models allow decision makers to set case mix and case costs in such a way that the institution is able to break even, while preserving physician income and minimizing disturbance to practice. The models also permit investigation of trade-offs between case mix and physician practice parameters. Results are presented from a decision-making scenario facing the surgical division of Toronto's Mount Sinai Hospital after the announcement of a 3-year, 18% reduction in funding.

A practical multicriteria methodology for assessing risky public investments

This paper proposes a simple, practical but also realistic, methodology of multicriteria decision aid for the assessment of public investment projects which takes into account the uncertainty of projects’ measures. It follows the general framework of the expected utility developed by von Neumann and Morgenstern and its operational modelling by an additive non-linear function proposed by Keeney and Raiffa. However, it builds upon the linear goal programming model of Jacquet-Lagrèze and Siskos which offers several convenient computational procedures for building non-linear (albeit, piecewise linear) partial utility functions reflecting, as well as possible, the decision-maker’s preferences. In order to simplify as much as possible the process of decision making, the paper proposes an alternative method, named Quasi-UTA, whereby the decision maker chooses directly for each criterion a (piecewise linear) partial utility function with only two parameters. These are the respective relative weights and a curvature parameter that models risk aversion or proneness. The method substantially reduces the number of questions to be answered by the decision-maker. In a context of budget constraint, the paper seeks to calibrate the utility function in equivalent money value, and shows how to compute such a value in multicriteria analysis. Money valuation has the advantage of permitting the use of standard financial rules of assessment. The paper also shows how to compute the cost of a project’s uncertainty, i.e. its risk premium, as proposed in the financial theory of risk. The method also suggests a procedure to generate and compute each criterion’s random distribution as a triangular, rectangular or discrete function. An example illustrates the use of the methodology.

A heuristic for bi-objective vehicle routing with time window constraints

This paper is concerned with the bi-objective vehicle routing problem with time window constraints (BVRPTW). The BVRPTW is to determine the most favorable vehicle routes that minimize the total vehicle travel time and the total customer wait time which are, more often than not, conflicting. We construct a linear goal programming (GP) model for the BVRPTW and propose a heuristic algorithm to relieve a computational burden inherent to the application of the GP model. The heuristic algorithm consists of a parallel insertion method for clustering and a sequential linear goal programming procedure for routing. The results of computational experiments showed that the proposed algorithm finds successfully the more favorable solutions in most cases than the Potvin an Rousseau's method that is known as a very good heuristic for the VRPs with time window constraints. The proposed algorithm was capable of generating a numerous nondominated solutions through the change of the target values of the two objectives and the decision maker's preference on the objectives expressed as α.

Integrated Multi-criterial Decision Model: a Case Study for the Allocation of Facilities in Chinese Agriculture

The proposed methodology of integrating the Analytic Hierarchy Process (AHP) and Goal Programming (GP) in this paper provides decision-makers with the flexibility needed to allocate resources by considering both quantitative and qualitative decision criteria. A large-scale linear goal programming model is established in order to optimize allocation of facilities for a grain harvesting and post-harvest system within a province in China. The proposed model includes multiple conflicting goals with inconsistent units requiring prioritization. The Analytic Hierarchy Process is used to set up priorities for strategic goals in a grain harvesting and post-harvest system, including the two most important goals in the linear goal programming model: grain loss and production cost. Multiple-phase Simplex Algorithm for linear goal programming is then used to get a solution. The original data in this case study are collected from an on-site investigation of Chinese agriculture. The results of AHP and the GP model show that decreasing the grain loss is the most important goal in a grain harvesting and post-harvest system, and it would be possible to decrease it to 13%, and even to 10%, but it is impossible to decrease the grain loss rate to 5% under the present conditions for facilities and techniques.

Scheduling customized bag production: an application of the Group Technology concept

Describes the application of the Group Technology concept in scheduling industrial bag production in a woven products division of a bag manufacturer. The labour assignments, determined through a linear goal programming model, minimize unbalanced workloads among the operations. This study shows a new application area of the Group Technology concept which leads to a better solution of labour assignments and provides management with valuable information essential to the development of a strategic competitive advantage.

Deriving the partial values in MCDM by goal programming

Preference for a set of alternatives evaluated under multiple criteria is frequently expressed in the form of pairwise comparisons. We propose a linear goal programming model for deriving the partial and overall preference values of the alternatives directly from pairwise comparisons. This model can be a useful alternative to AHP. The partial values represent the contribution of the criteria to the overall preference. Simulation experiments, which are conducted to compare the performance of the model with that of two other existing models, show that the model has good performance.

A linear goal programming model for human resource allocation in a health-care organization.

This paper presents the development of a goal programming (GP) model as an aid to strategic planning and allocation for limited human resources in a health-care organization. The purpose of this study is to assign the personnel to the proper shift hours that enable management to meet the objective of minimizing the total payroll costs while patients are satisfied. A GP model is illustrated using the data provided by a health-care organization in the midwest area. The goals are identified and prioritized. The model result is examined and a sensitivity analysis is performed to improve the model applicability. The GP model application adds insight to the planning functions of resource allocation in the health-care organizations. The proposed model is easily applicable to other human resource planning process.

Preference modelling by estimating local utility functions for multiobjective optimization

This paper is intended to design goal programming models for capturing the decision maker's (DM's) preference information and for supporting the search for the best compromise solutions in multiobjective optimization. At first, a linear goal programming model is built to estimate piecewise linear local utility functions based on pairwise comparisons of efficient solutions as well as objectives. The interactive step trade-off method (ISTM) is employed to generate a typical subset of efficient solutions of a multiobjective problem. Another general goal programming model is then constructed to embed the estimated utility functions in the original multiobjective problem for utility optimization using ordinary nonlinear programming algorithms. This technique, consisting of the ISTM method and the newly investigated search process, facilitates the identification and elimination of possible inconsistent information which may exist in the DM's preferences. It also provides various ways to carry out post-optimality analysis to test the robustness of the obtained best solutions. A modified nonlinear multiobjective management problem is taken as example to demonstrate the technique.

Goal Programming in Preference Decomposition

In choosing the best alternative with respect to multiple criteria, one approach is to estimate the criterion weights that influence the preferences of all the alternatives presented. When decision makers are able to make preference judgements based on the alternative as a whole, preference decomposition methods attempt to determine part-worths which represent the contribution of the criterion levels to the overall preference values. For each alternative, the sum of the part-worths estimates its overall preference value. In this work, we use linear goal programming to determine the part-worths of all the criterion levels. Simulation experiments are conducted to compare the performances of linear goal programming and ordinary least squares regression in preference decomposition and to examine the effectiveness of including constraints on the parameters. Our simulated results suggest that the linear goal programming model with constrained parameters has better predictive power.

A Linear Goal Programming Model for Trans-Shipment Problems with Flexible Supply and Demand Constraints

A Linear Goal Programming Model for Trans-Shipment Problems with Flexible Supply and Demand Constraints

A Linear Goal Programming Model for Trans-shipment Problems with Flexible Supply and Demand Constraints

This paper deals with the development of a linear goal programming model for solving transshipment problems with flexible supply and demand constraints. The model was constructed based on the data obtained from a nationwide retail firm. The Wilcoxon signed-ranked test was used to show the model's flexibility and applicability. The test results were analysed and interpreted for decision making.

A Linear Goal Programming Model for Trans-Shipment Problems with Flexible Supply and Demand Constraints

This paper deals with the development of a linear goal programming model for solving transshipment problems with flexible supply and demand constraints. The model was constructed based on the data obtained from a nationwide retail firm. The Wilcoxon signed-ranked test was used to show the model's flexibility and applicability. The test results were analysed and interpreted for decision making.

A Multiple Objective Model for a Just‐in‐Time Manufacturing System Environment

Presents a linear goal programming (LGP) model, which can be used to derive an optimal daily production schedule for JIT production systems. Also provides an explanation of how a detailed post‐optimal LGP analysis can enable a decision maker to examine the effects of production scheduling in a JIT “mixed‐model” production environment. To illustrate the informational efficacy of the proposed JIT‐based LGP model, presents an illustrative example.