Often, the coefficients of a linearprogramming problem represent estimates of true values of data or are subject to systematic variations. In such cases, it is useful to perturb the original data and to either comput...
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Often, the coefficients of a linearprogramming problem represent estimates of true values of data or are subject to systematic variations. In such cases, it is useful to perturb the original data and to either compute, estimate, or otherwise describe the values of the functionf which gives the optimal value of the linear program for each perturbation. If the right-hand derivative off at a chosen point exists and is calculated, then the values off in a neighborhood of that point can be estimated. However, if the optimal solution set of either the primal problem or the dual problem is unbounded, then this derivative may not exist. In this note, we show that, frequently, even if the primal problem or the dual problem has an unbounded optimal solution set, the nature of the values off at points near a given point can be investigated. To illustrate the potential utility of our results, their application to two types of problems is also explained.
This paper presents a new, interactive multi-objectivelinear-programming procedure to aid decision-makers in setting up goals for desired outputs. The procedure relies on empirical production functions generated by t...
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This paper presents a new, interactive multi-objectivelinear-programming procedure to aid decision-makers in setting up goals for desired outputs. The procedure relies on empirical production functions generated by the use of data envelopment analysis. It presents the decision-maker with a set of alternative efficient points in order either to compare different sets of inputs in terms of their effectiveness for goal achievement, or to set goals against which future management performance may be measured. With each iteration the new information provided by the decision-maker is used to adjust the procedure, leading to points which have greater effectiveness utility for the decision-maker. A numerical example is provided along with guidelines for future applications.
Various difficulties arise in using decision set-based vector maximization methods to solve a multiple-objective linear programming problem (MOLP). Motivated by these difficulties, some researchers in recent years hav...
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Various difficulties arise in using decision set-based vector maximization methods to solve a multiple-objective linear programming problem (MOLP). Motivated by these difficulties, some researchers in recent years have begun to develop tools for analyzing and solving problem (MOLP) in outcome space, rather than in decision space. In this article, we present and validate a new hybrid vector maximization approach for solving problem (MOLP) in outcome space. The approach systematically integrates a simplicial partitioning technique into an outer approximation procedure to yield an algorithm that generates the set of all efficient extreme points in the outcome set of problem (MOLP) in a finite number of iterations. Some key potential practical and computational advantages of the approach are indicated.
This paper deals with the problem of Supplier Selection and Order Allocation (SSOA) in a fuzzy sense. The demand and delivery lead time are treated as fuzzy numbers. The fuzzy number is first transformed into interval...
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ISBN:
(数字)9789811028571
ISBN:
(纸本)9789811028571;9789811028564
This paper deals with the problem of Supplier Selection and Order Allocation (SSOA) in a fuzzy sense. The demand and delivery lead time are treated as fuzzy numbers. The fuzzy number is first transformed into interval numbers. After doing some arithmetic operations, those fuzzy interval numbers are defuzzified to a crisp quantity. This crisp quantity is further used as an input parameter in the model. Essentially, the main approach in this paper is based on the function principle and the pascal triangular graded mean approach. The SSOA problem is constructed as a multiple Criteria Decision Making (MCDM) problem aiming to optimize the order quantities placed to many suppliers. The problem is solved by a fuzzy linearprogramming technique. A numerical example is also given for the illustration of the discussed issues.
The traffic police routine patrol vehicle mission is to provide service to the public, primarily through enforcement of traffic laws and assistance to road users after accidents or other calls for service. An efficien...
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The traffic police routine patrol vehicle mission is to provide service to the public, primarily through enforcement of traffic laws and assistance to road users after accidents or other calls for service. An efficient traffic police location and schedule assignment (TPLSAP) across a road network ensures that the traffic police undertake their mission effectively. In the search for effective road network cover solutions, a multiple-objectivelinear program is developed in the first stage with three distinct objectives. The objective functions maximize the following: (1) traffic police presence and conspicuousness;(2) police presence at blackspots where frequent traffic offences occur;and (3) the time available for proactive work. In the second stage of the TPLSAP formulation, distance and time halo effect integer linear programs produce a detailed, daily shift schedule across the planning horizon. Consequently, we formulate a routine traffic police schedule-location and activity problem, which incorporates road safety recommendations drawn from the literature, police policy and operational constraints. Finally, we apply the formulation to a case study of the interurban road network in Northern Israel, which highlights potential improvements over the current schedules. Copyright (C) 2014 John Wiley & Sons, Ltd.
Companies continuously plan their aggregate production quantities and are always faced with variations and uncertainties in demand which is one of the major inputs in those plans. Due to multipleobjectives in aggrega...
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Companies continuously plan their aggregate production quantities and are always faced with variations and uncertainties in demand which is one of the major inputs in those plans. Due to multipleobjectives in aggregate production plans, the problem usually requires more in-depth analysis. This paper provides some insights into the most common objectives in solving aggregate production planning problems under different environments.
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