# A special multi objective assignment problem

If such a solution is unique, then it is efficient. Problems of this kind, in which it is required to find efficient or other solutions, have been studied by various authors.

The bottle-neck assignment problem see Vajda1" shares the spirit of this paper. An alternative interpretation of the problem also exists.

Let us now turn to our theoretical analysis of our class of problems. To check if a-particularx is in E Xwe may use the auxiliary problem given in Philip,12 viz. If it is possible to aggregate the complete set of objectives into a single value function, or super objective, then one may optimize this value function in many cases.

Then z E E Xcontrary to the assumption. Let C C be the corresponding efficient set, with respect to X, expressed in cost vector form.

Computationally this is easily organized by This content downloaded from The problem tackled in this paper is more special than this and, as it turns out, has features which the general, multi-objective assignment problem does not have.

The following example illustrates this. We use information technology and tools to increase productivity and facilitate new forms of scholarship.

All rights reserved Copyright? We have only a finite number of different values for ci. In Theorem 2 it is A special multi objective assignment problem that when each efficient vector is determined by a single assignment solution, the efficient set is identical to the set of efficient vertices of the convex hull of the assignment solution set.

The simplest form of information is usually that of the monotone property of preferences in terms of the levels of the objective functions.

We shall also show that this is true for a particular class of problem. The standard, single-objective assignment problem deals with the optimization of the single-objective function, linear in the decision variables. If the aggregation was not linear, or was not known but still monotone, it would be of value to determine the efficient solutions by considering the problem as a multi-objective problem in which the jth objective function was the time associated with individual j.

There are n activities to be assigned to n personnel. Thus with objectives such as cost, time and distance, the lower the levels, then the more preferable the option. Using A Lemma 2 we now get the requisite result.

The individuals referred to may actually be part of the team of decision makers, and the assignment measures of performance for each activity and any given individual may merely be the ranking of the activities. It is a special problem within the class of all multi-objective assignment problems, and as such it does have special features, viz.

This paper then considers this problem.

As will be seen, this fits in with the definition of the general, multi-objective assignment problem by appropriately defining the objectives. A Proof Let x e E Xand without loss of generality, assume x is the diagonal assignment.

For example, if we were to assign tasks to individuals, we may need to take into account the costs, times and quality of completion of the tasks, and, although in principle we may conceive of a single aggregate objective function, for various reasons it may not be thought to be appropriate to do so.

The work in Charnes et al. Let S be the set of all such values. The next section will introduce the formal problems with which we shall deal. Such considerations give rise to the need to determine the so-called efficient set of the options, viz.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. This is not the case for X, even in the assignment class of problems.

For many problems, a single objective function is not adequate to represent the problem, and ci;e6Rm, representing m possible objectives, with clj being the measure of worth for the lth objective, 1 4 1 4 m. This paper deals with a special multi-objective problem, viz.It is a special problem within the class of all multi-objective assignment problems, and as such it does have special features, viz.

for this problem all the efficient solutions may be determined by the procedure of minimizing the weighted sum of the objectives, which is not generally true for all multi-objective assignment problems, and.

Keywords: Assignment, Multi-objective decision making, Fuzzy linear programming, The classical assignment problem refers to a special class of linear programming problems. Linear programming is one of the most Solve the multi-objective assignment problem as a single objective assignment.

WHITE1 considers an assignment problem, with n activities to be assigned to n people, and with n objective functions, being the costs of the activities assigned to each person. He. Multi-Criteria Vehicle Assignment Problem: An Application for a Security Organization Assignment problems are considered as a special case for transportation problems.

When we consider transportation and assignment problems as real-life for a multi-objective multi-choice assignment problem is studied by Mehlawat [17]. A study of. The assignment problems is a special case of Transportation problem.

Depending on the objective we want to optimize, we obtain the typical assignment problems. multi-objective assignment problem and demonstrates this new approach using the fighter squadron flight scheduling problem as an example.

In this research, the Value Focused Thinking method is applied to build a decision analysis model to help decision makers in fighter squadrons evaluate the mission-pilot.

A special multi objective assignment problem
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