Multicriteria Assignment Problem Research Articles

Oh, the Places You’ll Go: Optimizing Enlisted Personnel Assignments in the United States Army Using a Multicriteria Assignment Problem

Oh, the Places You’ll Go: Optimizing Enlisted Personnel Assignments in the United States Army Using a Multicriteria Assignment Problem

Linear Goal Programming Method for Optimal Decision Making of Multi-Criteria Assignment Problems

The decision making process is the essence of the administrative process and its means of achieving the goals of the service organizations or productivity because the decision contributes mainly to enable them to carry out their administrative activities efficiently and effectively. The assignment process is one of the most important problems affecting the organizations performance because to determine the administrative composition of the organization. The correct decision making to the assignment problem and the right person in the right place will increase the efficiency and effectiveness of the organization. The previous methods to solve these problems depend on a single criterion such as cost, profit, time and so on. In this paper, three models were formulated for the of multi-criteria assignment problem. The first model multiple objective for present assignment problem when the assignment matrix is square, while the second and third models are a non-square assignment problem. The second model is the number of rows is greater than the number of columns while the third model where the number of columns larger than the rows. The second model is applied to the assignment problem of unit managers in the college of Administration and Economics based on two criteria: deferring the employee's desire to leader of task and the other criterion of assignment cost and using goal programming method. The data were collected by questionnaire.

A DEA-based approach for the multi-criteria assignment problem

This paper proposes a DEA model for evaluating arc efficiency in the presence of multiple weights on arcs in a network. Thereafter, a multi-criteria assignment problem is formulated based on the efficiency of the arcs. Appraisal is given to some parts of the proposed DEA-model used for solving multi-criteria network ow problems and provide some examples. Finally, a numerical example is used to illustrate the applicability of the approach.

Finding efficient assignments: An innovative DEA approach

Finding and classifying all efficient assignments for a Multi-Criteria Assignment Problem (MCAP) is one of the controversial issues in Multi-Criteria Decision Making (MCDM) problems. The main aim of this study is to utilize Data Envelopment Analysis (DEA) methodology to tackle this issue. Toward this end, we first state and prove some theorems to clarify the relationships between DEA and MCAP and then design a new two-phase approach to find and classify a set of efficient assignments. In Phase I, we formulate a new Mixed Integer Linear Programming (MILP) model, based on the Additive Free Disposal Hull (FDH) model, to gain an efficient assignment and then extend it to determine a Minimal Complete Set (MCS) of efficient assignments. In Phase II, we use the BCC model to classify all efficient solutions obtained from Phase I as supported and non-supported. A 4×4 assignment problem, containing two cost-type and single profit-type of objective functions, is solved using the presented approach.

A fuzzy approach to multicriteria assignment problem using exponential membership functions

In this paper, we extend the classical assignment problem to the multicriteria assignment problem by considering three criteria: cost, time and quality subject to many realistic constraints including multi-job assignment and a knapsack-type resource constraint. The paper addresses the uncertainty of the real-life assignment problem by formulating a fuzzy cost–time–quality assignment problem using exponential membership functions. We define fuzzy goal for each criterion as per the preferences of the decision-maker and aggregate the fuzzy goals using product operator. In order to obtain optimal assignment plans, the resultant nonlinear 0-1 optimization problem is solved using genetic algorithm for different choices of the shape parameters in the exponential membership functions. As an illustrative example, we consider a fuzzy manpower planning problem.

Connection of users with a telecommunications network: Multicriteria assignment problem

The problem of connection of users with access points of a wireless telecommunications network is analyzed. An approach is based on the multicriteria assignment problem. A set of criteria involves the maximum bandwidth, the number of simultaneously served users, service reliability requirements, etc. Restrictions on the number of users served by access points and the frequency spectrum width of an access point are discussed. The combinatorial optimization problem employed belongs to the NP-hard class, and its solution is sought via the proposed heuristic methods. The proposed approach is illustrated by a numerical example.

Determining Feasible Solutions of a Multicriteria Assignment Problem.

This paper presents an important research tool in operations research as it applies to a particular structure of the multicriteria assignment problem. The paper addresses the problem of effectiveness of feasible solutions of a multicriteria assignment problem and this was done in two steps. In the first step, we determine whether or not a given feasible solution of a multicriteria assignment problem is a real efficient one. In the second step, if the feasible solution is not real efficient, we provide a real efficient solution that dominates that not real efficient solution, using our proposed method which consists of transforming the original problem into an assignment problem.

FUGEN: a tool for the design of layouts for cellular manufacturing systems

Design of layouts for Cellular Manufacturing Systems (CMSs) has not received attention by researchers as much as cell formation in cellular manufacturing. In this paper a mathematical model, formulated as a multicriteria Quadratic Assignment Problem (QAP) is proposed for the design of layouts for CMSs with the objective of minimising the material handling cost (quantitative) and maximising the closeness rating (qualitative). A Genetic Algorithm (GA)-based tool called FUGEN, which makes use of crossover, mutation (inversion) and direct entry (elitism) with embedded fuzzy logic and Analytic Hierarchy Process (AHP) models, is developed for the design of layouts for CMSs. An attempt is made to make the model practical by considering the production volume, transfer batch size and operational sequence of parts. The proposed tool is validated using an example from the literature.

On the Efficiency of Feasible Solutions of a Multicriteria Assignment Problem

The particular structure of the assignment problem made of it a very popular subject of study and an important research tool in operations research and management science. In addition to the importance that the assignment problem represents in its own, it can appear as a relaxation of more complex combinatorial optimization problems. That is why the assignment problem has received great attention from the operations research community. The assignment problem may appear as an optimization problem with multiple objectives. In this paper, we address the problem of efficiency of feasible solutions of a multicriteria assignment problem. It is done in two steps. In the first step, we determine whether or not a given feasible solution of a multicriteria assignment problem is efficient. In a second step, if the feasible solution is not ef- ficient, we provide an efficient solution that dominates it. The proposed method consists of transforming the original prob- lem into an assignment problem with side constraints for which solution techniques already exist.

Multi-criteria assignment problem with incompatibility and capacity constraints

The considered assignment problem generalizes its classical counterpart by the existence of some incompatibility constraints limiting the assignment of tasks to processing units within groups of mutually exclusive tasks. The groups are defined for each processing unit and the constraints allow at most one task from each group to be assigned to the corresponding processing unit. The processing units can normally process a certain number of tasks without any cost; this capacity can be extended, however, at some extra marginal cost that is non-decreasing with the number of additional tasks. Each task has to be assigned to exactly one processing unit and has some preference for the assignment; it is expressed for each pair ‘task-processing unit’ by a dissatisfaction degree. The quality of feasible assignments is evaluated by three criteria: g1-the maximum dissatisfaction of tasks, g2-the total dissatisfaction of tasks, g3-the total cost of processing units. If there is no feasible assignment, tasks and processing units creating a blocking configuration are identified and all actions of unblocking are proposed. Formal properties of blocking configurations and unblocking actions are proven, and an interactive procedure for exploring the set of non-dominated assignments is described together with illustrative examples processed by special software.

A multicriteria assignment problem

AbstractOur objective in this paper is to propose a procedure for solving a multicriteria assignment problem. Given qualitative and quantitative data, the proposed procedure makes assignments taking into consideration the multicriteria aspect of the problem. As an illustrative example, we consider the assignment of referees to the football matches in an Italian championship. Copyright © 2003 John Wiley & Sons, Ltd.