TY - JOUR

T1 - An extended assignment problem considering multiple inputs and outputs

AU - Chen, Liang Hsuan

AU - Lu, Hai Wen

PY - 2007/10

Y1 - 2007/10

N2 - The existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit incurred by each possible assignment. However, in real applications, various inputs and outputs are usually concerned in an assignment problem, such as a general decision-making problem. This paper develops a procedure for resolving assignment problems with multiple incommensurate inputs and outputs for each possible assignment. The concept of the relative efficiency in using various resources, instead of cost or profit, is adopted for each possible assignment of the problem. Data envelopment analysis (DEA) is employed in this paper to measure the efficiency of one assignment relative to that of the others according to a set of decision-making units. A composite efficiency index, consisting of two kinds of relative efficiencies under different comparison bases, is defined to serve as the performance measurement of each possible assignment in the problem formulation. A mathematical programming model for the extended assignment problem is proposed, which is then expressed as a classical integer linear programming model to determine the assignments with the maximum efficiency. A numerical example is used to demonstrate the approach.

AB - The existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit incurred by each possible assignment. However, in real applications, various inputs and outputs are usually concerned in an assignment problem, such as a general decision-making problem. This paper develops a procedure for resolving assignment problems with multiple incommensurate inputs and outputs for each possible assignment. The concept of the relative efficiency in using various resources, instead of cost or profit, is adopted for each possible assignment of the problem. Data envelopment analysis (DEA) is employed in this paper to measure the efficiency of one assignment relative to that of the others according to a set of decision-making units. A composite efficiency index, consisting of two kinds of relative efficiencies under different comparison bases, is defined to serve as the performance measurement of each possible assignment in the problem formulation. A mathematical programming model for the extended assignment problem is proposed, which is then expressed as a classical integer linear programming model to determine the assignments with the maximum efficiency. A numerical example is used to demonstrate the approach.

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U2 - 10.1016/j.apm.2006.08.018

DO - 10.1016/j.apm.2006.08.018

M3 - Article

AN - SCOPUS:34247196543

SN - 0307-904X

VL - 31

SP - 2239

EP - 2248

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

IS - 10

ER -