An extended assignment problem considering multiple inputs and outputs

Liang Hsuan Chen, Hai Wen Lu

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2239-2248
Number of pages10
JournalApplied Mathematical Modelling
Issue number10
Publication statusPublished - 2007 Oct

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics


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