On finding and detecting efficient assignments in the case of multiple inputs and outputs

Abstract

An interesting variant of the assignment problem is the case where each partial assignment of an individual to a job involves multiple inputs and outputs. In this paper, three issues about this problem are discussed: finding an efficient assignment, verifying the efficiency of a solution and restoring the efficiency of an inefficient assignment. For the first issue, a current method, proposed by Chen and Lu, is compared with a proposed multiobjective formulation and for the second and third ones, a two-phase method is developed, which is based on the simplex method and the Dantzig–Wolfe decomposition algorithm.

Keywords:

• assignment problem
• multiobjective programming
• data envelopment analysis
• Pareto efficiency
• Dantzig–Wolfe reformulation

2000 AMS Subject Classification :

• 90C05
• 90C08
• 90C10
• 90C29
• 90C49

Acknowledgements

The first author, Afzalinejad, would like to thank Professor Mehrdad Tamiz and the Department of Mathematics at the University of Portsmouth for their help during his time as a visiting researcher there. The authors would like to thank the anonymous referees for their comments that have helped to improve the paper.

Notes

Note that these models are different from the classical BCC model 1 of DEA methodology.