A turnpike approach to solving the linear bottleneck assignment problem
- 161 Downloads
The linear bottleneck assignment problem (LBAP), which is a variation of the classical assignment problem (CAP), seeks to minimize the longest completion time rather than the sum of the completion times when a number of jobs are to be assigned to the same number of workers. Several procedures have been proposed in the current literature to convert the LBAP into an equivalent CAP and then apply the Hungarian method to solve it efficiently. However, their applicability is limited because some of the elements in the transformed assignment matrix for the CAP can be too large to be handled by most computer programs. In this paper, we suggest a turnpike approach to alleviate the problem so that the conversion methodology will become more useful in practice. A numerical example is provided to demonstrate the superiority of the new algorithm to the existing ones.
KeywordsAssignment problem Hungarian method Linear bottleneck assignment problem Turnpike algorithm
Unable to display preview. Download preview PDF.
- 8.Burkard RE, Zimmermann U (1977) Weakly admissible transformations. Report No. 77-3, Köln, Germany: Mathematisches Institut, Universität zu KölnGoogle Scholar
- 18.Fulkerson, DR, Glicksberg, I, Gross, O (1953). A production line assignment problem. Research Memorandum RM-1102, Santa Monica, CA: Rand CorporationGoogle Scholar
- 22.Gross, O (1959). The bottleneck assignment problem. Paper P-1630, Santa Monica, CA: Rand CorporationGoogle Scholar
- 35.Trivedi KS (2002) Probability and statistics with reliability, queuing and computer science applications, 2nd edn. Wiley, New YorkGoogle Scholar
- 36.Weiss HJ, Gershon ME (1993) Production and operations management, 2nd edn. Allyn and Bacon, Needham HeightsGoogle Scholar