The International Journal of Advanced Manufacturing Technology

, Volume 71, Issue 5, pp 1059-1068

First online:

A turnpike approach to solving the linear bottleneck assignment problem

  • Ching-Chung KuoAffiliated withDepartment of Management, College of Business, University of North Texas Email author 
  • , Gillian NichollsAffiliated withDepartment of Industrial & Systems Engineering & Engineering Management, College of Engineering, The University of Alabama in Huntsville

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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.


Assignment problem Hungarian method Linear bottleneck assignment problem Turnpike algorithm