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A branch‐and‐price approach for the stochastic generalized assignment problem

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  • Subhash C. Sarin
  • Hanif D. Sherali
  • Seon Ki Kim

Abstract

In this article, we address a stochastic generalized assignment machine scheduling problem in which the processing times of jobs are assumed to be random variables. We develop a branch‐and‐price (B&P) approach for solving this problem wherein the pricing problem is separable with respect to each machine, and has the structure of a multidimensional knapsack problem. In addition, we explore two other extensions of this method—one that utilizes a dual‐stabilization technique and another that incorporates an advanced‐start procedure to obtain an initial feasible solution. We compare the performance of these methods with that of the branch‐and‐cut (B&C) method within CPLEX. Our results show that all B&P‐based approaches perform better than the B&C method, with the best performance obtained for the B&P procedure that includes both the extensions aforementioned. We also utilize a Monte Carlo method within the B&P scheme, which affords the use of a small subset of scenarios at a time to estimate the “true” optimal objective function value. Our experimental investigation reveals that this approach readily yields solutions lying within 5% of optimality, while providing more than a 10‐fold savings in CPU times in comparison with the best of the other proposed B&P procedures. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 131–143, 2014

Suggested Citation

  • Subhash C. Sarin & Hanif D. Sherali & Seon Ki Kim, 2014. "A branch‐and‐price approach for the stochastic generalized assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(2), pages 131-143, March.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:2:p:131-143
    DOI: 10.1002/nav.21571
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    1. Prabhjot Kaur & Kalpana Dahiya & Vanita Verma, 2021. "Time-cost trade-off analysis of a priority based assignment problem," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 448-482, June.

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