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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. François Vanderbeck, 2000. "On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm," Operations Research, INFORMS, vol. 48(1), pages 111-128, February.
    2. Robert M. Nauss, 2003. "Solving the Generalized Assignment Problem: An Optimizing and Heuristic Approach," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 249-266, August.
    3. Brian T. Denton & Andrew J. Miller & Hari J. Balasubramanian & Todd R. Huschka, 2010. "Optimal Allocation of Surgery Blocks to Operating Rooms Under Uncertainty," Operations Research, INFORMS, vol. 58(4-part-1), pages 802-816, August.
    4. Vanderbeck, F. & Wolsey, L. A., 1996. "An exact algorithm for IP column generation," LIDAM Reprints CORE 1242, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Martin Savelsbergh, 1997. "A Branch-and-Price Algorithm for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 45(6), pages 831-841, December.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    7. Maria Albareda-Sambola & Elena Fernández, 2000. "The stochastic generalised assignment problem with Bernoulli demands," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 165-190, December.
    8. Sakine Batun & Brian T. Denton & Todd R. Huschka & Andrew J. Schaefer, 2011. "Operating Room Pooling and Parallel Surgery Processing Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 220-237, May.
    9. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    10. repec:dgr:rugsom:02a11 is not listed on IDEAS
    11. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    12. Pisinger, David, 1995. "An expanding-core algorithm for the exact 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 87(1), pages 175-187, November.
    13. Albareda-Sambola, Maria & Vlerk, Maarten H. van der & Fernandez, Elena, 2002. "Exact solutions to a class of stochastic generalized assignment problems," Research Report 02A11, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    14. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    15. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    16. Pisinger, David, 1995. "A minimal algorithm for the multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 394-410, June.
    17. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
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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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