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The Multi-Handler Knapsack Problem under Uncertainty

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  • Perboli, Guido
  • Tadei, Roberto
  • Gobbato, Luca

Abstract

The Multi-Handler Knapsack Problem under Uncertainty is a new stochastic knapsack problem where, given a set of items, characterized by volume and random profit, and a set of potential handlers, we want to find a subset of items which maximizes the expected total profit. The item profit is given by the sum of a deterministic profit plus a stochastic profit due to the random handling costs of the handlers. On the contrary of other stochastic problems in the literature, the probability distribution of the stochastic profit is unknown. By using the asymptotic theory of extreme values, a deterministic approximation for the stochastic problem is derived. The accuracy of such a deterministic approximation is tested against the two-stage with fixed recourse formulation of the problem. Very promising results are obtained on a large set of instances in negligible computing time.

Suggested Citation

  • Perboli, Guido & Tadei, Roberto & Gobbato, Luca, 2014. "The Multi-Handler Knapsack Problem under Uncertainty," European Journal of Operational Research, Elsevier, vol. 236(3), pages 1000-1007.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:3:p:1000-1007
    DOI: 10.1016/j.ejor.2013.11.040
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    References listed on IDEAS

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    Cited by:

    1. Diaz, Juan Esteban & Handl, Julia & Xu, Dong-Ling, 2018. "Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system," European Journal of Operational Research, Elsevier, vol. 266(3), pages 976-989.
    2. Mina Roohnavazfar & Daniele Manerba & Lohic Fotio Tiotsop & Seyed Hamid Reza Pasandideh & Roberto Tadei, 2021. "Stochastic single machine scheduling problem as a multi-stage dynamic random decision process," Computational Management Science, Springer, vol. 18(3), pages 267-297, July.
    3. Guido Perboli & Marco Ghirardi & Luca Gobbato & Francesca Perfetti, 2015. "Flights and Their Economic Impact on the Airport Catchment Area: An Application to the Italian Tourist Market," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1109-1133, March.
    4. Crainic, Teodor Gabriel & Perboli, Guido & Rosano, Mariangela, 2018. "Simulation of intermodal freight transportation systems: a taxonomy," European Journal of Operational Research, Elsevier, vol. 270(2), pages 401-418.
    5. Manerba, Daniele & Mansini, Renata & Perboli, Guido, 2018. "The Capacitated Supplier Selection problem with Total Quantity Discount policy and Activation Costs under uncertainty," International Journal of Production Economics, Elsevier, vol. 198(C), pages 119-132.
    6. Baldi, Mauro Maria & Manerba, Daniele & Perboli, Guido & Tadei, Roberto, 2019. "A Generalized Bin Packing Problem for parcel delivery in last-mile logistics," European Journal of Operational Research, Elsevier, vol. 274(3), pages 990-999.
    7. Bazargan, Amirhossein & Karray, Salma & Zolfaghari, Saeed, 2018. "‘Buy n times, get one free’ loyalty cards: Are they profitable for competing firms? A game theoretic analysis," European Journal of Operational Research, Elsevier, vol. 265(2), pages 621-630.
    8. Roohnavazfar, Mina & Manerba, Daniele & De Martin, Juan Carlos & Tadei, Roberto, 2019. "Optimal paths in multi-stage stochastic decision networks," Operations Research Perspectives, Elsevier, vol. 6(C).

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