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Unbounded knapsack problem with controllable rates: the case of a random demand for items

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  • K Kogan

    (Bar Ilan University and Holon Academic Institute of Technology)

Abstract

This paper focuses on a dynamic, continuous-time control generalization of the unbounded knapsack problem. This generalization implies that putting items in a knapsack takes time and has a due date. Specifically, the problem is characterized by a limited production horizon and a number of item types. Given an unbounded number of copies of each type of item, the items can be put into a knapsack at a controllable production rate subject to the available capacity. The demand for items is not known until the end of the production horizon. The objective is to collect items of each type in order to minimize shortage and surplus costs with respect to the demand. We prove that this continuous-time problem can be reduced to a number of discrete-time problems. As a result, solvable cases are found and a polynomial-time algorithm is suggested to approximate the optimal solution with any desired precision.

Suggested Citation

  • K Kogan, 2003. "Unbounded knapsack problem with controllable rates: the case of a random demand for items," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(6), pages 594-604, June.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:6:d:10.1057_palgrave.jors.2601554
    DOI: 10.1057/palgrave.jors.2601554
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    References listed on IDEAS

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    1. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    2. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
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