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Economic lot sizing problem with inventory dependent demand

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Abstract

We consider an economic lot sizing problem where the demand in a period is a piecewise linear and concave function of the amount of the available inventory after production in that period. We show that the problem is \({{\mathcal {N}}}{{\mathcal {P}}}\)-hard even when the production capacities are time invariant, and propose a polynomial time algorithm to the case where there are no capacity restrictions on production.

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Acknowledgements

The work of this author was supported by the Scientific and National Research Council of Turkey (TÜBİTAK) under Grant No. 119M278.

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  1. Department of Industrial Engineering, Özyeğin University, Çekmeköy, İstanbul, Turkey

    Mehmet Önal & Erinç Albey

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  1. Mehmet Önal
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  2. Erinç Albey
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Correspondence to Mehmet Önal.

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Appendix A. Data generation

Appendix A. Data generation

For each data instance, slope of the first segment is drawn randomly from UNIF(0.6,0.9). Once a segment slope is realized, the slope of the next segment is obtained by subtracting a random number drawn from UNIF(0.03,0.04). Low \(u_t^b\) values are drawn from UNIF(1,10) while high \(u_t^b\) values are generated by drawing from UNIF(10,20). Then, all the segment lengths are generated by drawing from UNIF(1,20).

For each data instance, prices are generated by drawing from UNIF(0,3); unit holding costs from UNIF(0,1); and unit production costs from UNIF(0,1). Low, medium, and high set up costs are generated by drawing from UNIF(250,300), UNIF(350,400), and UNIF(450,500), respectively.

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Önal, M., Albey, E. Economic lot sizing problem with inventory dependent demand. Optim Lett 14, 2087–2106 (2020). https://doi.org/10.1007/s11590-020-01532-z

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