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Polynomial cases of the economic lot sizing problem with cost discounts

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  • Archetti, Claudia
  • Bertazzi, Luca
  • Grazia Speranza, M.

Abstract

In this paper we study the economic lot sizing problem with cost discounts. In the economic lot sizing problem a facility faces known demands over a discrete finite horizon. At each period, the ordering cost function and the holding cost function are given and they can be different from period to period. There are no constraints on the quantity ordered in each period and backlogging is not allowed. The objective is to decide when and how much to order so as to minimize the total ordering and holding costs over the finite horizon without any shortages. We study two different cost discount functions. The modified all-unit discount cost function alternates increasing and flat sections, starting with a flat section that indicates a minimum charge for small quantities. While in general the economic lot sizing problem with modified all-unit discount cost function is known to be NP-hard, we assume that the cost functions do not vary from period to period and identify a polynomial case. Then we study the incremental discount cost function which is an increasing piecewise linear function with no flat sections. The efficiency of the solution algorithms follows from properties of the optimal solution. We computationally test the polynomial algorithms against the use of CPLEX.

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  • Archetti, Claudia & Bertazzi, Luca & Grazia Speranza, M., 2014. "Polynomial cases of the economic lot sizing problem with cost discounts," European Journal of Operational Research, Elsevier, vol. 237(2), pages 519-527.
  • Handle: RePEc:eee:ejores:v:237:y:2014:i:2:p:519-527
    DOI: 10.1016/j.ejor.2014.02.044
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    References listed on IDEAS

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    5. Mao Tan & Bin Duan & Yongxin Su, 2018. "Economic batch sizing and scheduling on parallel machines under time-of-use electricity pricing," Operational Research, Springer, vol. 18(1), pages 105-122, April.
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    7. Akbalik, Ayse & Hadj-Alouane, Atidel B. & Sauer, Nathalie & Ghribi, Houcem, 2017. "NP-hard and polynomial cases for the single-item lot sizing problem with batch ordering under capacity reservation contract," European Journal of Operational Research, Elsevier, vol. 257(2), pages 483-493.
    8. Bertazzi, Luca & Bosco, Adamo & Laganà, Demetrio, 2015. "Managing stochastic demand in an Inventory Routing Problem with transportation procurement," Omega, Elsevier, vol. 56(C), pages 112-121.
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    10. Weihong Hu & Zhuoting Yu & Alejandro Toriello & Maged M. Dessouky, 2020. "Decomposition‐based approximation algorithms for the one‐warehouse multi‐retailer problem with concave batch order costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 503-523, October.

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