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Dynamic lot sizing with all-units discount and resales

Authors

  • Chung-Lun Li,

    1. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
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  • Jinwen Ou,

    Corresponding author
    1. Department of Administrative Management, Jinan University, Guangzhou 510632, People's Republic of China
    • Department of Administrative Management, Jinan University, Guangzhou 510632, People's Republic of China
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  • Vernon N. Hsu

    1. Department of Decision Sciences and Managerial Economics, Faculty of Business Administration, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
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Abstract

We consider a single-product dynamic lot-sizing model with an all-units quantity discount pricing scheme available to the buyer, where the discount price breakpoints are stationary. To capture the real-life behavior of a typical buyer who often takes advantage of quantity discounts through purchasing in excess of the anticipated demand, our model allows the buyer to resell or dispose of any leftover inventory that he/she does not need. We show that the general problem with an arbitrary number of discount price breakpoints is NP-hard. We then develop a polynomial algorithm for the problem with an O(Tm+3) running time when the number of price breakpoints, m, is fixed, where T is the number of time periods in the planning horizon. We further develop an O(T2) algorithm for the special case with a single price breakpoint. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

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