In this paper we consider the capacitated lot-sizing problem (CLSP) with linear costs. It is known that this problem is NP-hard, but there exist special cases that can be solved in polynomial time. We derive a backward algorithm, based on the forward algorithm by Chen et al. (1994), to solve the general CLSP. By adapting this backward algorithm, we arrive at a new O(T^2) algorithm for the CLSP with non-increasing setup cost, general holding cost, non-increasing production cost and non-decreasing capacities over time. Numerical tests show the superior performance of our algorithm compared to the algorithm proposed by Chung and Lin (1988). We also analyze why this is the case.

capacitated lot-sizing problem, inventory, production
Production, Pricing, and Market Structure; Size Distribution of Firms (jel L11), Business Administration and Business Economics; Marketing; Accounting (jel M), Production Management (jel M11), Transportation Systems (jel R4)
ERIM Report Series Research in Management
Erasmus Research Institute of Management

van den Heuvel, W, & Wagelmans, A.P.M. (2003). A Geometric Algorithm to solve the NI/G/NI/ND Capacitated Lot-Sizing Problem in O(T^2) Time (No. ERS-2003-066-LIS). ERIM Report Series Research in Management. Retrieved from