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Exact Algorithms for Lot-Sizing Problems with Multiple Capacities, Piecewise Concave Production Costs, and Subcontracting

Kartik Kulkarni (kartikrf***at***vt.edu)
Manish Bansal (bansal***at***vt.edu)

Abstract: In this paper, we introduce a new generalization of the classical capacitated lot-sizing problem with concave production, holding, and subcontracting costs, denoted by CLSP-S, in which the total production capacity in each time period is the summation of binary multiples of n different capacities. We refer to this problem as multi-capacitated lot-sizing problem (with subcontracting), and denote it by MCLS-(S). We present a dynamic programming approach to optimally solve the MCLS and MCLS-S, for a given n, in polynomial time. Note that for n = 1, the MCLS-S reduces to the CLSP-S and therefore, our algorithm generalizes the algorithm of Atamturk and Hochbaum [Management Science 47(8):1081-1100, 2001] for CLSP-S. We also develop another dynamic programming algorithm for the MCLS-S with piecewise concave production costs and no capacity constraint, i.e. n = 0, denoted by LS-PC-S. Furthermore, we perform computational experiments to evaluate the efficiency of our algorithms and their parallel computing implementations for solving instances of MCLS and LS-PC, in comparison to CPLEX 12.7 and the only known algorithm for LS-PC-S by Koca, Yaman, and Akturk [INFORMS J. on Computing 26(4):767-779, 2014]. The results of these experiments show that our algorithms are computationally efficient and their solution times are stable.

Keywords: multi-capacitated lot-sizing, piecewise concave production cost, dynamic programming, concave subcontracting costs, production planning

Category 1: Integer Programming (0-1 Programming )

Category 2: Applications -- OR and Management Sciences (Production and Logistics )

Category 3: Other Topics (Dynamic Programming )

Citation: Report#07122019, Virginia Tech, July 2019

Download: [PDF]

Entry Submitted: 07/17/2019
Entry Accepted: 07/17/2019
Entry Last Modified: 07/19/2019

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