Research Magazine 2017

Multiechelon Lot Sizing with Intermediate Demands and Production Capacity

Ming Zhao and Minjiao Zhang

Coles Working Paper Series, FALL16-02, November 2016

Overview We study a multiechelon supply chain model where production takes place at the first echelon and the products are either stored as inventory or transported to the next echelon. Demands can exist in the production echelon as well as any transportation echelons. With the presence of stationary production capacity and general cost functions, our model integrates production, inventory and transportation decisions, and generalizes existing literature on many multi-echelon lot-sizing models, most of which allow demands at the end echelon only. We prove that the multi-echelon lot-sizing problem is NP-hard. For uncapacitated cases, we propose an algorithm to solve the multi-echelon lot-sizing problem with general concave costs. With fixed-charge costs, an innovative algorithm is developed, which outperforms known algorithms for different variants of the multi-echelon lot-sizing problem and gives a tight, compact extended formulation with much fewer variables and constraints. For cases with stationary production capacity, we propose efficient dynamic programming based algorithms to solve the problem with general concave costs as well as the fixed-charge transportation costs without speculative motives. More importantly, our algorithms improve the computational complexities of many lot-sizing models with demand occurring at end echelon only, which are the special cases of our multi-echelon lot-sizing model.

24 | Coles Working Paper

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