Capacitated Dynamic Lot Sizing with Capacity Acquisition

One of the fundamental problems in operations management is to determine the optimal investment in capacity. Capacity investment consumes resources and the decision is often irreversible. Moreover, the available capacity level affects the action space for production and inventory planning decisions directly. In this paper, we address the joint capacitated lot sizing and capacity acquisition problem. The firm can produce goods in each of the finite periods into which the production season is partitioned. Fixed as well as variable production costs are incurred for each production batch, along with inventory carrying costs. The production per period limited by a capacity restriction. The underlying capacity must be purchased up front for the upcoming season and remains constant over the entire season. We assume that the capacity acquisition cost is smooth and convex. For this situation, we develop a model which combines the complexity of time-varying demand and cost functions and that of scale economies arising from dynamic lot-sizing costs with the purchase cost of capacity. We propose a heuristic algorithm that runs in polynomial time to determine a good capacity level and corresponding lot sizing plan simultaneously. Numerical experiements show that our method is a good trade-off between solution quality and running time. Keyword: supply chain management, lot sizing, capacity, approximation, heuristics Please reference this paper as: Hongyan Li, Joern Meissner. Capacitated Dynamic Lot Sizing with Capacity Acquisition. Working Paper (available at http://www.meiss.com), Lancaster University Management School, 2009. BibTEX and plain text references are available for download here: http://www.meiss.com/en/publications/lot-sizing-capacity-acquisition.html