An Optimal Policy for the Capacitated Lot Sizing Problem with financing of the Working Capital Requirement

We study a capacitated version of the classical lot-sizing problem that incorporates financial aspect to the operational decisions. Namely, we consider a case in which the manufacturer does not have enough financing capacity to cover the expenses of the operations and must use bank loans to finance its operations before receiving payment from its customers. We propose a mathematical model for this problem and exhibit a non speculative assumption that extends the Wagner-Whitin cost structure to this class of problem. We show that when this assumption is satisfied, the problem reduces to finding a shortest path in an acyclic graph, which implies that it can be solved using a dynamic programming approach. A short numerical study also show that adding financing considerations to a capacitated lot-sizing problem may modify the production sequence of the optimal policy. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.