Single item lot-sizing problem for a warm/cold process with immediate lost sales

We consider the dynamic lot-sizing problem with finite capacity and possible lost sales for a process that could be kept warm at a unit variable cost for the next period t + 1 only if more than a threshold value Q(t) has been produced and would be cold, otherwise. Production with a cold process incurs a fixed positive setup cost, K-t and setup time, S-t, which may be positive. Setup costs and times for a warm process are negligible. We develop a dynamic programming formulation of the problem, establish theoretical results on the structure of the optimal production plan in the presence of zero and positive setup times with Wagner-Whitin-type cost structures. We also show that the solution to the dynamic lot-sizing problem with lost sales are generated from the full commitment production series improved via lost sales decisions in the presence of a warm/cold process. (C) 2006 Elsevier B.V. All rights reserved.