Cataloged from PDF version of article.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 Qt has been produced and would
be cold, otherwise. Production with a cold process incurs a fixed positive setup cost, Kt and setup time, St, 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.
2006 Elsevier B.V. All rights reserved
