Fuzzy heuristic approaches to the warm/cold lot sizing problem

Abstract

We consider the dynamic lot-sizing problem with warm/cold process, which has been introduced by Toy and Berk [3]. The system parameters are: horizon length, demand at each period, production capacity at each period, warm system threshold, setup cost, inventory carrying cost and warming cost. The objective is to find the cost minimizing production scheme throughout the horizon. Under the warm/cold system setting if the production quantity in a given period is at least as much as a pre-specified level (threshold), the process can be kept warm on the next period by incurring warming cost. If, however, the production quantity is below the threshold, the process will have to start next period cold. When the process is warm, the production can start without incurring any setup cost, whereas the production of a cold process requires a cold setup cost. We extend the current literature by incorporating the fuzzy parameters where (i) the demand, and (ii) warm system threshold are fuzzy numbers. We introduce "fuzzy silver meal algorithm", "fuzzy part period algorithm", and "fuzzy least unit cost algorithm" in the existence of warm/cold process setting. Our numerical study consists of comparison of suggested algorithms based of various performance criteria.