Fuzzy heuristic solution approaches for the warm/cold lot sizing problem

• The warm/cold production process occurs where the production process can be kept warm at some cost if production quantity in a period exceeds a threshold value.
• Real-world lot sizing problems involves a great deal of uncertainty; therefore, it is not realistic to assume such parameters deterministically.
• This study introduces fuzzy versions of three fuzzy heuristics for the warm/cold lot sizing problem.
• Results indicate that the Fuzzy Least Unit Cost heuristic and the Fuzzy Silver-Meal heuristic yield lower total cost rates than the Fuzzy Part Period Balancing heuristic on most of the occasions.

In this paper we introduce fuzzy versions some rule based lot sizing heuristics for the dynamic lot-sizing problem with warm/cold process. In our setting “the demand at each period” and “the warm system threshold” (production/order quantity required for keeping the system warm on to next period) are fuzzy numbers. Similar to the crisp counterpart setting of the problem, horizon length, production capacity at each period, inventory carrying cost and warming cost are the parameters with crisp values. The objective is to find the cost minimizing production scheme throughout the horizon. The rule based fuzzy heuristics we introduce are: “fuzzy silver meal algorithm”, “fuzzy part period algorithm”, and “fuzzy least unit cost algorithm”. We illustrate implementation of proposed heuristics through examples. In a numerical study we present comparison results of heuristics based on various performance criteria.

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