Optimal production stopping and restarting times for an EOQ model with deteriorating items
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Optimal production stopping and restarting times for an EOQ model with deteriorating items H Yan and TCE Cheng The Hong Kong Polytechnic University, Kowloon, Hong Kong A perishable single item production-inventory system is studied in this paper. The objective is to describe a general model in which the production rate, the product demand rate, and the item deterioration rate are all considered as functions of time, and to discuss the optimal production stopping and restarting times which minimise the total relevant cost per unit time. In the general model, demand shortage is allowed, where some of the demand is lost and the rest is backlogged. Popular models, such as the pure inventory system and the zero shortage system, are shown to be special cases of our model. The conditions for a feasible stationary point to be optimal are given. The simplest cases with constant rates of production, demand and deterioration are discussed and shown as illustrative examples. Keywords: EOQ; production; demand; deterioration; shortage
Introduction EOQ inventory models have long been attracting considerable amount of research attention. For the last ®fteen years, researchers in this area have extended investigation into various models with considerations of item shortage, item deterioration, demand patterns, item order cycles, as well as their combinations. For example, Goel1 studied the model with a variable deterioration rate, the rate is represented as a function of the inventory level and shortages are allowed with both partially lost and backlogged items. Sachan2 also discussed the cases of partially lost and backlogged items. Cheng3 extended the results of Smith4 to the case of a constant decaying rate for the deteriorating items. Murdeshwar5 extended the work of Deb and Chaudhuri,6 who studied the inventory replenishment policy for items having demand with linear trend and shortages. Goswami and Chaudhuri7 considered the model for deteriorating items with shortage and a linear trend in demand. However, all this research is limited to the pure inventory replenishment situation. In other words, items are purchased or ordered in batches. Typical questions for such an inventory system are when and how much to order. The decisions on the optimal time and optimal quantity of ordering are based on the minimum total relevant cost per unit time. On the other hand, research on production-inventory models has emphasised various production factors, such as the production size, the set up time, the production learning and forgetting effects, and the issues of machine breakdown, etc. Research ®ndings in this area can be found Correspondence: Professor TCE Cheng, Of®ce of the Vice-President (Research and Postgraduate Studies), The Hong Kong Polytechnic University, Kowloon, Hong Kong.
in an abundance of publications. Cheng8 studied a model with demand-dependent unit production costs and solved the problem using geometric
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