Solution of Interval-valued Manufacturing Inventory Models With Shortages

Abstract

Abstract —A manufacturing inventory model with shortages withcarrying cost, shortage cost, setup cost and demand quantity asimprecise numbers, instead of real numbers, namely interval numberis considered here. First, a brief survey of the existing works oncomparing and ranking any two interval numbers on the real lineis presented. A common algorithm for the optimum productionquantity (Economic lot-size) per cycle of a single product (so asto minimize the total average cost) is developed which works wellon interval number optimization under consideration. Finally, thedesigned algorithm is illustrated with numerical example. Keywords —EOQ, Inventory, Interval Number, Demand, Produc-tion, Simulation I. I NTRODUCTION R ECENTLY much attention has been focused on EOQmodels with fuzzy carrying cost, fuzzy shortage cost,fuzzy setup cost, fuzzy demand etc; this means that elementsof carrying cost, shortage cost, setup costs and demand arefuzzy numbers [8], [14], [19]. However EOQ model has playedan important role in the field of control theory, when weapply the EOQ model to some practical problems whichwe encounter in real situation, it is difficult to know thevalues of carrying cost, shortage cost, setup cost and demandquantity exactly; we can only know the values approximately.Generally, uncertainties are considered as randomness andare handled by probability theory in conventional inventorymodels. Usually, researchers considered parameters either asconstant or dependent on time or probabilistic in nature. Butwe cannot estimate the probability distribution due to lackof historical data. The research on fuzzy EOQ models hasbeen developed by Park [11], Vujosevic [13], Kacprzyk andStaniewski [9], Mahato and Goswami [5], [6], Lin and Yao[3] has explored EOQ model with fuzzy lead time, fuzzydemand and fuzzy cost coefficients. However, in reality, itis not always easy to specify the membership function orprobability distribution in an inexact environment. Since, theoptimal total average cost of the model should be interval-valued no studies have yet been attempted for interval valuedmanufacturing inventory models with shortages, which willbe examined in this paper. We choose the interval numbersinstead of the fuzzy numbers due to the following facts.