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The objective of this study is to develop a deterministic inventory model with price breaks, pricing and partial backordering when the units in inventory are subject to deterioration with respect to time. Weibull distributed deteriorating units are considered. Most of the researches on deteriorating items consider deterioration to be a complete loss. Here, the salvage value is associated with the deteriorated units. The demand rate is a decreasing function of selling price. The decision variables maximize the profit. The results of this study are relevant to retailers of deteriorating items in a competitive environment. A numerical example is given to validate the mathematical model developed.
The researchers define deterioration as decay, damage, spoilage, evaporation, obsolescence, pilferage, or loss of utility of a commodity. Vegetables and fruits, radioactive chemicals, fashion goods, medicines are a few examples to list. In this paper, a mathematical model has been developed to determine the replenishment time and the selling price of the units when on-hand inventory depletes due to demand and Weibull rate of deterioration. The salvage value is associated with these deteriorated units. The purchase cost of units is assumed to have quantity discounts, and demand is deterministic and decreasing function of selling price. The lead time is zero. The partial backordering is allowed. The effect of partial backordering is studied in the model formulation.
The inventory model with partial backordering for non-deteriorating items has been studied by Rosenberg (1979), Kalro and Gohil (1982), and Wee (1989). Ghare and Schrader (1963) derived an Economic Order Quantity (EOQ) model when units in inventory deteriorate at a constant rate. Covert and Philip (1973) formulated an EOQ model for items which deteriorate following the Weibull distribution. Related articles are by Philip (1974), Shah (1976), Aggarwal and Jaggi (1989), Dave (1979), etc. Elsayed and Teresi (1983), Raafat et al. (1991) and Wee (1993) assumed finite replenishment rate (see review articles by Raafat, 1991; Shah and Shah, 2000; and Goyal and Giri, 2001). |
