# AN EOQ MODEL FOR NON-INSTANTANEOUS DETERIORATING ITEM WITH TWO- PHASE DEMAND RATES, TIME-DEPENDENT LINEAR HOLDING COST AND TIME- DEPENDENT PARTIAL BACKLOGGING RATE UNDER TRADE CREDIT POLICY

## Keywords:

time-dependent partial backlogging rate, time-dependent linear holding cost, trade credit policy, time-dependent quadratic demand rate, Non-instantaneous deterioration## Abstract

In this article, an EOQ model for non-instantaneous deteriorating item with two-phase demand rates, time- dependent linear holding cost and time-dependent partial backlogging rate under trade credit policy has been considered. The demand rate

before deterioration sets in is assumed to be time-dependent quadratic after which it is considered as constant. Shortages are allowed and partially backlogged. When shortages occur, some customers may wait for backorders to be fulfilled and others

may opt to buy from other sellers. For most items, such as fashionable goods, electronics, photographic films, seasonal products, automobiles and its spare parts and so on, the length of the waiting time for the next replenishment would determine whether the backlogging will be accepted or not. Hence, the backlogging rate is variable and depends on the waiting time for the next replenishment. The model determined the optimal time with positive inventory, cycle length and order quantity that minimise total variable cost. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions have been established. Some numerical examples have been given to illustrate the theoretical results of the model. Sensitivity analysis of some model parameters on optimal solutions has been carried out and suggestions toward minimising the total variable cost of the inventory system were also given.

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