Abstract

AN INVENTORY MODEL FOR NON-INSTANTANEOUS DETERIORATING ITEMS WITH TIME DEPENDENT QUADRATIC DEMAND AND COMPLETE BACKLOGGING UNDER TRADE CREDIT POLICY

B. Babangida1 & Y. M. Baraya2

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Abstract In the classical economic order quantity model, it was assumed that the purchaser must pay for the items received immediately. In real practices, the supplier may provide the purchaser a permissible delay of payments so as to settle for the goods supplied. This motivates retailers to order more which in turns lead higher turnover by the supplier. In this paper, an inventory model for non-instantaneous deteriorating items with two-phase demand under trade credit policy and complete backlogging has been considered. The demand rate before deterioration sets in is assumed to be time dependent quadratic function after which it is considered as constant. Shortages are allowed and are completely backlogged. Optimal time with positive inventory, cycle length and order quantity are determined so as to minimise the total variable cost. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions are provided. Three numerical examples are provided to demonstrate the application of the model for each case. Finally, sensitivity analysis of some model parameters on optimal solutions have been carried out and the implications are discussed. In the discussions, suggestions toward minimizing the total variable cost of the inventory system are also given. Keywords: Non-instantaneous deteriorating item, Quadratic demand, Trade credit policy, Complete backlogging.

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