An Optimal Ordering Policy for a Probabilistic Fixed Lifetime Inventory Model with Continuous Demand Rate

Abstract

This paper deals with the problem of computing optimal ordering policies for the probabilistic fixed lifetime inventory model with continuous demand rate. We proposed a probabilistic fixed lifetime inventory model with continuous demand rate. The necessary condition for minimizing the expected proposed cost model was derived. The condition is also sufficient because the model is convex in S. The optimal ordering policies for this probabilistic fixed lifetime inventory system with continuous demand rate were given. The objective of the study is to examine decisions regarding when to order or not. This was investigated under some conditions. The operating characteristics obtained in this article are very significant because, for practical problems, available mathematically optimal solutions to the fixed lifetime inventory problem cannot be realized due to their computational complexity arising from the fact that exact formulation of the problem requires information on the age distribution of the items in inventory and the corresponding quantity of items of each age. Hence there is a gap between theoretical results and practical requirements for computational results. We have been able to bridge the gap between theoretical results and practical requirements for computational results. We computed the ordering cost, expected holding cost, expected shortage cost and expected outdates cost, and these computations were applied to determine the expected cost for the fixed lifetime inventory system. The expected cost model with Set- up Cost and without Set- up Cost were useful costs for the determination of the optimal ordering policy for this type of inventory system Finally, organization may like to operate under a given aspiration scenario, values of inventory level that satisfy such condition are identified and are used in the cost function to determine optimal operating conditions, this will go a long way to reduce waste and holding cost.