Constrained Probabilistic Inventory with Varying Rent and Discount of Expiration Cusp for Crisp and Fuzzy: Power Lomax Distribution

Document Type : Original Article

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Department of Mathematics, Faculty of science, Tanta University, Tanta, Egypt

Abstract

Two models of the multi-item probabilistic continuous review inventory model of expiration cusp with varying rent cost and all units discount are deduced. The restricted mathematical model is solved utilising the Lagrange multiplier approach. Here, the shortage is permissible, which is a combination of the backorder cost and lost sales cost. Also, the holding cost is a mixture of insurance cost and rent cost. The expected total cost is composed of the expected purchase cost, the expected ordering cost, the expected mixture holding cost, the expected mixture shortage cost, and the expected deterioration cost. The distribution of lead time demand depends on the distribution of the demand that follows the Power Lomax distribution which is studied for unimodal case and decreasing case. The first model assumes that the total cost components are crisp values, whereas the second model assumes that the costs are trapezoidal fuzzy numbers. For these proposed models, we found the optimal order quantity and the optimal reorder point which minimises the expected total cost. To demonstrate the suggested two models in two cases a numerical example was added.

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