A Joint Replenishment Inventory Model with Lost Sales

Abstract

This paper deals with two items joint replenishment inventory problem, in which the demand of each items are constant and deterministic. Inventory replenishment of items is conducted periodically every T time intervals. Among of these replenishments, joint replenishment of both items is possible. It is defined that item i is replenished every ZiT time intervals. Replenishment of items are instantaneous. All of shortages are considered as lost sales. The maximum allowance for lost sales of item i is Si. Mathematical model is formulated in order to determining the basic time cycle T, replenishment multiplier Zi , and maximum lost sales Si in order to minimize the total cost per unit time. A solution methodology is proposed for solve the model and a numerical example is provided for demonstrating the effectiveness of the proposed methodology.