A Study on Two-Warehouse Inventory Systems with Integrated Multi-Purpose Production Unit and Partitioned Rental Warehouse

Abstract

A study of two warehouse inventory systems with a production unit is developed in this article with some constraints which are of practical applicability to optimize the total production cycle and its cost. A production unit evolves in three different states to retain its quality and prolong its lifetime: the state of producing items, the state of reworking the identified defective items, and the state of being idle. It processes the items up to a certain time point. The screening process starts immediately after a product comes out of the production unit. The classified non-defective items are first stored in own warehouse (OW), after filling to its maximum capacity, and the remaining items fill in the first block RW1 of the rental warehouse RW. All identified defective items are stored in the second block RW2 of RW. The holding cost of an item is higher in RW than OW. All defective items are sent to the production unit for re-do processes as a single lot immediately after the stop of the production and re-do items are stored in RW1 to satisfy the demand. The items in the RW1 are of higher priority in satisfying the demands after the stop of the production unit in producing new items as to deduce the total cost. Demand is assumed as both time and advertisement dependent and is encouraged once production starts. The deterioration rate differs in both warehouses. No backlog is entertained. The study is directed to achieve optimum total cycle cost towards the attainment of the optimum production time slot and the entire cycle of the system. We have arrived at explicit expressions for the total cost function of the entire production cycle. An analytic optimization process of the discriminant method is employed in the form of an algorithm to arrive at the optimum total cost. It provides a numerical illustration of a specific environment. The implications of the current research work are as follows. The optimum utility of production units in three different states in arriving at the optimum total cost is extensively studied with respect to deterioration, demand, and production rates. It also examined the influence of fluctuating deterioration, demand, and production parameters in arriving at optimum deterioration cost, holding cost, and total cycle cost, as they have important managerial insights. The effect of rental charges on the optimum total cost is examined as the system is used for multi-purpose storage.