This study examines the effect of monetary inflation for a two-warehouse single-product inventory system, in which items are stored in a limited capacity Own Warehouse (OW) and an unlimited capacity Rental Warehouse (RW). Demand for an item is considered stock dependent. Items may deteriorate at a different constant rate in both warehouses. Shortages are allowed in the stock-out period and are partially backlogged and satisfied in the next replenishment point. The supplier permits flexible payment options for the retailer to pay the amount in three equal payments at different time points. The retailers’ preferred payment option is as follows: the first payment is prior to the replenishment point with some discount; the second payment is one-third of the total purchasing cost, which is paid at the time of the replenishment epoch; and the third payment is after the replenishment point and before the start of the next cycle, with some penalty. The influence of inflation on the cost calculation is considered, and an analytic expression for optimal minimal cost is explicitly derived from this. We performed arrived sensitivity analysis to discern the effects of the inflation and backlogging rates, as well as the effects of the discount rate on purchasing cost, and the effects of penalties upon the late payment of purchasing costs in optimizing the total cost.

This model considers a two-warehouse inventory system of deteriorated items with ramp-type demand and a constant rate of deterioration. It is maintained a rental warehouse ($RW$) of infinite capacity to load the excess items of replenished goods after filling the items of finite capacity in the own warehouse ($OW$). Retailers are encouraged to opt for the prepayment option of paying their purchase cost in equal installments prior to the delivery of the ordered items with a considerable discount, which will ensure the purchase guarantee of their orders. The slotted backlog interval of the stock out period is handled in two different ways to retain the customers and ease their impatience. Customers in the first slot of the stock out period are satisfied by the emergency purchases from local suppliers with high purchasing costs to avoid losing customers. Customers in the next slot are satisfied immediately after the next replenishment point. Essential measures of the system are derived: optimal ordering quantities from both regular and local suppliers; replenishment cycle length; and a partitioned backlog interval. A numerical example is given along with the optimal solutions for a particular environment with sensitive analysis in order to validate the model’s efficacy.

Introduction: A two-warehouse deterministic inventory system for purchases of short-expiry items with low purchasing costs is modelled. The total cost of the replenishment cycle is arrived at by implementing multiple just-in-time (JIT) purchases for the slotted backlogged customers. It avoids the loss of impatient customers who are virtually waiting for a long time.Methods: The inventory system consists of an own warehouse (OW) with finite capacity and an integral rental warehouse (RW) with unlimited capacity. Handlingand selling items with short expiry is a challenging task in revenue generation in commercial inventory management. Two categories of identical items are purchased: Category 1 consists of items whose expiry date falls within the replenishment cycle period, while Category 2 includes items with longer expiry dates. Unlike the traditional assumption in the literature, the items in Category 1 are purchased for a low price and stored in RW. Items in Category 2 are stored in OW. Due to short expiry of items, demands are first satisfied from the RW. The items in the RW are emptied before the expiry date of the items, due to expiry date-dependent deterioration and constant demand. At the same time, the items in the OW are decreasing due to exponential demand and constant deterioration. All customers are backlogged during the stock-out period and slotted into three intervals. The finite number of JIT purchases is employed to satisfy the backlogged slotted demands that occur before the last slot.Results and Discussion: We optimize the total cost of the replenishment cycle, RW utility, and total items purchased. The model is illustrated with an appropriate numerical example, and extensive sensitivity analysis is conducted on the system’s performance.

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 $\left({RW}_1\right)$ of the rental warehouse $\left(RW\right)$. All identified defective items are stored in the second block $\left({RW}_2\right)$ 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 ${RW}_1$ to satisfy the demand. The items in the ${RW}_1$ 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.