Optimal inventory dispatching policies for a two-warehouse system with price and freshness-dependent demand

The deterioration rate and selling value of perishable items, such as fruits, milk, vegetables, meat, seafood, and packaged goods, directly impact an organisation's profit. Therefore, to leverage profit, efforts are required to reduce the deterioration rate of these perishable items. However, an excessive amount of freshness-keeping effort may lead to an increase in the selling price, which could result in customer dissatisfaction. This problem has been the subject of investigation by various researchers, who have employed different mathematical models that treat demand as a function of the freshness parameter, along with a constant or variable deterioration rate. However, the freshness parameter and deterioration rate are time-dependent; still, mathematical models that consider both these parameters as functions of time in two-warehouse environments have been developed. Hence, this paper fills this gap by providing mathematical models for two-warehouse inventory systems under First In First Out (FIFO) and Last In First Out (LIFO) dispatching policies. The perishability rate of items is assumed to be Weibull-distributed with respect to time, and demand is a continuous function of the freshness parameter, selling price, and time. Additionally, these mathematical models include parameters such as inflation, price elasticity, and partial backlogging. The primary objective of this study is to maximise profit by optimising the selling price and inventory size. The findings of this study reflect the superiority of the LIFO policy over the FIFO policy under these conditions. Furthermore, the behaviour of these models has been studied through a comprehensive sensitivity analysis, along with an examination of their applicability and managerial implications.