Optimal inventory policy under price and time-dependent demand and partial backlogging supported by preservation strategy

The present study outlines an inventory model for non-instantaneous deteriorating items with an investment in preservation technology. The deterioration rate is modelled using a two-parameter Weibull distribution, and customer demand is dependent on both time and selling price. Accordingly, the demand rate is a multiplication of a power time function and an exponential price function. The inventory system permits partial backlogging of demand. Additionally, the supplier extends a trade credit facility to the retailer for the smooth operation of the business. Three cases are analysed based on the credit facility. The primary objective of the study is to ascertain the maximum profit by identifying the optimal values for preservation technology investment, selling price, positive inventory time, and cycle time. An algorithm for profit maximisation is formulated and validated through numerical examples. Subsequently, a sensitivity analysis is conducted, and the study provides valuable managerial insights derived from the findings.