An analysis of retailer’s inventory in a two-echelon centralized supply chain co-ordination under price-sensitive demand

As the industrial environments become more competitive, managing specific inventory levels and coordination between channel members of a companies supply chain is very much crucial. In this paper, we have analyzed a two-echelon supply chain containing a manufacturer and a retailer in which the manufacturer offers a single product to the retailer and the retailer takes the responsibility of managing the inventory of the product. The products deteriorate at the retailer warehouse at a constant deterioration rate. We have generalized our model for two different demand functions faced by the retailer from the customers’ side. The demand functions are (a) a linear function of price (b) an iso-elastic function of price. The shortage is also allowed and partially backlogged with a constant backlogging rate. Total profit of the supply chain under two different demand scenarios is evaluated for a joint centralized coordination. The prime objective of our paper is to compare the total profit under two different demand functions in joint centralized coordination such that the channel member can decide their optimal sales price, inventory scheduling of retailer, ordering lot size to maximize the total profit. A numerical example has been illustrated to validate the theoretical results. Also, sensitivity analysis of some key parameters is carried out which gives some managerial applications. The findings of this paper demonstrate that linear demand would increase the joint profit of a centralized system. This analysis has an important guiding significance for the supply chain coordination of deteriorating items under linear and iso-elastic demand.