Pricing and inventory decisions for non-instantaneous deteriorating items with price and promotional effort stochastic demand

This study investigates an inventory model for a non-instantaneous deteriorating item with partial backlogging wherein the demand is stochastic in nature and depends on price and promotional effort whereas the deterioration rate is time proportional.Under these settings,a mathematical model is developed with the objective to maximise the expected profit per unit time by determining the optimal price and the length of replenishment cycle.Some useful theoretical results are established to deduce the optimal replenishment schedule.An effective algorithmic procedure is developed to find the optimal solutions to the proposed model.The applicability of the proposed model is illustrated by numerical example.Sensitivity analysis of the optimal solution with respect to key parameters has been carried out and the implications are discussed.The study indicates that though promotional effort stimulates the market demand,it is beneficial in an economic sense when it applies in a conservative manner.