optimizing two multi-echelon inventory systems for perishable products with price and stock dependent demand in supply chain

In this paper, two inventory models with starting shortages and without shortages for perishable products in supply chain are proposed. the demand for perishable products is dependent on price and stock. supply chain is composed of one manufacturer, one distribution center, and one retailer. the objective of these two models is to maximize the average profit per unit time by determining the optimal replenishment cycle, frequency, and quantity. the property of optimal solutions for two cases of two models is discussed to verify the existence of optimal solutions. algorithms for searching optimal solutions are presented. in order to investigate the effect of parameters on optimal solutions and obtain some management insights, computational experiments with sensitivity analyses are carried out. finally, conclusions and future researches are provided.