An inventory-dependent demand model with deterioration, all-units discount, and return

Abstract

In this paper, we propose an inventory model with inventory-dependent demand, deterioration, all-units discount and return. Conditions considered in the model are reflected in the real life when a retailer deal with products with deterministic demand having constant deterioration rate. Also, occasionally retailer faces offer from the supplier to buy more products with all-units discount and on the other occasion can return some products to the supplier at some costs. We develop the model that will determine the optimal return time and optimal order quantity that minimize the total cost. The total cost consists of purchasing cost, ordering cost, holding cost, shortage cost and the return cost. We also assume that all shortages are backordered and one tenth of the order quantity are returned to the supplier. We provide some numerical examples to give clearer understanding of our model and find that as the deterioration rate and demand increase, the optimal return time decreases making the optimal order quantity and the total cost increase. Sensitivity analysis is also conducted to analyse the effect of changes in parameter values to the optimal return time, optimal order quantity and the total cost. We consider changes in deterioration rate, inventory-dependent demand rate, return cost and time between replenishment. It is found that changes in return cost do not significantly change the optimal return time, the optimal order quantity and the total cost, compared with changes in deterioration rate, inventory-dependent demand rate and time between replenishment.