A distribution-free newsvendor model considering environmental impact and shortages with price-dependent stochastic demand

In today's competitive and volatile market, demand prediction for seasonal items is a challenging task. The variation in demand is so quick that the retailer cannot face the risk of understocking or overstocking. Unsold items need to discarded, which has environmental implications. It is often difficult to calculate the effects of lost sales on a firm's monetary values, and environmental impact is not a concern to most businesses. These issues concerned with the environmental impact and the shortages are considered in this paper. A single-period inventory mathematical model is formulated to maximize expected profit in a stochastic scenario while calculating the optimal price and order quantity. The demand considered in this model is price-dependent, with several emergency backordering options to overcome the shortages. The demand probability distribution is unknown to the newsvendor problem. The only available demand data are the mean and standard deviation. In this model, the distribution-free method is applied. A numerical example is provided to demonstrate the model's applicability. To prove that this model is robust, sensitivity analysis is performed.