Ordering and pricing policies for random discount offerings and permissible shortages

This study develops the ordering and pricing policies of a retailer, confronted with a price-dependent demand and a vendor offering a discount on the wholesale/regular price during sales sub-periods, which are repeated randomly and last for a random amount of time. The inventory level forms a regenerative stochastic process, with regeneration points at the start of the discount sub-periods. The objective is to maximise the long run expected profit per unit time, expressed as a function of the order quantity, reorder level and retail price for regular and discount sub-periods.