The newsboy problem with inventory financing and multi-phases clearance prices

There are many extensions about newsboy problem in recent researches. They have been applied for the newsboy-type products like seasonal products, fashion products and holiday products etc. But only one salvage price for the excess inventory is considered in most literatures, one extension that adopts a multi-phases clearance prices policy has approved better profit for the retailer. On the other hand, not until recent years has the retailer´s limited initial cash been taken into consideration with the inventory financing. Real world settings, especially the fashion products and holiday products, often involve a combined condition of adopting a multi-phases clearance prices policy and financing the initial purchasing plan. In this paper, we formulate and solve the Newsboy problem with these two conditions and show how a retailer decides the purchase order quantity in order to maximize his profit.