An integrated model of EOQ and newsboy problem for substitutable items with space constraints

Abstract

This paper develops multi-items Economic Order Quantity (EOQ) inventory models for a wholesaler and several retailers. A single period newsboy type inventory problem for two substitutable items is studied with a space constraint. The demands for wholesaler and retailers are random and stock dependent respectively. To make it more realistic, it is assumed that the wholesaler sells a certain portion of the stock instantaneously to the retailers as per their initial demands. For wholesaler, if items are not completely exhausted, then these are stored and sold instantaneously at a salvage price which are lower than normal selling price. Again, if one item is exhausted but system is surplus, then under co-operation the exhausted item is substitute by the other item and excess item is sold by using salvage price. As the items are substitutable, several mutual cases between wholesaler and retailers are considered as subsystem. Retailers sell their stocks with stock dependent demands and shortages are allowed. Assuming that wholesaler and retailers under a single management, an integrated model is formulated to maximize a single objective profit function with the space constraint. A numerical results have been presented for illustration. Finally, it is solved through LINGO technique.