An application of bi-level newsboy problem in two substitutable items under capital cost

A single period newsboy type inventory problem for two substitutable deteriorating items is studied with a resource constraint. In this system, a wholesaler and several retailers with their probabilistic demands and random lot sizes are considered. 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 and later on, sells the rest on push-sale basis if a surplus exists but gets the sale proceed for this amount at the end of the time period for which an interest is charged and paid by the wholesaler. Following newsboy system, retailers also sell a portion of their stocks instantaneously and the rest amount, if it remains, also is instantaneously sold towards the end of the time period T. The deterioration of the left-over amount after the first sale of the retailers is considered for the time period T. As the items are substitutable, several cases of their mutual uses are considered as subsystem cases. 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. It is solved through Genetic Algorithm. Taking wholesaler and retailers to be from different management houses, a multi-objective model has been developed, the expected profit functions are maximized and compromise optimum solutions are obtained via Multi-objective Genetic Algorithm based on the dominant criteria for each member of the system. Finally, numerical results have been presented for illustration.