An integrated imperfect production system with advertisement dependent demand using branch and bound technique

This paper develops an integrated imperfect production-inventory system consisting of a retailer and a manufacturer who produces breakable items. As breakable items are very sensitive to transport, in this paper, to stimulate the retailer, the manufacturer offers (1) free transportation subject to the condition that the retailer must have to order a minimum replenishment quantity specified by the manufacturer and (2) a credit period depending on the replenishment quantity. Moreover, malfunctioning of the production system increases due to several kinds of problem and consequently it produces a mixture of perfect and imperfect quality items. So, to maintain the reliability of the production system, development cost has been incorporated. Also to aware the customer about the reliability of the production system, the manufacturer has paid attention to give a constant amount of advertisement regularly during his/her production period. Henceforth, the advertisement dependent demand has been considered here. Under such circumstances, an integrated profit function has been developed and solved by branch and bound technique to obtain the optimum values of the system. From numerical studies, it is revealed that in case of incorporation of the advertisement, the retailer’s average profit, the manufacturer’s average profit and the average integrated profit are higher than that in the case without advertisement.