Jointly control of inventory and its pricing for a deteriorating Item under multiple advance payments and delay in payments with partial backordering

Contrary to the past that inventory decisions and pricing are taken into consideration separately, due to the influence of these decisions on each other and thus profit, researchers have investigated these two issues simultaneously. Sometimes, wholesalers offer incentive financial policies to their customers in order to increase their sale. In this paper, a different combined model of inventory control and the way of its pricing for a deteriorating item with different incentive schemes including totally advance payment and partially advance, partially delayed payment are developed. We adopt a demand function jointly time and price-dependent and a backordering rate waiting time-dependent. Also shortage of allowable inventory considered. In each case, optimum price, replenishment cycle, the time with no shortage are obtained. Sensitivity analysis is performed and represented in several figures and tables. The results show that with increasing deterioration and backordering rates, the total annual profit is reduced.