Simultaneous procurement and pricing policy for inventory model with price and time dependent seasonal demand

In real life we can observe that there are so many products whose demand depends upon price and time. Another practical observation in seasonal products is replenish their inventory at the beginning of season is considered. In this paper we considered price & time dependent demand function. A single replenished opportunity at the beginning of the season is considered. Replenished inventory are used for more than one successive seasons and after depletion, at the end of the season order is placed for replenishment. Shortages are considered only for one season. Time dependent partial backlogging is considered. Concavity of the profit function with respect to decision variables is shown. Solution procedure with a numerical example is presented.