Periodic inventory management when demand stochastically depends on shelf-stock

Marketing researches reveal that displayed inventory and allocated shelf space affect the demand of some retail items. We study periodic inventory policy when demand is uncertain and its probability distribution function depends on inventory level and period length. Profit function including sale revenue, holding, shortage, and ordering costs is presented. To capture real world situation we propose natural properties for demand probability distribution. Considering those properties well fitted demand distributions are presented. Finally optimal policy is explored via numerical examples. Numerical study reveals that optimal value of decision variables is not monotonic with respect to demand sensitivity to the inventory.