Coordinating replenishment and marketing policies for non-instantaneous deteriorating items with imprecise deterioration free time and general deterioration and holding cost rates

In this paper an inventory system for non-instantaneous deteriorating items with imprecise deterioration free time is developed. We adopt a price and advertisement frequency dependent demand function, and in order to reach a general framework, arbitrary functions of deterioration and holding cost rates are hired. The major objective is to determine the optimal selling price, the optimal replenishment cycle and the optimal frequency of advertisement such that, the total profit is maximised. In order to determine the optimal solution several theoretical results are derived which indicate existence and uniqueness of the optimal solution. Thereafter, based on these theoretical results an iterative solution is developed. Finally, numerical examples are provided to demonstrate solution procedure, then sensitivity analysis is performed, it is shown that optimal policy under uncertain environment and crisp environment are identical and finally some managerial insights are proposed.