Integrating optimal production size and selling price of a production-inventory system with power-time and exponential-price demand

This paper presents and studies a new production-inventory model with constant production rate in which demand depends simultaneously on price and time. Thus, it is assumed that the demand rate is the multiplication of an exponential function of the selling price and a power function of time. This price- and time-dependent demand can be useful for describing the behavior of demand for some products, because it can be better and more easily adjusted to empirical data. To the best of our knowledge, this is the first time that this demand rate has been used in an EPQ system. The aim is to find the optimal production lot size and the optimal selling price that maximize the profit per unit of time. An efficient algorithm to establish the best solution of the problem based on the parameters of the model is developed. This procedure determines whether the production-inventory system is profitable and, in this case, finds the optimal selling price, the optimal inventory cycle, the optimal production lot size and the maximum profit. Some numerical examples are presented to illustrate how the algorithm works. Finally, a sensitivity analysis on the input parameters of the optimal production-inventory policy is presented and managerial insights from these results are discussed.