A production-inventory model with promotional effort, variable production cost and probabilistic deterioration

Abstract

This article presents an economic production quantity (EPQ) model for deteriorating items involving probabilistic deterioration where the demand is dependent on sales team’s initiatives. Here, we assumed that the production rate is variable and the unit production cost is the function of the production rate. The unit selling price is calculated by a mark-up over the unit production cost. This model aids in minimizing the total inventory cost of the manufacturer by finding the optimal cycle length and the quantity. On this backdrop, a few theorems have been developed and, the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are suggested. Moreover, numerical examples and sensitivity analysis were also carried out. The results reveal that the total cost will be minimized when the deterioration follows uniform distribution and when the initiatives of the sales team equal to one.