An inventory model with truncated exponential replenishment intervals and special sale offer

•An optimal purchase quantity model for a special sale offer is developed.•A closed form solution is derived.•The consecutive replenishment time follows a truncated exponential distribution.•The study provides managerial insights to decision makers in their planning.

In this study, we develop an inventory model with stochastic replenishment intervals and special sale offer from a supplier. The replenishment interval is assumed to obey a truncated exponential distribution and shortage is partially backordered. Our goal in this research is to maximize the total profit of cost savings due to special sale offer from supplier. A closed-form solution of the model and its convexity condition is developed. A numerical example with real world data is provided to illustrate the theory.