Optimal control of a stochastic production inventory system with controllable backorder rate and investment to reduce inventory level variability

This paper develops an inventory model that allows the backorder rate and inventory level variability to be control variables to widen the scope of applications of Lin's (2017a) model. We assume that the backorder rate is dependent on the amount of shortages according to a negative exponential function and the supplier could offer a backorder price discount on the stock-out item by negotiation to determine a target value of backorder rate and secure more backorders. Moreover, we investigate the impact of investing in inventory level variability reduction on inventory related costs. The objective of this paper is to simultaneously determine the optimal backorder price discount, inventory level variability, and switch-over control parameters m and M to minimise the long-run total expected cost of the system and improve the competitive edge. Numerical examples are also given to demonstrate the benefits of the model. © 2020 Inderscience Enterprises Ltd.