EPQ for an unreliable production system with endogenous reliability and product deterioration

In this paper, we study an economic production quantity problem for a production line subject to random shift from the in‐control state (with high production rate) to out‐of‐control state (with low production rate). Different from previous research, we model the expected shift time as a controllable variable, based on the fact that, by investment in resources, the reliability of the production line can be improved. In the mathematical model, we consider three possible scenarios: no shift, shift without demand shortage, and shift with demand shortage, which are determined by the values of actual shift time and shifted production rate. Combining the three possible scenarios, the goal is to minimize the expected total cost per unit time by finding the optimal production time, as well as the optimal expected shift time. In addition, we extend the model to deterioration products and study the influence of product deterioration to the optimal decisions. Numerical examples are presented to illustrate the optimal solutions, followed by the sensitive analysis on important parameters. Comparing the optimal solutions under no reliability investment, reliability investment can help companies save more cost. Some other managerial insights are also proposed based on the numerical tests.