A piecewise nonlinear optimization for a production-inventory model under maintenance, variable setup costs, and trade credits

Abstract

This study investigates a production-inventory model considering system maintenance, variable setup costs, and trade credits. In production systems, manufacturers usually carry out system maintenance when systems are in an out-of-control state. We also consider setup costs because these costs may decrease over time, for example, when manufacturers effectively improve production efficiency because of the effect of the learning curve. The model considers trade credits because suppliers commonly provide credit periods to manufacturers. This study determines the optimal replenishment frequencies that minimize total costs. We provide lemmas for optimality, develop a piecewise nonlinear optimization algorithm to solve the problems described, and verify the model using a practical case in the automotive parts industry. Based on numerical experiments, we discuss how system parameters affect the decision behaviors of manufacturers. The results of this study can serve as references for business managers and administrators.