Simultaneous optimization of Production, Maintenance, and Quality in a Multi-Product System under Demand Scenarios

Abstract

This study addresses the integrated optimization of production, preventive maintenance, inspection, and quality control decisions in a multi-period and multi-product manufacturing system subject to two distinct types of stochastic failures. Type I failure represents a shift from an in-control to an out-of-control state, leading to the production of nonconforming items, which can only be identified through inspection. Type II failure is a complete system breakdown that halts production and requires corrective maintenance. The proposed model incorporates multiple levels of preventive maintenance, each associated with different costs, durations, and age-reduction effects on the production system. To reflect real-world market variability, three demand scenarios are considered, representing high, medium, and low demand levels with different associated lost-order costs. The objective is to maximize the expected total profit by jointly determining production quantities, inspection schedules, preventive maintenance levels, and inventory and sales decisions. The problem is formulated as a mixed-integer nonlinear programming model. Due to its complexity, a step-by-step solution procedure and a genetic algorithm are developed and compared with exact solutions obtained via GAMS for smaller instances. Computational results indicate that increasing the number of inspections up to a certain threshold improves profitability by reducing nonconforming output and failure-related losses, while the optimal preventive maintenance level depends on the interaction between maintenance costs, production requirements, and demand conditions. The findings provide practical insights for managers in knowledge-intensive and high-mix manufacturing environments seeking to balance equipment reliability, product quality, and customer service under uncertain demand.