Joint optimal production control/preventive maintenance policy for imperfect process manufacturing cell

Production, maintenance, and quality are often modeled as separate problems, despite the strong link that exists between these primary components of any manufacturing system. This paper deals with an integrated approach for the joint optimization of production‐inventory control and preventive maintenance policy for a manufacturing cell comprising an imperfect process where the ‘in‐control’ period has a general deterioration distribution. The production‐inventory control policy based on the hedging point policy consists of building and maintaining a security stock of finished products in order to respond to demand and to avoid shortages during restoration actions. Restoration actions are planned when the system switches to the ‘out‐of‐control’ state and starts producing non‐conforming items. The manufacturing cell is also subject to an age‐based preventive maintenance policy in order to reduce the shift rate to the ‘out‐of‐control’ state. The main objective of this paper is to determine the joint optimal policy that minimizes the overall cost, which is comprised of setup, maintenance, inventory holding, and shortage costs, as well as the cost incurred by producing non‐conforming items. A mathematical model is proposed, and the expression of the overall incurred cost is derived and used as a basis for the optimal determination of the joint production‐inventory control and preventive maintenance policy. These issues are illustrated using numerical examples. It is found that performing preventive maintenance will yield reductions in the overall incurred cost. Sensitivity analyses are also carried out in order to illustrate the robustness of the proposed methodology.