Optimization of integrated preventive maintenance based on infinitesimal perturbation analysis

• A strategy combining preventive maintenance and production control is proposed.
• Gradient estimates with respect to each decision variable are determined via IPA.
• IPA has not been used to find the optimal preventive maintenance period as proposed.
• Gradients based on the sample paths are integrated in a simulation algorithm.
• Transfer and transportation delays are considered explicitly in this model.

This paper considers jointly the production control and preventive maintenance problem in a manufacturing system. This system is composed of a single unreliable machine that produces one or two types of products with constant and different demand, a customer and a buffer between the machine and the customer. Machine failures are time-dependent, i.e. the machine can fail at any time, so a block-type preventive maintenance policy is proposed to increase the system life. This policy is coupled with a hedging point policy which controls the machine production speed. Between each element of the system, constant transportation delays are considered, i.e. a conveyor between the machine and its downstream buffer and a transport between the buffer and the customer. Then, a continuous-flow model is proposed to represent the overall dynamics of the system. This model allows us to take into account explicitly the transportation delays. The main objective of this work is to find the optimal preventive maintenance period by means of infinitesimal perturbation analysis technique as well as the optimal hedging point in order to minimize the expected average cost function. For this, we find the gradient estimators of the cost function from a theoretical sample path study. Then we integrate them in a simulation algorithm to find a numerical estimation of the solution. Simulation results highlight our theoretical results.