FPA method for optimal production planning under availability/degradation machine and subcontracting constraint

This work treats an industrial problematic of a manufacturing system M-1 subject to random failure and that satisfies a random demand under required service level. To ensure the satisfaction of the demand, it calls up on a second manufacturing system M-2 that is a subcontractor and has a stochastic service level. This paper aims to determine an optimal production plan taking into account the degradation of the manufacturing system following its production rate and its availability. The unavailability of the machine M-1 is due to the non-negligible preventive and corrective maintenance actions duration. To consider a realistic case of the subcontractor, we consider that is not able to respond to the variation of the demand, and then it assumed that the manufacturer can order a minimum fixed quantity. We then derive an optimal production plan taking into account the degradation of the machine and simultaneously minimising: inventory, degradation and production cost. An algorithm based on finite perturbation analysis is proposed to determine the optimal production plan and the sensitivity study of the availability is presented.