Impact of the delay of subcontracting in a context of integrated maintenance: analytical approach

In this article we treat the problem of the delay of subcontracting and its impact on a system controlled by a policy joining the production and maintenance management. We will study a system made up of a machine M which can break down in a random way, and on which we carry out actions of corrective maintenance of random durations. Indeed, each interval T the machine is subject of actions of preventive maintenance. The system is provider of subcontracting services defined as periodic tasks in each cycle T, during which the machine is allocated to produce for a third party. Our objective is to study analytically this system, and determine the expression of the overcost generated by a delay of subcontracting.