Production planning and inventory allocation of a single‐product assemble‐to‐order system with failure‐prone machines

We consider the optimal production and inventory allocation of a single‐product assemble‐to‐order system with multiple demand classes and lost sales. Each component is replenished by a dedicated machine that is subjected to unpredictable breakdowns. We find that the machine state not only influences the production and allocation decisions on its own component but also influences the decisions on the other components. Specifically, the optimal component production policy is a base‐stock policy with the base‐stock level non‐decreasing in the inventory levels of the other components and the states of the other machines. The optimal component allocation policy is a rationing policy with the rationing level non‐increasing in the inventory levels of the other components, the states of the other machines, and its own machine state. We use an exponential distribution to approximate the distribution of the total processing times and propose two heuristic policies to address the production and allocation decisions. The importance of taking machine failures into consideration is revealed through computational experiments.