Setting planned leadtimes in customer-order-driven assembly systems

We study an assembly system with a number of parallel multistage processes feeding a multistage final assembly process. Each stage has a stochastic throughput time. We assume that the system is controlled by planned leadtimes at each stage. From these planned leadtimes the start and due times of all stages can be derived. If a job finishes at a particular stage and has to wait before the start of the next job(s), a holding cost proportional to the waiting time is incurred. A penalty cost proportional to the lateness is incurred when the last stage of the final assembly process finishes after its due time. The objective is to determine planned leadtimes for each individual stage, such that the expected cost of a customer order is minimized. We derive the recursive equations for the tardiness and earliness at all stages and an exact expression for the expected cost. We discuss the similarity between these expressions and those for serial inventory systems. Based on this observation and a conjecture related to the generalized Newsvendor equations, we develop an iterative heuristic procedure. Comparison with a numerical optimization method confirms the accuracy of the heuristic. Finally, we discuss an application of the model to a real-life case, showing the added value of a system-wide optimization of planned leadtimes compared to current practice.