Performance modeling of supply chains using queueing networks

Supply chain networks are formed out of complex interactions amongst several companies whose aim is to produce and deliver goods to the customers at the time and place specified by them. Computing the total lead time for customer orders entering such a complex network of companies is an important exercise. In this paper, we present analytical models for evaluating the average lead times of make-to-order supply chains. In particular, we illustrate the use of fork-join queueing networks to compute the mean and variance of the lead time. The existing literature on approximate methods of analysis of fork-join queueing systems assume heavy traffic and require tedious computations. We present two applications of a tractable approximate analytical method for lead time computations in a class of fork-join queueing systems. For the case where the arrivals are deterministic and service times are normally distributed, we present an easy to use approximate method. Specifically, we illustrate the use of the above method in setting service levels in assemble-to-order type supply chains.