A Convolution Algorithm for Evaluating Supply Chain Delivery Performance

The effective management of a supply chain requires performance measures that accurately represent the underlying structure of the supply chain. Measures such as delivery performance to the final customer often require summing a set of random variables that capture the stochastic nature of activities across the various stages of the supply chain. The convolution calculus required to evaluate these measures is complex and often leads to intractable results. In this paper we present a discrete convolution algorithm that simplifies this evaluation. The algorithm is demonstrated for a delivery performance measure in a three stage serial supply chain. Numerical results and a supporting error analysis are presented for a set of experiments utilizing reproductive and non-reproductive probability density functions