Exact and approximate solutions for fulfilment metrics in open pipeline order fulfilment systems

Open pipeline order fulfilment systems have emerged in sectors such as the automotive industry that offer a large number of product variants to the marketplace. In an open pipeline a customer can be fulfilled from anywhere in the system–by a stock product, by a product in the distribution system, by allocating a product in production or a product in the plan, or by supplying a product specially built to order (BTO). Here new results are presented to estimate the performance metrics for open pipeline systems. An exact expression is developed based on a Markov analysis to calculate the BTO proportion for any combination of the key system parameters–pipeline length, the variety level and the initial stock level. Approximation schemes are developed to estimate the pipeline and stock fulfilment proportions, the mean lead time and the mean stock level. The approximation schemes provide accurate estimates for a large range of systems. Specific issues that affect the estimation of performance metrics in low variety, open pipeline systems are discussed. The results presented provide generic insights for open pipeline systems design and management and provide a platform for further work in extending the applicability of open pipeline concepts.