Analysis of decentralized multi-product pull systems with lost sales

We study a pull-type, flexible, multi-product, and multi-stage production/inventory system with decentralized two-card kanban control policies. Each stage involves a processor and two buffers with finite target levels. Production stages, arranged in series, can process several product types one at a time. Transportation of semi-finished parts from one stage to another is performed in fixed lot sizes. The exact analysis is mathematically intractable even for smaller systems. We present a robust approximation algorithm to model two-card kanban systems with batch transfers under arbitrary complexity. The algorithm uses phase-type modeling to find effective processing times and busy period analysis to identify delays among product types in resource contention. Our algorithm reduces the effort required for estimating performance measures by a considerable margin and resolves the state–space explosion problem of analytical approaches. Using this analytical tool, we present new findings for a better understanding of some tactical and operational issues. We show that flow of material in small procurement sizes smooths flow of information within the system, but also necessitates more frequent shipments between stages, raising the risk of late delivery. Balancing the risk of information delays vis-à-vis shipment delays is critical for the success of two-card kanban systems. Although product variety causes time wasted in setup operations, it also facilitates relatively short production cycles enabling processors to switch from one product type to another more rapidly. The latter point is crucial especially in high-demand environments. Increasing production line size prevents quick response to customer demand, but it may improve system performance if the vendor lead-time is long or subject to high variation. Finally, variability in transportation and processing times causes the most damage if it arises at stages closer to the customer.