When implementing the kanban method in non-serial production lines, an interesting prioritization problem arises. Often a single server station will be linked withMdifferent downstream stations viaMseparate kanban loops. Then the K-priority problem may be described as determining which kanban card should be processed next, given that empty cards are waiting in more than one loop. The objective in prioritizing the kanbans is to reduce back order or shortage costs and inventory costs at the downstream stations. Utilizing the theory of Markovian decision process and dynamic programming concepts, a solution to the K-priority problem is developed. This solution is labelled the K-rule, and was found to outperform the first-come-first-served and longest queue rules, plus a cost inclusive heuristic rule, in experimental tests,