Dynamic programming model for multi-stage single-product Kanban-controlled serial production line

The executive concern of this paper is how to control and synchronize the flow of materials in Kanban controlled serial production line so as to build a dynamic material-flow system that successfully meets customer demand Just-In-Time. The proposed approach should yield a consistent integrated control policy with a feasible level of Work-In-Process and a feasible corresponding operational cost. The production line is described as queuing network, and then a Dynamic Programming (DP) algorithm is used to solve the network by decomposing it into several numbers of single-stage sub-production lines. Backward computations of DP are done recursively with synchronization mechanism, in the since that the solution of one sub-production line is used as an input to the previous one. A performance measure is then developed to determine and to compare the values of production parameters. Numerical examples are used to demonstrate the computations of different system parameters, the results are validated by discrete events simulation using ProModel software version 6.0, the performance measure coincided with the results of the model with very small error (0.044). As a result the number of Kanbans that are needed to deliver the batches from upstream stage to the downstream stage is determined in such a way that keeps the stages synchronized with the external customer demand.