J Intell Manuf DOI 10.1007/s10845-009-0336-0 Dynamic programming model for multi-stage single-product Kanban-controlled serial production line Mohammad D. Al-Tahat · Doraid Dalalah · Mahmoud A. Barghash Received: 14 October 2008 / Accepted: 7 October 2009 © Springer Science+Business Media, LLC 2009 Abstract The executive concern of this paper is how to control and synchronize the flow of materials in Kanban con- trolled serial production line so as to build a dynamic mate- rial-flow system that successfully meets customer demand Just-In-Time. The proposed approach should yield a consis- tent 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 sin- gle-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 parame- ters, the results are validated by discrete events simulation using ProModel software version 6.0, the performance mea- sure 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. M. D. Al-Tahat (B ) · M. A. Barghash Industrial Engineering Department, University of Jordan, Amman 11942, Jordan e-mail: altahat@ju.edu.jo M. A. Barghash e-mail: mbarghash@ju.edu.jo D. Dalalah Industrial Engineering Department, Jordan University of Science and Technology, P.O. Box: 3030, Irbid 22110, Jordan e-mail: doraid@just.edu.jo Keywords Kanban · Pull production · Manufacturing flow control · Dynamic programming · Practice of OR Introduction Kanban has been invented by Dr. Taichi Ohno, manager of Toyota Motors, to improve production control. The principal role of Kanban is to bring the material Just-In-Time (JIT) to the manufacturing workstations, and to spread information, through the use of cards to the earlier workstations regarding what and how much to produce. The idea of Kanban is origi- nated from US supermarkets (Ohno 1988; Huang and Kusiak 1996). Kanban is just one part of an overall pull production philosophy that has be adopted to reduce inventory, reduce production cycle time, reduce lead times, increase productiv- ity, increase the speed of information exchange, and improve customer satisfaction (Huang and Kusiak 1996). As a pull production control strategy Kanban is applied in production lines where a workstation is allowed to pro- duce only when it receives a production order from down- stream station, thus only the last workstation in the line has a production schedule, i.e. the production of the cur- rent workstation depends on the demand of the subsequent ones. Production plan is given only to the final workstation. When WIP are withdrawn from the previous workstations, a chain of communication is established with each of the relevant preceding workstations (Huang and Kusiak 1996), and every workstation directly knows how much and when to produce the required products. The number of Kanbans represents the inventory level embed in the production line. Hence increasing (decreasing) the number of Kanbans equiv- alent to increasing (decreasing) the WIP level. 123