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We develop a general purpose analytical approximation method for the performance evaluation of a multi-stage, serial, echelon kanban control system. The basic principle of the method is to decompose the original system into a set of nested subsystems, each subsystem being associated with a particular echelon of stages. Each subsystem is analyzed in isolation using a product-form approximation technique. An iterative procedure is used to determine the unknown parameters of each subsystem. Numerical results show that the method is fairly accurate. IntroductionIn this paper, we develop an analytical approximation method for the performance evaluation of an echelon kanban control system, used for the coordination of production in a multi-stage, serial, production/inventory system. We then test the behavior of this method on several numerical examples. The term "echelon kanban" was introduced in [19]. The basic principle of the operation of the echelon kanban control system is very simple: When a part leaves the last stage of the system to satisfy a customer demand, a new part is demanded and authorized to be released into each stage. It is worth noting that the echelon kanban control system is equivalent to the integral control system described in [8]. The echelon kanban control system differs from the conventional kanban control system, which is also referred to as installation kanban control system or policy in [19], in that in the conventional kanban control system, a new part is demanded and authorized to be released into a stage when a part leaves this particular stage and not when a part leaves the last stage, as is the case with the echelon kanban control system. This implies that in the conventional kanban control system, the placement of a demand and an authorization for the production of a new part into a stage

We develop a general purpose analytical approximation method for the performance evaluation of a multi-stage, serial, echelon kanban control system. The basic principle of the method is to decompose the original system into a set of nested subsystems, each subsystem being associated with a particular echelon of stages. Each subsystem is analyzed in isolation using a product-form approximation technique. An iterative procedure is used to determine the unknown parameters of each subsystem. Numerical results show that the method is fairly accurate. IntroductionIn this paper, we develop an analytical approximation method for the performance evaluation of an echelon kanban control system, used for the coordination of production in a multi-stage, serial, production/inventory system. We then test the behavior of this method on several numerical examples. The term "echelon kanban" was introduced in [19]. The basic principle of the operation of the echelon kanban control system is very simple: When a part leaves the last stage of the system to satisfy a customer demand, a new part is demanded and authorized to be released into each stage. It is worth noting that the echelon kanban control system is equivalent to the integral control system described in [8]. The echelon kanban control system differs from the conventional kanban control system, which is also referred to as installation kanban control system or policy in [19], in that in the conventional kanban control system, a new part is demanded and authorized to be released into a stage when a part leaves this particular stage and not when a part leaves the last stage, as is the case with the echelon kanban control system. This implies that in the conventional kanban control system, the placement of a demand and an authorization for the production of a new part into a stage

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