An Integrated Production Planning Problem for a Multi-State Production System Using Kanban

Abstract. Kanban has been known as a superior tool to control a complex production and inventory system. Even if this tool operates well using a local rule without any detailed ordering schedule, a production planning is still necessary to determine production capacity and the number of kanbans. The production planning is made in consideration of a monthly forecasted demand while the kanban orders production and procurement several times a day. For an effective use of the kanban system, an integration of the monthly production planning to the kanban system will become impor-tant. In this study, we propose an integrated production planning problem in which the number of kanbans for each of multiple items as well as production quantity and production capacity during several months is determined. The prob-lem formulated in this paper will be hard to solve exactly since the problem contains many integer decision variables and nonlinear constraints. In order to solve the problem efficiently, a decomposed problem is solved after making linear