Simultaneously determining the number of kanbans, container sizes, and the final-assembly sequence of products in a just-in-time shop

This paper presents a solution to the multiple-level, capacitated resource problem of determining container sizes, number of kanbans, and product sequence in a just-in-time (JIT) shop with kanbans. Previous research has looked at these issues independently, but this is the first paper that provides an integrated approach which addresses all three of these problems simultaneously. The solution procedure described in this paper is called JACKS (JIT Algorithm for Containers, Kanbans and Sequence), and it is based on an algorithm published previously by the authors for solving the economic lot scheduling problem referred to as the method of prime subperiods (MOPS). MOPS is used to determine container sizes and product sequence at a stage of the production process that processes all products (e.g. the final stage), and then JACKS is employed to determine feasibility and the number of kanbans at other stages. Feasibility is guaranteed, and the algorithm attempts to drive costs as low as possible, although optimality is not assured. The solution approach, based on a depth-first, branch-and-bound search, is demonstrated via an example shop.