A mathematical programming approach for determining workcentre lotsizes in a just-in-time system with signal Kanbans

An essential condition necessary for the implementation of the Japanese just-in-time (JIT) technique with Kanbans is small setup times relative to processing times. Without this condition bottlenecks occur at workcentres which delay production. However, the Japanese have developed a variation of the strict JIT technique that employs a special type of Kanban, referred to as a ‘signal Kanban’, at workcentres with relatively high setup times. While a normal Kanban triggers the production of larger than normal lots this altered version of the JIT technique provides an alternative approach for firms that desire to use the JIT technique, but are unable to reduce setup times at all workstations. The purpose of this paper is to describe the signal Kanban technique and demonstrate two versions of an integer mathematical programming approach for determining the optimal lotsizes to be used in conjunction with signal Kanbans. A simulation model is subsequently employed to test the effectiveness of the integer programming models and to explore some of the characteristics and conditions a firm might encounter when implementing a JIT system.