The Maximum Setup Time and Setup Cost of Achieving Just-in-Time System

The primary topic of operation management has turned to setup cost reduction because of the success of Just-in-Time (JIT) system. Setup cost is treated as a policy variable that can be reduced. A few papers prove that setup cost reduction will increase the number of setups and approach to JIT. However, those papers do not discuss the maximum setup time allowed that will successfully achieve to JIT. The Wagner-Whitin (WW) algorithm is known to produce optimal lot size for T-period dynamic lot-sizing problems. This paper develops an extension of the WW algorithm to establish a recursive model and find the sufficient and necessary conditions of yielding JIT. Furthermore, the limited maximum setup time that will yield JIT system is discussed. The maximum setup time of achieving JIT can be easily computed and understood in practice. The formula and table of the setup time allowed are obtained to act as a goal of reducing setup time in JIT system.