Analyzing the impact of process improvement on lot sizes in JIT environment when capacity utilization follows Beta distribution

Abstract

Even after many years one kind picture still floating in my eyes: I see professor Szidarovszky, facing the blackboard, sponge and chalk at the upheld left and right hands, and writing and cleaning the lines simultaneously he put on the table, to fill up our heads with numerical methods. This style expresses his very dynamic and efficient research work at the same time, and hopefully this paper indicates that his efforts have not been useless as numerical methods are very intensively used in order to characterize the nature of lot sizing problems in JIT environment. In JIT environment the jidoka principle empowers employees to signal quality problems, and these result in frequent stoppages. This way we consider the output of the assembly line random variable that follows Beta distribution, but with low beta values. For specific beta values we derive explicit forms of the expected values of the inventory related and the annual total costs as function of alpha, the other parameter of the Beta distribution. But increasing alpha expresses increasing process quality. We found that increasing process quality decreases the expected annual cost, and the explicit forms give the saved cost volumes. Two simulation analyses are conducted to reveal the development of the variance of annual costs. The estimations of the variance of the minimum total annual costs indicate that with process improvement the variance of the minimum of the annual total costs will decrease.