The stochastic flowshop makespan. Part II. Some general results for the unbuffered case
研究了无缓冲随机流水车间中有限数量工件的期望完工时间表达式，发现“碗形效应”源于双反射性质的失效，并给出三机器三工件时最优均值比约为10:9:10，但改进幅度仅约0.05%。
Abstract This paper, which should be read in conjunction with Part I, (Middleton 1994), discusses how expressions for the expected makespans in unbuffered stochastic flowshops may be derived for a finite number of jobs and it is shown that the 'bowl effect'discussed by Hunt (1956), Makino( 1964), Hillierand Boling(1967) is brought about by a breakdown of the double-reflection property which holds for buffered flowshops. In particular, if three (unbuffered) jobs are to pass through three machines, the job times being exponentially distributed, the minimum makespan is achieved when the mean times of the machines are (approximately) in ratio 10:9:10. The mean elapsed time is then only about 0.05%shorter than for the corresponding balanced production line. (Corresponding figures for the equilibrium distribution are an approximate ratio 4:3:4 for an improvement of just over 0.5%.)