The stochastic flowshop makespan. Part II. Some general results for the unbuffered case

This paper 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’ 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 0ë05% 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 0ë5%.) [See previous abstract.]