A note on makespan minimization in proportionate flow shops

A study was conducted to demonstrate the process of makespan minimization in proportionate flow shops. The objective was to find a sequence for the n jobs that minimized the makespan, denoted by Cmax. It was assumed that job j had a processing requirement pj that affected the time job j spends on each one of the m machines. It was assumed that machine i had a characteristic value qi that affected the time each job spends on machine i. Models were considered where the time job j spends on machine i, pij was a given function of pj and qi. These models were regarded as proportionate flow shops with processing times that were machine dependent. It was demonstrated that the processing times of job j on all m machines were equal to pj in the proportionate flow shop environment. The proportionate flow shop model was also generalized by describing the processing time on each machine as a function of a processing requirement and a machine-dependent parameter.