A MILP model for then-job,M-stage flowshop with sequence dependent set-up times

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Abstract
The problem of an n-job, M-stage flowshop with sequence dependent set-up times is discussed. A mixed integer linear program (MILP) is formulated with considerably reduced number of integer binary variables, than if the same problem were formulated with integer variables defined as X ij=1 if job i is sequenced immediately before job j, and 0 otherwise. The inclusion of set-up times, sequence dependency and M stages makes this formulation different from most other flowshop formulations in the literature, since such problems have not been given due consideration. This paper contributes a unique formulation to handle flowshop problems in the process industry where the set-up times have a definite dependence on the sequence in which jobs are processed. Computational results have been compared for problems up to six jobs and stages where the objective has been to minimize the makespan. The MILP has been solved using the SCICONIC-V/M mixed integer solution package on the Prime-550 minicomputer.