On the Development of a Mixed-Integer Linear Programming Model for the Flowshop Sequencing Problem

This paper describes the development of a mixed-integer linear programming (MILP) model for the standard N-job, M-machine flowshop sequencing problem. Based on an earlier all-integer model developed by Wagner, this MILP model has been used to solve optimally problems with as many as 25 jobs and as many as 10 machines. Variants of the standard flowshop model, including a variety of performance measures, are also presented. Computational experience involving the successful solution of over 175 flowshop problems is discussed, and suggestions for future research projects are offered.