Global lower bounds for flow shops with multiple processors

Flow shop with multiple processors (FSMP) scheduling involves sequencing jobs in a flow shop where, at any processing stage, there exists one or more identical processors. Any methodology to determine the optimal makespan for this type of problem is NP-complete. This necessitates the use of sub-optimal heuristic methods to address problems of moderate to large scale. This paper presents global lower bounds on FSMP makespan problems which may be used to assess the quality of heuristic solutions when the optimal solution is unknown.