Makespan minimization for two-stage hybrid Flow shop with dedicated machines and additional constraints

This paper considers a two-stage hybrid flow shop scheduling problem. The objective is the minimizing of maximum completion time of all the jobs. There exist two dedicated machines at stage 1 and one machine at stage 2. Each job is defined by two operations processed on the two-stages in series. Depending on the job type, the job is processed on either of the two machines at stage1 and must be processed on the single machine at stage2. the jobs are transported between the stages by a robot or a conveyor. After the problem formulation, we present lower bounds for the objective function. We then discuss a few polynomially solvable cases of the problem and present the solution algorithms. Since a general case of the problem is strongly NP-hard, we propose two heuristics to find approximate solutions to the general case. Computational experiments are done on a number of randomly generated test problems, and the test results are reported.