- A two-stage flow shop scheduling problem on a batching machine and a discrete machine with blocking and shared setup times
- Computers & Operations Research
- Volume | Issue number
- 37 | 5
- Pages (from-to)
- Document type
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
Motivated by applications in iron and steel industry, we consider a two-stage flow shop scheduling problem where the first machine is a batching machine subject to the blocking constraint and the second machine is a discrete machine with shared setup times. We show that the problem is strongly NP-hard when the objective is to minimize the makespan. When solved with a heuristic priority rule, the worst case ratio with the minimum makespan is 2. For a more general objective, the minimization of a linear combination of the makespan and the total blocking time, a quadratic mixed integer program is presented first. Then we pinpoint two cases with polynomial time algorithms: the case without blocking constraint and the case with a given job sequence. Also for the general objective, we analyze an approximation algorithm. Finally, we evaluate the algorithms, giving experimental results on randomly generated test problems.
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