Abstract
In this paper, we study two versions of the two machine flow shop scheduling problem, where schedule length is to be minimized. First, we consider the two machine flow shop with setup, processing, and removal times separated. It is shown that an optimal solution need not be a permutation schedule, and that the problem isNP-hard in the strong sense, which contradicts some known results. The tight worst-case bound for an optimal permutation solution in proportion to a global optimal solution is shown to be 3/2. An O(n) approximation algorithm with this bound is presented. Secondly, we consider the two machine flow shop with finite storage capacity. Again, it is shown that there may not exist an optimal solution that is a permutation schedule, and that the problem isNP-hard in the strong sense.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Conway RW, Maxwell WL, Miller LW (1967) Theory of scheduling. Addison-Wesley, Reading
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory ofNP-completeness, Freeman, San Francisco
Garey MR, Johnson DS, Sethi R (1976) The complexity of flow shop and job shop scheduling. Mathematics of Operations Research 1:117–129
Gilmore PC, Gomory RE (1964) Sequencing a one-state variable machine: a solvable case of the traveling salesman problem. Operations Research 12:665–679
Johnson SM (1954) Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics Quarterly 1:61–68
Lawler EL, Lenstra JK, Rinnooy Kan AHG, Shmoys DB (1993) Sequencing and scheduling: algorithms and complexity. In: Handbook in operations research and management Science, Vol. 4: Logistics of production and inventory (Graves SC et al. eds), North-Holland 445–522
Papadimitriou CH, Kanellakis PC (1980) Flowshop scheduling with limited temporary storage. Journal of the Association for Computing Machinery 27:533–549
Strusevich VA (1993) Two machine open shop scheduling problem with setup, processing and removal times separated. Computers and Operations Research 20:597–611
Sule DR (1982) Sequencingn jobs on two machines with setup, processing and removal times separated. Naval Research Logistics Quarterly 29:517–519
Sule DR and Huang KY (1983) Sequencing on two and three machines with setup, processing and removal times separated. International Journal of Production Research 21:723–732
Yoshida T and Hitomi K (1979) Optimal two-stage production scheduling with setup times separated. AIIE Transactions 11:261–263
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Strusevich, V.A., Zwaneveld, C.M. On non-permutation solutions to some two machine flow shop scheduling problems. ZOR - Methods and Models of Operations Research 39, 305–319 (1994). https://doi.org/10.1007/BF01435460
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01435460