Scheduling a single server in a two-machine flow shop

Authors:
T. C. E. Cheng;M. Y. Kovalyov
Affiliations:
Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Faculty of Economics, Belarus State University, K. Marxa 31, room 70, 220050 Minsk, Belarus
Venue:
Computing
Year:
2003

Citing 9
Cited 1

Batch sizing and job sequencing on a single machine

Annals of Operations Research
The complexity of one-machine batching problems

Discrete Applied Mathematics - Special issue on new frontiers in the theory and practice of combinatorial optimization: applications in manufacturing and VLSI design
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Scheduling computer and manufacturing processes
One-operator–two-machine flowshop scheduling with setup and dismounting times

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Parallel machine scheduling with a common server

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Scheduling Algorithms

Scheduling Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Parallel machine scheduling problems with a single server

Mathematical and Computer Modelling: An International Journal
Improved dynamic programs for some batching problems involving the maximum lateness criterion

Operations Research Letters

Flow shop scheduling to minimize the total completion time with a permanently present operator: Models and ant colony optimization metaheuristic

Computers and Operations Research

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Abstract

We study the problem of scheduling a single server that processes n jobs in a two-machine flow shop environment. A machine dependent setup time is needed whenever the server switches from one machine to the other. The problem with a given job sequence is shown to be reducible to a single machine batching problem. This result enables several cases of the server scheduling problem to be solved in O(n log n) by known algorithms, namely, finding a schedule feasible with respect to a given set of deadlines, minimizing the maximum lateness and, if the job processing times are agreeable, minimizing the total completion time. Minimizing the total weighted completion time is shown to be NP-hard in the strong sense. Two pseudopolynomial dynamic programming algorithms are presented for minimizing the weighted number of late jobs. Minimizing the number of late jobs is proved to be NP-hard even if setup times are equal and there are two ditstinct due dates. This problem is solved in O(n3) time when all job processing times on the first machine are equal, and it is solved in O(n4) time when all processing times on the second machine are equal.