Minimizing Sum of Completion Times and Makespan in Master-Slave Systems
IEEE Transactions on Computers
Two machine flow shop scheduling problem with weighted WIP costs
Computers and Operations Research
Flow shops with WIP and value added costs
Journal of Scheduling
A two-machine flowshop problem with two agents
Computers and Operations Research
Minimizing total completion time in two-stage hybrid flow shop with dedicated machines
Computers and Operations Research
A note on makespan minimization in proportionate flow shops
Information Processing Letters
Two-machine flowshop scheduling with truncated learning to minimize the total completion time
Computers and Industrial Engineering
Minimizing makespan in an ordered flow shop with machine-dependent processing times
Journal of Combinatorial Optimization
Joint optimization of overlapping phases in MapReduce
Performance Evaluation
Several flow shop scheduling problems with truncated position-based learning effect
Computers and Operations Research
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We consider the problem of minimizing total completion time in a two-machine owshop. We present a heuristic with worst-case bound 2β/(α + β), where α and β denote the minimum and maximum processing time of all operations. Furthermore, we analyze four special cases: equal processing times on the first machine, equal processing times on the second machine, processing a job on the first machine takes time no less than its processing on the second machine, and processing a job on the first machine takes time no more than its processing on the second machine. We prove that the rst special case is NP-hard in the strong sense and present an O(n log n) approximation algorithm for it with worst-case bound 4/3. We repeat the easy polynomial algorithms for the cases two and three, and show that problem four is solvable in polynomial time as well.