论文信息 - Three is easy, two is hard: open shop sum-batch scheduling problem refined

Three is easy, two is hard: open shop sum-batch scheduling problem refined

For the two-machine open shop sum-batch problem to minimize the makespan an optimal schedule is known to contain one, two or three batches on each machine, and finding a two-batch optimal schedule is NP-hard. We adapt the open shop algorithm by de Werra for finding a three-batch optimal schedule in linear time.

Chung-Yee Lee | Dominique de Werra | Vitaly A. Strusevich | Irina Gribkovskaia

[1] Roman Słowiński,et al. Advances in project scheduling , 1989 .

[2] Kevin Mahon,et al. Deterministic and Stochastic Scheduling , 1983 .

[3] Teofilo F. Gonzalez,et al. Open Shop Scheduling to Minimize Finish Time , 1976, JACM.

[4] David Pisinger,et al. Linear Time Algorithms for Knapsack Problems with Bounded Weights , 1999, J. Algorithms.

[5] Steve Weal. History of Mathematical Programming , 1992 .

[6] Chris N. Potts,et al. Scheduling Batches with Sequential Job Processing for Two-Machine Flow and Open Shops , 2001, INFORMS J. Comput..

[7] Jan Karel Lenstra,et al. History of mathematical programming : a collection of personal reminiscences , 1991 .

[8] D. de Werra,et al. Graph-theoretical models for preemptive scheduling , 1989 .

[9] Michael Pinedo,et al. Stochastic Shop Scheduling: A Survey , 1982 .