The k-track assignment problem is a scheduling problem in which a collection of jobs, represented by intervals, are to be processed by k machines. Two different jobs can be processed by the same machine only if the corresponding intervals do not overlap. We give a compact formulation of the problem and state some polyhedral results for the associated polytope, working in the more general context where job compatibility stems not necessarily from intervals but rather from an arbitrary strict partial order.
Keywordsk-track assignment partial orders compact formulations polytopes
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- Arkin, E. M. and E. B. Silverberg, “Scheduling jobs with fixed start and end times” Discrete Applied Mathematics, 18, 1–8 (1987).Google Scholar
- Barcia, P. and J. O. Cerdeira, “Node packings on cocomparability graphs” Operations Research Letters, 31, 341–342 (2003).Google Scholar
- Brucker, P. and L. Nordmann, “The k-track assignment problem” Computing, 52, 97–122 (1994).Google Scholar
- Faigle, U. and W. M. Nawijn, “Note on scheduling intervals on-line” Discrete Applied Mathematics, 58, 13–17 (1995).Google Scholar
- Faigle, U., W. Kern, and W. M. Nawijn, “A greedy on-line algorithm for the k-track assignment problem” Journal of Algorithms, 31, 196–210 (1999).Google Scholar
- Golumbic, M. C., Algorithmic Graph Theory and Perfect Graphs. Academic Press, 1980.Google Scholar
- Kolen, A. W. J. and J. K. Lenstra, “Combinatorics in operations research” in R. L. Graham, M. Grotschel, and L. Lovasz (eds.), Handbook of Combinatorics, Vol. II, Elsevier, 1995, pp. 1875–1910.Google Scholar
- Martin, R. K., “Using separation algorithms to generate mixed integer models reformulations” Operations Research Letters, 10, 119–128 (1991).Google Scholar
- Padberg, M. W., “On the facial structure of set packing polyhedra” Mathematical Programming, 5, 199–215 (1973).Google Scholar