Linear programming-based algorithms for the minimum makespan high multiplicity jobshop problem
- 336 Downloads
We study a generalized version of the minimum makespan jobshop problem in which multiple instances of each job are to be processed. The system starts with specified inventory levels in all buffers and finishes with some desired inventory levels of the buffers at the end of the planning horizon. A schedule that minimizes the completion time of all the operations is sought. We develop a polynomial time asymptotic approximation procedure for the problem. That is, the ratio between the value of the delivered solution and the optimal one converge into one, as the multiplicity of the problem increases. Our algorithm uses the solution of the linear relaxation of a time-indexed Mixed-Integer formulation of the problem. In addition, a heuristic method inspired by this approximation algorithm is presented and is numerically shown to out-perform known methods for a large set of standard test problems of moderate job multiplicity.
KeywordsOptimization Jobshop Approximations Heuristics
- Amin, J., Shafia, M. A., & Tavakkoli-Moghaddam, R. (2011). A hybrid algorithm based on particle swarm optimization and simulated annealing for a periodic job shop scheduling problem. The International Journal of Advanced Manufacturing Technology, 54(1–4), 309–322.Google Scholar
- Beasley, J. E. (1990). Or-library, http://people.brunel.ac.uk/~mastjjb/jeb/info.html.
- Chekuri, C., & Khanna, S. (2004). Handbook of sheduling: Algorithms, models, and performance analysis. Approximation algorithms for minimizing average weighted completion time (Vol. 33431, pp. 11-1–11-30). Boca Raton, FL: CRC Press.Google Scholar
- Correa, J. R., Wagner, M. R. (2005). Lp-based online scheduling: From single to parallel machines. In M. Jnger & V. Kaibel (Eds.), Integer programming and combinatorial optimization. Lecture Notes in Computer Science, vol. 3509 (pp. 196–209). Berlin Heidelberg: SpringerGoogle Scholar
- Goldberg, L. A., Mike, P., Aravind S., Elizabeth S. (1997). Better approximation guarantees for job-shop scheduling (pp. 599–608). In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: SODA ’97, Society for Industrial and Applied Mathematics.Google Scholar
- Savelsbergh, Martin W. P., Uma, R. N., Joel W. (1998). An experimental study of Lp-based approximation algorithms for scheduling problems (pp. 453–462). In Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: SODA ’98, Society for Industrial and Applied Mathematics. Google Scholar
- Skutella, M. (2006). List scheduling in order of \(\alpha \)-points on a single machine. Lecture Notes in Computer Science, 3484 250291.Google Scholar