The impact of core precedences in a cyclic RCPSP with precedence delays
- 247 Downloads
In this paper, we introduce a new kind of constraint, called a core precedence constraint, in a cyclic resource-constrained project scheduling problem (RCPSP) with precedence delays. We show, by an example, which kind of industrial constraints might be modeled by such core precedences in a periodic production setting. We then establish that these constraints can be quite easily added to an integer linear programming formulation of the cyclic RCPSP. Although core precedences seem to be very similar to classical precedence, they can induce infeasibility even without resource constraints. Moreover, we show that the feasibility checking problem is NP-complete in the strong sense, even assuming unit processing times and no resource constraints.
KeywordsPrecedence Constraint Feasibility Problem Periodic Schedule Integer Linear Programming Model Very Long Instruction Word
This work was supported by the Grant Agency of the Czech Republic under Project GACR P103/12/1994.
- Ayala, M., & Artigues, C. (2010). On integer linear programming formulations for the resource-constrained modulo scheduling problem. LAAS report 10393.Google Scholar
- Behrmann, G., Brinksma, E., Hendriks, M., & Mader, A. (2005). Production scheduling by reachability analysis: A case study. Workshop on Parallel and Distributed Real-Time Systems (WPDRTS) (p. 140.1). Los Alamitos: IEEE Computer Society Press.Google Scholar
- Bonfietti, A., Lombardi, M., Benini, L., & Milano, M. (2011). A constraint based approach to cyclic rcpsp. In CP’11, pp. 130–144.Google Scholar
- Dasdan, A., Irani, S., & Gupta, R. K. (1999). Efficient algorithms for optimum cycle mean and optimum cost to time ratio problems. In: Design Automation Conference (pp. 37–42).Google Scholar
- Dupont de Dinechin, B., Artigues, C., & Azem, S. (2008). Resource constrained modulo scheduling. In C. Artigues, S. Demassey, & E. Neron (Eds.), Resource-constrained project scheduling: models, algorithms, extensions and applications, control systems, robotics and manufacturing series (pp. 267–277). London: ISTE and Wiley.CrossRefGoogle Scholar
- Dupont de Dinechin, B. (2004). From machine scheduling to vliw instruction scheduling. ST Journal of Research, 1(2), 1–35.Google Scholar
- Dupont de Dinechin, B. (2007). Time-indexed formulations and a large neighborhood search for the resource-constrained modulo scheduling problem. In P. Baptiste, G. Kendall, A. Munier-Kordon, & F. Sourd (Eds.), 3rd Multidisciplinary International Scheduling Conference: Theory and Applications.Google Scholar
- Eichenberger, A., & Davidson, E. (1997). Efficient formulation for optimal modulo schedulers. SIGPLAN-PLDI’97.Google Scholar
- Hanen, C., & Munier, A. (1994). Cyclic scheduling on parallel processors: An overview. In P. Chrétienne, E. G. Coffman, J. K. Lenstra, & Z. Liu (Eds.), Scheduling theory and its applications. Chichester: Wiley.Google Scholar
- Hanzalek, Z., & Pacha, T. (1998). Use of the fieldbus systems in academic setting. In Proceedings of Real-Time Systems Education III (pp. 93–97). doi: 10.1109/RTSE.1998.766518
- Huff, R. A. (1993). Lifetime-sensitive modulo scheduling. In Proceedings of the ACM SIGPLAN ’93 Conference on Programming Language Design and Implementation (pp. 258–267).Google Scholar
- Llosa, J. (1996). Swing modulo scheduling: A lifetime-sensitive approach. In Proceedings of the 1996 Conference on Parallel Architectures and Compilation Techniques, PACT ’96 (pp. 80). Washington, DC: IEEE Computer Society. http://dl.acm.org/citation.cfm?id=882471.883302.
- Munier-Kordon, A. (2010). A graph-based analysis of the cyclic scheduling problem with time constraints: Schedulability and periodicity of the earliest schedule. Journal of Scheduling, 1–15. doi: 10.1007/s10951-009-0159-z.
- Proth, J. M., & Xie, X. (1995). Modélisation, analyse et optimisation des systèmes à fonctionnement cyclique. Masson (1995).Google Scholar
- Rau, B. R. (1994). Iterative modulo scheduling: An algorithm for software pipelining loops. In Proceedings of the 27th Annual International Symposium on Microarchitecture (MICRO 27) (pp. 63–74). New York, NY: ACM.Google Scholar
- Smelyanskiy, M., Mahlke, S., & Davidson, E. (2004). Probabilistic predicate -aware modulo scheduling. In International Symposium on Code Generation and Optimization: Feedback-Directed and Runtime Optimization.Google Scholar