Abstract
This paper considers online stochastic reservation problems, where requests come online and must be dynamically allocated to limited resources in order to maximize profit. Multi-knapsack problems with or without overbooking are examples of such online stochastic reservations. The paper studies how to adapt the online stochastic framework and the consensus and regret algorithms proposed earlier to online stochastic reservation systems. On the theoretical side, it presents a constant sub-optimality approximation of multi-knapsack problems, leading to a regret algorithm that evaluates each scenario with a single mathematical programming optimization followed by a small number of dynamic programs for one-dimensional knapsacks. On the experimental side, the paper demonstrates the effectiveness of the regret algorithm on multi-knapsack problems (with and without overloading) based on the benchmarks proposed earlier.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benoist, T., Bourreau, E., Caseau, Y., Rottembourg, B.: Towards stochastic constraint programming: A study of online multi-choice knapsack with deadlines. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 61–76. Springer, Heidelberg (2001)
Bent, R., Katriel, I., Van Hentenryck, P.: Sub-Optimality Approximation. In: Eleventh International Conference on Principles and Practice of Constraint Programming, Stiges, Spain (2005)
Bent, R., Van Hentenryck, P.: A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows. Transportation Science 8(4), 515–530 (2004)
Bent, R., Van Hentenryck, P.: Online Stochastic and Robust Optimization. In: Maher, M.J. (ed.) ASIAN 2004. LNCS, vol. 3321, pp. 286–300. Springer, Heidelberg (2004)
Bent, R., Van Hentenryck, P.: Regrets Only. Online Stochastic Optimization under Time Constraints. In: Proceedings of the 19th National Conference on Artificial Intelligence (AAAI 2004), San Jose, CA (July 2004)
Bent, R., Van Hentenryck, P.: Scenario Based Planning for Partially Dynamic Vehicle Routing Problems with Stochastic Customers. Operations Research 52(6) (2004)
Bent, R., Van Hentenryck, P.: The Value of Consensus in Online Stochastic Scheduling. In: Proceedings of the 14th International Conference on Automated Planning & Scheduling (ICAPS 2004), Whistler, British Columbia, Canada (2004)
Bent, R., Van Hentenryck, P.: Online Stochastic Optimization without Distributions. In: Proceedings of the 15th International Conference on Automated Planning & Scheduling (ICAPS 2005), Monterey, CA (2005)
Campbell, A., Savelsbergh, M.: Decision Support for Consumer Direct Grocery Initiatives. Report TLI-02-09, Georgia Institute of Technology (2002)
Chang, H., Givan, R., Chong, E.: On-line Scheduling Via Sampling. In: Artificial Intelligence Planning and Scheduling (AIPS 2000), pp. 62–71 (2000)
Dean, B., Goemans, M.X., Vondrak, J.: Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, Rome, Italy, pp. 208–217 (2004)
Puterman, M.: Markov Decision Processes. John Wiley & Sons, New York (1994)
Shaw, P.: Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Van Hentenryck, P., Bent, R., Vergados, Y. (2006). Online Stochastic Reservation Systems. In: Beck, J.C., Smith, B.M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2006. Lecture Notes in Computer Science, vol 3990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11757375_18
Download citation
DOI: https://doi.org/10.1007/11757375_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34306-6
Online ISBN: 978-3-540-34307-3
eBook Packages: Computer ScienceComputer Science (R0)