Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

Volume 3990 of the series Lecture Notes in Computer Science pp 212-227

Online Stochastic Reservation Systems

  • Pascal Van HentenryckAffiliated withDepartment of Computer Science, Brown University
  • , Russell BentAffiliated withDepartment of Computer Science, Brown University
  • , Yannis VergadosAffiliated withDepartment of Computer Science, Brown University

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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.