S ysteemianalyysin Laboratorio Teknillinen korkeakoulu Janne Sorsa Graduate School Seminar – / 1 Elevator Group Control Problem – Stochastic and Dynamic Vehicle Routing Problem Janne Sorsa, Supervisors: Prof. Harri Ehtamo (HUT) Dr. Marja-Liisa Siikonen (KONE)

S ysteemianalyysin Laboratorio Teknillinen korkeakoulu Janne Sorsa Graduate School Seminar – / 2 Background EGCP: Integer programming based methods not found in literature Multi-deck control methods not available in literature Contribution: Complete formulation and solution method ready for implementation for multi-deck elevators SVRP: Modeling framework and terminology Typically optimal policies solved with heuristics Contribution: practical way to solve SVRP to optimality for an on-line optimization

S ysteemianalyysin Laboratorio Teknillinen korkeakoulu Janne Sorsa Graduate School Seminar – / 3 Modeling and Analysis Formulate VRP as Generalized Assignment Problem as Integer Programming Problem Traveling Salesman Problem for an elevator as stochastic optimal control problem Solve GAP with Genetic Algorihm Solve TSP as a Certainty Equivalent Controller (CEC) Simulation of several case studies: Measure computation time Compare service level to other algorithms

S ysteemianalyysin Laboratorio Teknillinen korkeakoulu Janne Sorsa Graduate School Seminar – / 4 Results Method realized for on-line optimization Linear growth of computation time with respect to problem size Optimization based method beats heuristics in passenger service level Objective affects directly to the corresponding service level statistic Objective of optimization not straightforward for double-deck elevators

S ysteemianalyysin Laboratorio Teknillinen korkeakoulu Janne Sorsa Graduate School Seminar – / 5 Conclusions and the way forward Practical approach, which works in reality! Future research: Pickup and Delivery Problem formulation (partly done by Ruokokoski, 2007) Integer Programming solution Theoretical properties (lower bounds for WT etc à la Bertsimas and van Ryzin) Effect and reliability of forecasting accuracy (HUT 2008?)

S ysteemianalyysin Laboratorio Teknillinen korkeakoulu Janne Sorsa Graduate School Seminar – / 6 References Closs, The Computer Control of Passenger Traffic in Large Lift Systems. PhD Thesis Google Scholar: 7 Scopus: 4 Bertsimas, van Ryzin, A stochastic and dynamic vehicle routing problem in the Euclidean plane Google Scholar: 117 Scopus: 49 (Transp. Sc., EJOR, OR)