Elevator Group Control Problem

1
Elevator Group Control Problem Stochastic and
Dynamic Vehicle Routing Problem

• Janne Sorsa, janne.sorsa_at_kone.com
• Supervisors
• Prof. Harri Ehtamo (HUT)
• Dr. Marja-Liisa Siikonen (KONE)

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

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

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

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?)

6
References

• Closs, 1970. The Computer Control of Passenger
  Traffic in Large Lift Systems. PhD Thesis
• Google Scholar 7
• Scopus 4
• Bertsimas, van Ryzin, 1991. A stochastic and
  dynamic vehicle routing problem in the Euclidean
  plane
• Google Scholar 117
• Scopus 49 (Transp. Sc., EJOR, OR)