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TripBased Integer Linear Programming Model for Static MultiCar Elevator Operation Problems
Tsutomu INAMOTO Yoshinobu HIGAMI Shinya KOBAYASHI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E100A
No.2
pp.385394 Publication Date: 2017/02/01
Online ISSN: 17451337 Type of Manuscript: Special Section PAPER (Special Section on Mathematical Systems Science and its Applications) Category: Keyword: elevator operation problem, multicar elevator system, integer linear programming, interference prevention,
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Summary:
In this paper, the authors propose an integer linear programming (ILP) model for static multicar elevator operation problems. Here, “static” means that all information which make the behavior of the elevator system indeterministic is known before scheduling. The proposed model is based on the tripbased ILP model for static singlecar elevator operation problems. A trip of an elevator is a onedirectional movement of that elevator, which is labaled upward or downward. In the tripbased ILP model, an elevator trajectory is scheduled according to decision variables which determine allocations of trips to users of an elevator system. That model has such an advantage that the difficulty in solving ILP formulations resulted by that model does not depend on the length of the planning horizon nor the height of the considered building, thus is effective when elevator trajectories are simple. Moreover, that model has many variables relevant to elevators' positions. The proposed model is resulted by adding 3 constraints which are basically based on those variables and make it possible to prevent elevators in a same shaft from interfering. The first constraint simply imposes the first and last floors of an upper trip to be above those of its lower trip. The second constraint imagines the crossing point between upper and lower trips and imposes it ahead of or behind the lower trip according to their directions. The last constraint estimates future positions of elevators and imposes the upper trip to be above floors of passengers on the lower trip. The basic validity of the proposed model is displayed by solving 90 problem instances and examining elevator trajectories generated from them, then comparing objective function values of elevator trajectories on a multicar elevator system with those on singlecar elevator systems.

