Elevator Scheduling via Pairwise Delay Minimization
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Solution Overview
Problem
Scheduling elevator cars efficiently under a reassignment policy is challenging due to the large number of possible solutions, uncertainty in passenger destinations, and the need to minimize average waiting time, which existing methods like the Empty the System Algorithm by Dynamic Programming (ESA-DP) do not fully exploit.
Innovation Solution
The method combines Branch-and-Bound (B&B) with the ESA-DP to systematically assign hall calls to elevator cars, using a search tree to minimize waiting times by determining mutual delays and waiting times, and employing a depth-first lazy B&B strategy with incremental calculations to prune the search space effectively.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If the reassignment policy is implemented to improve scheduling flexibility, then the average waiting time is reduced, but the computational complexity increases
Solution Approach 1:
The patent segments the scheduling problem into independent subproblems by considering only pairwise interactions between hall calls. Instead of evaluating the entire solution space, the method divides the complex optimization into smaller units (pairs of calls), making the computation tractable while still capturing the essential interactions that affect waiting times under reassignment policy.
Solution Approach 2:
The patent changes the optimization parameter from evaluating complete schedules to evaluating pairwise delays. By transforming the objective function to sum of pairwise delays rather than total waiting time of all calls, the method achieves a computationally simpler formulation that can be optimized efficiently while maintaining effectiveness in reducing average waiting time.
2Manufacturing precision
If the solution space is fully explored to find the optimal schedule, then the scheduling quality is improved, but the computational time increases exponentially
Solution Approach 1:
The patent extracts the essential interaction component from the full scheduling problem by focusing only on pairwise delays between hall calls. This extraction allows the method to capture the most significant factors affecting scheduling quality without needing to evaluate the complete exponential solution space, achieving a practical balance between optimality and computational feasibility.
Solution Approach 2:
The patent applies partial action by considering only pairwise interactions rather than all possible multi-call interactions. This partial approach is sufficient to achieve high scheduling quality because pairwise delays represent the dominant factor in waiting time calculation, while avoiding the computational burden of analyzing higher-order interactions.
3Measurement precision
If the ESA-DP method is used to determine waiting times, then the estimation accuracy is improved, but the computational burden increases
Solution Approach 1:
The patent applies preliminary action by pre-calculating pairwise delays between all pairs of hall calls for each elevator car. These pre-computed values are then reused in the optimization process, avoiding repeated calculations of the same waiting time estimates. This approach maintains the accuracy of ESA-DP method while significantly improving computational efficiency through memoization of intermediate results.
Data Source
AI summary
A method schedules cars of an elevator system, the elevator system including a set of cars, and a set of hall calls. For each car, a waiting time is determined independently if the hall call is the only hall call assigned to the car. For each car, a mutual delay ΔW(h|g) is determined for each possible pair of unassigned hall calls h and assigned hall calls g. The waiting time and mutual delays are summed. Then, the assignments are made to the set of cars so that the sum is a minimum.