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Peer-reviewedCC BY 4.0Mathematics

Fixed Hall-Call Assignments and Floor-Ordered Pair Costs in Elevator Dispatch

  • JangHo Seo1
  • Joonwoo Lee1,2,3,4
4 affiliations
  1. 1School of Electronic and Electrical Engineering, Kyungpook National University, Daegu 41566, Republic of Korea
  2. 2Department of Electrical Engineering, Kyungpook National University, Daegu 41566, Republic of Korea
  3. 3Department of Smart Mobility Engineering, Kyungpook National University, Daegu 41566, Republic of Korea
  4. 4School of Aerospace Engineering Sciences, Kyungpook National University, Daegu 41566, Republic of Korea
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Abstract

Existing elevator-dispatch research uses quadratic waiting-cost models and restricts reassignment near pickup to preserve service decisions. Although fixing a hall-call assignment removes it from the decision variables, its service remains on the route, so omitting its interactions changes the objective for the remaining calls. This study examines the resulting omission loss and the computation of the retained interactions. Conditioning on fixed assignments yields a unary correction. Its omission loss is bounded, and reachable three-floor states approach the bound even for arbitrarily short reassignment thresholds. Under explicit service assumptions, floor-ordered pair-cost formulas include the merged-turnaround boundary and permit linear arithmetic for supported fixed-call interaction sums after unary evaluation. Across 30 paired seeds and 75 synthetic interfloor settings, adding the correction to move-and-swap search reduced mean waiting time by 0.50 s (95% interval 0.40–0.59 s). Separately, structured coefficient assembly reduced the equal-cell mean of complete dispatch time from 46.039 to 36.945 microseconds on identical inputs, a 19.8% reduction. The omission bound and interaction formulas provide an analytical basis for retaining fixed-call service costs, with measured service and computational benefits in the tested interfloor regime.

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Cite

BibTeXRIS
BibTeX
@article{seo2026fixed,
  title = {{Fixed Hall-Call Assignments and Floor-Ordered Pair Costs in Elevator Dispatch}},
  author = {JangHo Seo and Joonwoo Lee},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203829},
  url = {https://www.mdpi.com/2227-7390/14/20/3829},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Fixed Hall-Call Assignments and Floor-Ordered Pair Costs in Elevator Dispatch
AU  - JangHo Seo
AU  - Joonwoo Lee
PY  - 2026
DA  - 2026/10/21
JO  - Mathematics
DO  - 10.3390/math14203829
UR  - https://www.mdpi.com/2227-7390/14/20/3829
AB  - Existing elevator-dispatch research uses quadratic waiting-cost models and restricts reassignment near pickup to preserve service decisions. Although fixing a hall-call assignment removes it from the decision variables, its service remains on the route, so omitting its interactions changes the objective for the remaining calls. This study examines the resulting omission loss and the computation of the retained interactions. Conditioning on fixed assignments yields a unary correction. Its omission loss is bounded, and reachable three-floor states approach the bound even for arbitrarily short reassignment thresholds. Under explicit service assumptions, floor-ordered pair-cost formulas include the merged-turnaround boundary and permit linear arithmetic for supported fixed-call interaction sums after unary evaluation. Across 30 paired seeds and 75 synthetic interfloor settings, adding the correction to move-and-swap search reduced mean waiting time by 0.50 s (95% interval 0.40–0.59 s). Separately, structured coefficient assembly reduced the equal-cell mean of complete dispatch time from 46.039 to 36.945 microseconds on identical inputs, a 19.8% reduction. The omission bound and interaction formulas provide an analytical basis for retaining fixed-call service costs, with measured service and computational benefits in the tested interfloor regime.
SN  - 2227-7390
ER  -