Performance Comparing and Analysis for Slot Allocation Model
Abstract
:1. Introduction
2. Related Work of Difficulty in Slot Allocation
3. Proposed Slot Displacement Models
3.1. Difficulty Index and Difficulty of Displacement
3.2. Standardized Priority
3.3. Comprehensive Displacement Cost
3.4. Displacement Model for all Flights
4. LIP for Slot Displacement Models
Algorithm 1. Iterative linear integer programming algorithms based on datasplitting. 
Priority calculation ${f}_{m}^{P}$ For i = 1:7

5. Testing and Results
 (1)
 Whether there is opportunity to reduce implementation difficulty while not to increase too much displacement.
 (2)
 With our algorithm, is it possible for high priority movement to have a lower probability of being displaced?
 (3)
 Can priority be considered as the cost of displacing the unit time to ensure that the high priority movement has a low probability of being displaced (HPLA)?
 (4)
 What are the differences in performance indicators when priority is fed into a computer program in priority order or in the order of morning to night (final slottable presentation) when priority is considered as the cost of displacing the unit time?
5.1. Performances Compare with Different Weight Factors of Evaluation Objectives
5.2. Analysis of the Correlation between Average Displacement and Average Difficulty
6. Discussion and Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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historic series of slots  [1501,2000] 
“change to historic” series of slots  [1001,1500] 
new entrant slots  [501,1000] 
remaining slots  [1,500] 
i  1  2  3  4  …  M  ${\mathit{C}}_{\mathit{e}}$  

$\mathit{e}$  
1  1  0  0  0  …  0  ${C}_{1}$  
2  0  0  1  0  …  1  ${C}_{2}$  
3  0  0  0  0  …  0  ${C}_{3}$  
…  …  …  …  …  …  …  …  
E−1  0  0  0  1  …  0  ${C}_{E1}$  
E  0  1  0  0  …  0  ${C}_{E}$ 
Execution batch equals P = $M/Q$  ${\displaystyle \sum}_{m\in M}}{\displaystyle {\displaystyle \sum}_{t\in T}}{f}_{m}^{t}{x}_{m}^{t}\phantom{\rule{0ex}{0ex}}={\displaystyle {\displaystyle \sum}_{m\in M}}{\displaystyle {\displaystyle \sum}_{t\in T}}\left{t}_{m}{\tau}_{m}\right{\delta}_{m}^{DP}{x}_{m}^{t$  ${f}_{m}^{t}$  ${f}_{m}^{t}{x}_{m}^{t}$=${f}_{1}^{1}{x}_{11}$+${f}_{1}^{2}{x}_{12}$+${f}_{1}^{3}{x}_{13}$+$\cdots $+${f}_{1}^{24}{x}_{124}$+ ${f}_{2}^{1}{x}_{21}$+${f}_{2}^{2}{x}_{22}$+${f}_{2}^{3}{x}_{23}$+$\cdots $+${f}_{2}^{24}{x}_{224}$+ $\cdots $ ${f}_{m}^{1}{x}_{m1}$+${f}_{m}^{2}{x}_{m2}$+${f}_{m}^{3}{x}_{m3}$+$\cdots $+${f}_{m}^{24}{x}_{m24}$  (a.0) 
$\sum _{m\in M}\sum _{t\in {T}_{c}^{s}}{a}_{m}^{d}{b}_{mc}{x}_{m}^{t}\le {u}_{c}^{ds}$, c$\in hour$, $\mathrm{d}\in \left[1,2,\dots ,7\right]$, S$\in \left[1,2,\dots 24\right]$ ${a}_{m}^{d}=1,{b}_{mc}=1$  ${A}_{1}$  ${x}_{11}$+${x}_{21}$+${x}_{31}$+$\cdots $+${x}_{m1}$≤${u}_{hour}^{1}$  (a.1)  
${x}_{12}$+${x}_{22}$+${x}_{32}$+$\cdots $+${x}_{m2}$≤${u}_{hour}^{2}$  (a.2)  
$\vdots $  $\vdots $  
${x}_{124}$+${x}_{224}$+${x}_{324}$+$\cdots $+${x}_{m24}$≤${u}_{hour}^{24}$  (a.24)  
$\sum _{m\in M}\sum _{t\in {T}_{c}^{s}}{a}_{m}^{d}{b}_{mc}{x}_{m}^{t}\le {u}_{c}^{ds}$, c$\in c1$, corridor 1 $\mathrm{d}\in \left[1,2,\dots ,7\right]$, S$\in \left[1,2,\dots 24\right]$ ${a}_{m}^{d}=1,{b}_{mc}=1$  $Y$  ${y}_{1}^{1}{x}_{11}$+${y}_{2}^{1}{x}_{21}$+${y}_{3}^{1}{x}_{31}$+$\cdots $+${y}_{m}^{1}{x}_{m1}$≤${u}_{c1}^{1}$  (b.1)  
${y}_{1}^{1}{x}_{12}$+${y}_{2}^{1}{x}_{22}$+${y}_{3}^{1}{x}_{32}$+$\cdots $+${y}_{m}^{1}{x}_{m2}$≤${u}_{c1}^{2}$  (b.2)  
$\vdots $  $\vdots $  
${y}_{1}^{1}{x}_{124}$+${y}_{2}^{1}{x}_{224}$+${y}_{3}^{1}{x}_{324}$+$\cdots $+${y}_{m}^{1}{x}_{m24}$≤${u}_{c1}^{24}$  (b.24)  
$\vdots \cdots \vdots \le \vdots $  $\vdots \cdots \vdots \le \vdots $  $\vdots $  
$\sum _{m\in M}\sum _{t\in {T}_{c}^{s}}{a}_{m}^{d}{b}_{mc}{x}_{m}^{t}\le {u}_{c}^{ds}$, c$\in c8$, corridor 8 $\mathrm{d}\in \left[1,2,\dots ,7\right]$, S$\in \left[1,2,\dots 24\right]$ ${a}_{m}^{d}=1,{b}_{mc}=1$  ${y}_{1}^{8}{x}_{11}$+${y}_{2}^{8}{x}_{21}$+${y}_{3}^{8}{x}_{31}$+$\cdots $+${y}_{m}^{8}{x}_{m1}$≤${u}_{c8}^{1}$  (b.169)  
${y}_{1}^{8}{x}_{12}$+${y}_{2}^{8}{x}_{22}$+${y}_{3}^{8}{x}_{32}$+$\cdots $+${y}_{m}^{8}{x}_{m2}$≤${u}_{c8}^{2}$  (b.170)  
$\vdots $  $\vdots $  
${y}_{1}^{8}{x}_{124}$+${y}_{2}^{8}{x}_{224}$+${y}_{3}^{8}{x}_{324}$+$\cdots $+${y}_{m}^{8}{x}_{m24}$≤${u}_{c8}^{24}$  (b.216)  
$\sum _{t\in T}{x}_{m}^{t}$ = 1, $m\in Q$ ${x}_{m}^{t}\in \left\{0,1\right\},$ $m\in Q$ $t\in \left[1,2,\dots 24\right]$  $Aeq$  ${x}_{11}$+${x}_{12}$+${x}_{13}$+$\cdots $+${x}_{124}$ = 1 ${x}_{21}$+${x}_{22}$+${x}_{23}$+$\cdots $+${x}_{224}$ = 1 $\vdots $ ${x}_{m1}$+${x}_{m2}$+${x}_{m3}$+$\cdots $+${x}_{m24}$ = 1  (d.1)  
(d.2)  
$\vdots $  
(d.m) 
Tests  Weights of Disp, Diff, Prio  Total Diff  Average Diff  Total Disp  Average Disp  Capacity  Min (Disp)  Max (Disp)  Order  Figure 

1  1,0,0  8.2E+06  5752.40  27200  19.18  88,23,7  −340  385  SD  5, 6 
2  0,1,0  4.5E+06  3177.89  29290  20.66  88,23,7  −430  310  SD  7, 8 
3  0,0,1  6.4E+06  4480.08  29220  20.61  88,23,7  −485  405  SD  9, 10 
4  0,0.9,0.1  5.1E+06  3582.03  30130  21.25  88,23,7  −565  360  SD  N 
5  0,1,1  6.4E+06  4480.08  27015  19.05  88,23,7  −485  405  SD  N 
6  0,0.5,0.5  6.6E+06  4650.95  29045  20.48  88,23,7  −485  340  SD  N 
7  0,1,1  9.0E+06  6367.90  44330  31.26  78,20,7  −520  460  SD  N 
8  0,0.5,0.5  7.2E+06  5064.14  28305  19.96  88,23,7  −585  375  not SD  11–13 
9  1,0.1,0.9  5.2E+06  3670.50  29385  21.00  88,23,7  −545  350  SD  N 
10  1,0,0  8.3E+06  5855.00  28170  20.00  88,23,8  −270  419  not SD  N 
11  0.8,0.01,0.09  5.0E+06  3544.65  28440  20.06  88,23,8  −510  410  SD  N 
12  100,0.1,0  5.3E+06  3707.60  28060  19.79  88,23,8  −545  365  SD  N 
The First Set of Tests  Average Displacement X  Average Difficulty Y 

5  19.05  4480.08 
1  19.18  5752.40 
12  19.79  3707.60 
8  19.96  5064.14 
10  20.00  5855.00 
11  20.06  3544.65 
6  20.48  4650.95 
3  20.61  4480.08 
2  20.66  3177.89 
9  21.00  3670.50 
4  21.25  3582.03 
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Ye, Z.; Li, Y.; Bai, J.; Zheng, X. Performance Comparing and Analysis for Slot Allocation Model. Information 2019, 10, 188. https://doi.org/10.3390/info10060188
Ye Z, Li Y, Bai J, Zheng X. Performance Comparing and Analysis for Slot Allocation Model. Information. 2019; 10(6):188. https://doi.org/10.3390/info10060188
Chicago/Turabian StyleYe, ZhiJian, YanWei Li, JingTing Bai, and XinXin Zheng. 2019. "Performance Comparing and Analysis for Slot Allocation Model" Information 10, no. 6: 188. https://doi.org/10.3390/info10060188