Table 7 Problem complexity.
From: An optimization model of tram timetables considering various signal priority strategies
Type | Variables of constraints | Theoretical dimension | Counts |
|---|---|---|---|
Continuous variables | \({t}_{q, k}\) | \(\sum \left|K\right|\cdot \left|Q\right|\) | 440 |
\({t}_{q, s}^{W}\), \({t}_{q,s}^{D}\),\({t}_{q,s}^{A}\) | \(\sum \left|S\right|\cdot \left|Q\right|\) | 460 | |
\({t}_{q,s}^{ot},\) \({t}_{q,s}^{rt}\),\({u}_{q,s},\) | \(\sum \left| {S^{\prime}} \right| \cdot \left| Q \right|\) | 160 | |
Binary | \({\alpha }_{q,b,s}\) | \(\sum \left|S\right|\cdot \left|Q\right|\) | 460 |
\({\theta }_{b}^{s},\) \({\beta }_{b}^{s}\) | \(\sum \left| {S^{\prime}} \right| \cdot \left| Q \right|\) | 160 | |
Constraints | Constraints (1) | \(\sum \left|K\right|\cdot \left|Q\right|\) | 440 |
Constraints (2) | \(\sum \left|\widetilde{S}\right|\cdot \left|Q\right|\) | 140 | |
Constraints (3) | \(\sum \left| {S^{\prime}} \right| \cdot \left| Q \right|\) | 160 | |
Constraints (4) | \(\sum \left| {S^{\prime\prime}} \right| \cdot \left| Q \right|\) | 160 | |
Constraints (5) | \(\sum \left|Q\right|\) | 20 | |
Constraints (6)–(7) | \(\sum \left|S\right|\cdot \left|Q\right|\) | 460 | |
Constraints (8)–(13) | \(\sum \left| {S^{\prime}} \right| \cdot \left| Q \right|\) | 160 | |
Constraints (14) | \(\sum \left|S\right|\cdot \left|Q\backslash \left\{\left|r\right|\right\}\right|\) | 437 |
