Table 2 Iterations of the proposed searching algorithm for \(t_{1}^{*}\) for the extended EMQ model 2
β | Step # | \(t_{{1{\text{U}}}}^{*}\) | u L = \(e^{{ - \beta t_{{1{\text{U}}}} }}\) | \(t_{{1{\text{L}}}}^{*}\) | u U = \(e^{{ - \beta t_{{1{\text{L}}}} }}\) | Difference between \(t_{{1{\text{U}}}}^{*}\) and \(t_{{1{\text{L}}}}^{*}\) | [U] E[TCU(\(t_{{1{\text{U}}}}^{*}\))] | [L] E[TCU(\(t_{{1{\text{L}}}}^{*}\))] | Difference between [U] and [L] |
|---|---|---|---|---|---|---|---|---|---|
0.5 | Initial | – | 0.0000 | – | 1.0000 | – | – | – | – |
1st | 0.2848 | 0.8673 | 0.1951 | 0.9071 | 0.0898 | $11,642.46 | $11,481.07 | $161.39 | |
2nd | 0.2086 | 0.9009 | 0.2046 | 0.9027 | 0.0040 | $11,477.72 | $11,477.28 | $0.44 | |
3rd | 0.2052 | 0.9025 | 0.2051 | 0.9026 | 0.0001 | $11,477.28 | $11,477.27 | $0.01 | |
4th | 0.2051 | 0.9025 | 0.2051 | 0.9025 | 0.0000 | $11,477.27 | $11,477.27 | $0.00 |