Table 1 Iterations of the proposed searching algorithm for \(t_{1}^{*}\) for the extended EMQ model 1
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 | 0.4595 | 0.7947 | 0.3056 | 0.8583 | 0.1539 | $10,417.21 | $10,323.69 | $93.52 | |
2nd | 0.3407 | 0.8434 | 0.3301 | 0.8479 | 0.0106 | $10,317.90 | $10,317.30 | $0.60 | |
3rd | 0.3326 | 0.8468 | 0.3318 | 0.8472 | 0.0008 | $10,317.28 | $10,317.27 | $0.01 | |
4th | 0.3321 | 0.8470 | 0.3320 | 0.8471 | 0.0001 | $10,317.27 | $10,317.27 | $0.00 | |
5th | 0.3320 | 0.8471 | 0.3320 | 0.8471 | 0.0000 | $10,317.27 | $10,317.27 | $0.00 |