Table 1. Forwarding time consumption (minutes/load). Total time consumption consists of productive machine (PM) time and other time. Means and medians are respectively followed by standard deviations (SD) and median absolute deviations (MAD) in brackets. In addition, 5th, 25th, 75th and 95th percentiles are given to provide general indications of the distribution of observations for each work element. The unit of observation is one load and unit of analysis is a minute per load. The number of observations varied from 8555 to 8868. | ||||||

Percentiles | ||||||

Work element | Mean, SD | Median, MAD | 5th | 25th | 75th | 95th |

Total driving empty time | 7.0 (7.7) | 5.2 [3.2] | 0.3 | 2.5 | 9.1 | 19.1 |

Driving empty PM time | 4.3 (3.6) | 3.5 [2.1] | 0.2 | 1.7 | 5.9 | 11.1 |

Driving empty other time | 2.3 (5.8) | 0.5 [0.5] | 0.0 | 0.1 | 2.3 | 9.3 |

Total loading time | 22.9 (16.0) | 19.9 [6.6] | 8.5 | 13.9 | 27.6 | 45.5 |

Loading PM time | 21.0 (11.8) | 18.8 [6.1] | 8.2 | 13.4 | 25.9 | 40.0 |

Loading other time | 1.9 (7.3) | 0.5 [0.4] | 0.1 | 0.2 | 1.4 | 7.7 |

Crane work only PM time | 14.3 (7.2) | 13.0 [3.7] | 6.0 | 9.7 | 17.4 | 26.2 |

Simultaneous crane work and driving ^{a)} | 1.4 (1.5) | 0.9 [0.6] | 0.1 | 0.4 | 1.9 | 4.2 |

Driving only PM time ^{b)} | 5.3 (5.0) | 4.2 [2.2] | 0.7 | 2.3 | 6.8 | 13.2 |

Loading drive PM time ^{= a + b)} | 6.7 (5.7) | 5.6 [2.7] | 1.1 | 3.1 | 8.7 | 16.0 |

Total driving loaded time | 4.8 (4.2) | 3.7 [2.2] | 0.5 | 1.8 | 6.5 | 12.7 |

Driving loaded PM time | 3.8 (3.6) | 2.8 [1.9] | 0.1 | 1.2 | 5.3 | 11.1 |

Driving loaded other time | 0.6 (1.6) | 0.3 [0.2] | 0.0 | 0.1 | 0.6 | 2.0 |

Total unloading time | 10.2 (9.9) | 8.2 [2.5] | 3.7 | 6.0 | 11.3 | 23.0 |

Unloading PM time | 8.8 (5.8) | 7.5 [2.2] | 3.5 | 5.6 | 10.2 | 18.8 |

Unloading other time | 1.4 (6.2) | 0.3 [0.3] | 0.0 | 0.1 | 1.1 | 4.7 |

Crane work only PM time | 7.4 (3.8) | 6.8 [1.7] | 3.2 | 5.2 | 8.8 | 13.4 |

Unloading drive PM time ^{1)} | 1.4 (2.8) | 0.5 [0.4] | 0.0 | 0.2 | 1.5 | 6.1 |

Total time per load | 45.8 (24.1) | 42.1 [11.8] | 19.1 | 31.0 | 55.3 | 84.5 |

PM time | 39.3 (17.4) | 36.8 [10.1] | 17.3 | 27.5 | 48.2 | 68.2 |

Other time | 6.5 (11.9) | 3.4 [2.2] | 0.6 | 1.6 | 7.1 | 21.6 |

^{1) }Can also include simultaneous crane work |

Table 2. Descriptive forwarder work variables. Means and medians are respectively followed by standard deviations (SD) and median absolute deviations (MAD) in brackets. In addition, 5th, 25th, 75th and 95th percentiles are given. The unit of observation is one load. | |||||||

Percentiles | |||||||

Variable | Sort | Mean, SD | Median, MAD | 5th | 25th | 75th | 95th |

Driving empty distance | m/load | 256.3 (234.5) | 199.4 [129.3] | 4.9 | 90.6 | 358.1 | 702.1 |

Loading drive distance | m/load | 236.8 (255.3) | 183.0 [91.0] | 37.3 | 102.5 | 289.3 | 596.1 |

Driving loaded distance | m/load | 181.3 (171.8) | 134.8 [95.7] | 3.1 | 52.4 | 262.4 | 524.2 |

Unloading drive distance | m/load | 71.4 (166.4) | 18.6 [17.2] | 0.0 | 4.3 | 72.4 | 305.4 |

Extraction distance^{ 1)} | m/load | 219.0 (177.5) | 173.9 [99.8] | 24.8 | 87.6 | 302.1 | 578.6 |

Total driven distance | m/load | 779.8 (518.5) | 666.2 [275.0] | 197.2 | 425.5 | 1006.8 | 1720.2 |

Driving empty speed^{ 2)} | km/h | 3.4^{a} (1.0) | 3.3 [0.5] | 1.8 | 2.8 | 3.9 | 5.1 |

Loading drive speed | km/h | 2.1^{b} (0.5) | 2.0 [0.3] | 1.3 | 1.7 | 2.4 | 3.0 |

Driving loaded speed | km/h | 2.9^{c} (0.8) | 2.8 [0.5] | 1.6 | 2.4 | 3.4 | 4.4 |

Loading crane cycle numbers^{ 3)} | cycles/load | 34.9^{a} (12.0) | 34.0 [7.0] | 17.0 | 27.0 | 42.0 | 56.0 |

Unloading crane cycle numbers | cycles/load | 16.7^{b} (5.9) | 16.0 [3.0] | 9.0 | 13.0 | 20.0 | 25.0 |

Loading crane cycle time | s/cycle | 23.7 (5.2) | 22.5 [2.8] | 17.6 | 20.2 | 26.2 | 33.3 |

Unloading crane cycle time | s/cycle | 23.4 (5.3) | 22.5 [3.0] | 16.9 | 19.8 | 25.9 | 33.0 |

Proportion of crane work during loading drive PM time | % | 22.1 (16.3) | 18.3 [9.1] | 3.1 | 10.4 | 29.8 | 53.8 |

^{1) }Extraction distance = mean of Driving loaded and Driving empty distances.^{2) }Different superscript letters within speed variables indicate significant differences (p < 0.001, one-way ANOVA with Tukey test, n = 8868).^{3) }Different superscript letters within crane cycle numbers indicate significant differences (p < 0.001, paired t-test, = 8868). Differences between the pairs were normally distributed. n |

Table 3. Forwarding time consumption (second/load) in total (Tot.), during PM work and during Other time (Other) as functions of extraction distance (Ext.Dist.) (metre). Models were also derived separately for work elements Driving empty (D.E.), Loading (L.), Driving loaded (D.L.) and Unloading (Unl.). SE = standard error, n = number of loads, S = standard error of the estimate. Ext.Dist. = mean of Driving loaded and Driving empty distances. | |||||||||

Dependent variable | Predictor | Coefficient | SE coeff. | T-value | Model | Bias correction | |||

F | R^{2}(adj) (%) | S | n | ||||||

Ln(Tot.) | Ln(Ext.Dist.) | 0.20568 | 0.00440 | 46.70 | 2180.63 | 19.8 | 0.412911 | 8857 | 1.09104 |

Constant | 6.7821 | 0.0225 | 301.25 | ||||||

Ln(PM) | Ln(Ext.Dist.). | 0.20492 | 0.00403 | 50.85 | 2585.46 | 22.6 | 0.377802 | 8857 | 1.07189 |

Constant | 6.6508 | 0.0206 | 322.87 | ||||||

Ln(Tot. Other) | Ln(Ext.Dist.) | 0.2438 | 0.0116 | 21.06 | 443.57 | 4.8 | 1.08514 | 8856 | 1.85197 |

Constant | 4.1012 | 0.0592 | 69.32 | ||||||

Ln(D.E. Tot.) | Ln(Ext.Dist.) | 0.82937 | 0.00895 | 92.71 | 8594.49 | 49.3 | 0.837579 | 8843 | 1.27755 |

Constant | 1.3692 | 0.0457 | 29.93 | ||||||

Ln(D.E. PM) | Ln(Ext.Dist.) | 0.91374 | 0.00772 | 118.36 | 14009.34 | 61.8 | 0.692162 | 8676 | 1.13247 |

Constant | 0.5266 | 0.0396 | 13.28 | ||||||

Ln(L. Tot.) | Ln(Ext.Dist.) | 0.07133 | 0.00575 | 12.41 | 153.91 | 1.7 | 0.539013 | 8857 | 1.16125 |

Constant | 6.7165 | 0.0294 | 228.54 | ||||||

Ln(L. PM) | Ln(Ext.Dist.) | 0.08332 | 0.00539 | 15.45 | 238.80 | 2.6 | 0.505486 | 8857 | 1.13196 |

Constant | 6.5926 | 0.0276 | 239.20 | ||||||

Ln(D.L. Tot.) | Ln(Ext.Dist.) | 0.67811 | 0.00797 | 85.06 | 7235.81 | 45.0 | 0.747323 | 8857 | 1.24241 |

Constant | 1.8581 | 0.0407 | 45.60 | ||||||

Ln(D.L. PM) | Ln(Ext.Dist.) | 0.85758 | 0.00877 | 97.73 | 9551.91 | 52.8 | 0.770664 | 8555 | 1.23240 |

Constant | 0.6436 | 0.0452 | 14.25 | ||||||

Ln(Unl. Tot.) | Ln(Ext.Dist.) | 0.06774 | 0.00589 | 11.50 | 132.34 | 1.5 | 0.552018 | 8857 | 1.19892 |

Constant | 5.8954 | 0.0301 | 195.87 | ||||||

Ln(Unl. PM) | Ln(Ext.Dist.) | 0.07086 | 0.00526 | 13.48 | 181.77 | 2.0 | 0.492719 | 8857 | 1.14050 |

Constant | 5.7843 | 0.0269 | 215.31 | ||||||

Ln(D.E. Other) | Ln(Ext.Dist.) | 0.7479 | 0.0228 | 32.77 | 1073.97 | 11.3 | 2.02959 | 8402 | 4.12739 |

Constant | –0.420 | 0.118 | –3.58 | ||||||

Ln(L. Other) ^{1)} | Ln(Ext.Dist.) | –0.0165 | 0.0158 | –1.05 | 1.09 | 0.0 | 1.47879 | 8853 | 3.38023 |

Constant | 3.6225 | 0.0807 | 44.91 | ||||||

Ln(D.L. Other) | Ln(Ext.Dist.) | 0.2328 | 0.0174 | 13.40 | 179.43 | 2.1 | 1.57333 | 8508 | 2.74649 |

Constant | 1.3921 | 0.0892 | 15.60 | ||||||

Ln(Unl. Other) | Ln(Ext.Dist.) | 0.0677 | 0.0183 | 3.70 | 13.66 | 0.1 | 1.71746 | 8854 | 4.51765 |

Constant | 2.5647 | 0.0937 | 27.38 | ||||||

p-value < 0.001 for all the coefficient estimates (including both ln(Ext.Dist) and constant) and models – ^{1)}except, p = 0.296 for both Ln(Ext.Dist) and the model. When estimating dependent variables, the predicted dependent variable may be multiplied by the given correction factor for logarithmic bias (i.e. bias correction). For example: Driving empty = 1.27755×exp(1.3692 + 0.82937×ln(Ext.Dist.)). |