Question 2 of 27

Question 1.2 (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

1.2.1 — shovel production vs. truck count. Production rises steeply and almost linearly as trucks are added while trucks are the constraint (shovel sits idle between trucks), then bends over and flattens to a horizontal asymptote once enough trucks are present that the SHOVEL itself becomes the bottleneck (loading continuously back-to-back) — the classic diminishing-returns (concave-down, saturating) curve. The bend occurs at the theoretical truck number Nt = truck cycle time / shovel loading time (Question 2.1.3 works this exact ratio).

1.2.2 — twice the theoretical trucks. The shovel is already saturated at Nt trucks, so a second Nt worth of trucks adds NO further production — the extra trucks simply queue at the shovel, idling and building a long, growing truck queue; match factor roughly doubles to about 2, truck utilization collapses toward 50%, and the operation wastes capital and fuel on standing, idle trucks while the shovel (the true bottleneck) sees no benefit. This is the practical reason dispatch systems exist — to prevent exactly this over-assignment.

1.2.3 — spotting, double back-up, drive-by. Spotting is the shovel operator or truck driver manoeuvring the truck into the single loading position at the shovel before loading starts — every truck must fully stop, back up and align before the shovel can load it, costing 0.3–0.7 min per truck. Double back-up (double-sided spotting) provides TWO truck positions on opposite sides of the shovel so the shovel finishes loading one truck and swings directly onto the next already-spotted truck with no shovel wait, at the cost of extra bench room and blast-pattern width to keep both approach roads open. Drive-by (or “live loading”/“flow-through”) loading lets the truck drive slowly past the shovel without stopping/backing at all (used with continuous loaders or very open blast layouts), eliminating spotting time entirely but requiring a much wider, straighter approach and departure lane than a conventional blast pattern provides.