Question 11 of 13: Truck-Shovel Match Factor and Dispatch

Question 5: Truck-Shovel Match Factor and Dispatch (15 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.

Given.

Find. Truck cycle time and match factor (5.3.1); trucks required, closed-out vs. dispatched (5.4.2/5.4.3); the more efficient configuration and its 8-hour shift production (5.4.4/5.4.5).

Approach. Define the dispatch algorithm classes conceptually, then work the two truck-cycle problems in sequence: the single-shovel cycle/match-factor calculation (5.3.1), and the two-shovel closed-out vs. dispatched fleet-size comparison (5.4), which turns on whether trucks are allowed to use the short cross-links (green, Fig. 5.1) instead of always returning to their own shovel.

1. 5.1 – BP, LP, DP dispatch methods. Best Path (BP) is a greedy, real-time rule: at the moment each truck becomes available, assign it to whichever shovel currently offers the best local outcome (e.g. shortest expected queue, or highest current shovel productivity) – simple and fast to compute, but myopic, since it does not look ahead to how that assignment affects the whole system a few cycles later. A Linear Program (LP) formulates the assignment as an optimization over a planning horizon – maximize total tonnage (or minimize truck-hours) subject to shovel-capacity, truck-availability and haul-route constraints – and solves for the globally optimal truck-to-route allocation for that horizon, accomplishing a genuinely optimal (not just locally reasonable) fleet allocation at the cost of needing to re-solve as conditions change. A Dynamic Program (DP) sequences a series of such assignment decisions over discrete time stages, explicitly accounting for how an assignment now constrains or enables options later (e.g. truck position, remaining shift time), which suits problems where the decision sequence itself (not just the final allocation) matters – it accomplishes a time-consistent optimal policy rather than a single-horizon snapshot.
2. 5.2.1/5.2.2 – production vs. truck count, and over-trucking. Shovel production (t/shift) rises with the number of trucks assigned, but with diminishing (concave) curvature: with too few trucks the shovel is starved (idle, waiting for the next empty truck), so each added truck raises production almost linearly at first; once enough trucks are assigned that the shovel is essentially never idle, production flattens to the shovel’s own maximum dig/swing/load rate, and further trucks add nothing but standing (queued) time at the shovel. Assigning roughly twice the theoretical requirement (5.2.2) therefore does not raise production beyond the shovel’s own ceiling – it simply creates a permanent truck queue at the shovel, wasting capital and operating cost on trucks that spend most of their cycle waiting rather than hauling, and can create a secondary congestion/safety hazard at the loading area.
3. 5.2.3 – spotting, double back-up, drive-by. Spotting is the truck manoeuvring into the shovel’s loading position (typically backing into place under the dipper/bucket) before loading begins; it is unavoidable dead time in every cycle, minimized by good approach/blast-pattern layout that gives the truck a straight, unobstructed spotting lane. In a double back-up configuration two trucks alternate spotting on either side of the shovel, so the shovel swings left-right-left between them with essentially no gap while the off-side truck spots – this needs a wider, symmetric muck-pile/blast layout with clear space on both sides of the shovel. A drive-by configuration has the next empty truck already positioned and driving directly into the loading spot the moment the loaded truck pulls away (a single-file, one-side approach), needing only one clear approach lane rather than two, at the cost of the shovel briefly waiting through each truck exchange rather than swinging continuously between two pre-spotted trucks.
4. 5.3 – Match factor, definition. Match factor is the ratio of truck arrival rate to shovel service rate for a given fleet: $MF = \dfrac{N_{trucks}\times t_{load}}{N_{shovels}\times t_{cycle}}$. MF < 1 means the shovel is under-trucked (idles waiting for trucks); MF = 1 means trucks and shovel are exactly matched (neither queues); MF > 1 means trucks queue at the shovel.
5. 5.3.1 – cycle time and trucks for MF = 1. $$T_{cycle} = t_{load}+t_{haul}+t_{dump}+t_{return} = 3.0+12.0+1.0+8.0 = \boxed{24.0\ \text{min}}$$ $$N_{trucks}(MF=1) = \frac{T_{cycle}}{t_{load}} = \frac{24.0}{3.0} = \boxed{8\ \text{trucks per shovel}}$$
6. 5.4.2/5.4.3 – closed-out fleet. Each shovel runs its own dedicated 24-min loop (identical cycle structure to 5.3.1 on both the ore and waste routes, since load/dump/haul/return times match), so each needs 8 trucks for MF = 1: $$N_{closed-out} = 8\ (\text{Shovel 1}) + 8\ (\text{Shovel 2}) = \boxed{16\ \text{trucks}}$$
7. 5.4.2/5.4.3 – dispatched fleet. A dispatched truck need not return empty to its own shovel – after dumping ore at the crusher it can take the short 4-min link to Shovel 2 (rather than the 8-min return to Shovel 1), load waste, haul to the dump, then take the short 3-min link back to Shovel 1 to load ore again, forming one combined circuit that services both shovels: $$T_{circuit} = \underbrace{12+1}_{\text{haul+dump ore}} + \underbrace{4}_{\text{Crusher}\to\text{S2}} + \underbrace{3+12+1}_{\text{load+haul+dump waste}} + \underbrace{3}_{\text{Dump}\to\text{S1}} = \boxed{36\ \text{min per circuit}}$$ Each 36-min circuit visits each shovel exactly once (one 3-min load event at each); spacing trucks 3 minutes apart around this single loop keeps both shovels continuously fed: $$N_{dispatched} = \frac{T_{circuit}}{t_{load}} = \frac{36}{3} = \boxed{12\ \text{trucks (for both shovels combined)}}$$
8. 5.4.4 – which is more efficient. $$\text{Fleet saving} = 16-12 = 4\ \text{trucks} \;\left(\frac{4}{16}=25\%\ \text{fewer}\right)$$ Dispatched operation is more efficient: by routing empty trucks over the short cross-links instead of forcing every truck back to its own shovel, the same two-shovel production is sustained with 25% fewer trucks – capital, fuel, tyres, maintenance and operators for four trucks are saved outright.
9. 5.4.5 – loads per 8-hour shift. Each of the 12 dispatched trucks completes one full circuit (delivering one ore load to the crusher and one waste load to the dump) every 36 minutes: $$\text{circuits/truck in 480 min} = \frac{480}{36} = 13.33 \;\Rightarrow\; 13\ \text{complete circuits}$$ $$\text{Total loads} = 12\ \text{trucks}\times13\ \text{circuits} = \boxed{156\ \text{ore loads to the crusher and 156 waste loads to the dump}}$$ This is realistic as an upper bound – it assumes continuous, delay-free operation for the full shift, so a real shift (shift-change, blast clearances, queueing variability, the un-completed 0.33 of a circuit) would deliver somewhat fewer than 156 loads per destination, but the order of magnitude is a sound production planning figure.
10. 5.5 – on-board dispatch hardware (2 marks).
    • GPS/GNSS receiver on every truck and shovel – continuous, high-accuracy position for real-time fleet tracking and automated cycle-segment timing.
    • On-board computer / vehicle terminal (VIMS-type unit) with a driver display – receives dispatch assignments, shows the next destination, and logs payload, cycle events and machine health data.
    • Two-way radio/wireless data network (trunked radio or dedicated WiFi/LTE mesh across the pit) linking every unit to the central dispatch server in real time.
    • Payload (weightometer) sensor on the truck suspension or body – logs each load’s tonnage automatically for production accounting and to flag under/over-loading.
    • Shovel-mounted swing/bucket sensors and pass counter – times each loading pass and estimates when the truck is full, feeding the dispatch system’s shovel-productivity model.
    • Central dispatch server running the BP/LP/DP assignment algorithm (5.1) against the live position/status feed from every unit, closing the loop back to each vehicle’s on-board terminal.