Question 6 of 13: 6 (6 marks, compulsory)

Question 1.6 (6 marks, compulsory)

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.

1.6.1 – Best Path (BP). A best-path (shortest-path) dispatch rule assigns each empty truck to the shovel/dump combination that minimises that individual truck’s own travel/queue time at the moment of the decision – a purely local, greedy, real-time rule (closely related to a network shortest-path calculation over the current haul-road graph and queue states). It accomplishes low complexity and instant decisions with minimal computation, but because it is greedy it can starve one shovel while over-serving another, and it does not explicitly optimise any fleet-wide objective.

1.6.2 – Linear Program (LP). An LP dispatch model formulates truck-to-shovel assignment (or, more often, the fraction of the fleet’s time allocated to each shovel-dump route over a planning interval) as a linear objective (e.g. maximise total tonnage, or minimise total truck-hours) subject to linear constraints (shovel digging capacity, truck fleet size, required blend/grade ratios, dump/crusher capacity), solved to global optimality for that interval by standard LP methods (simplex/interior point). It accomplishes a mathematically optimal STEADY-STATE allocation of the whole fleet across all shovels simultaneously, honouring blend and capacity constraints that a greedy rule like BP cannot see, but it is a static snapshot – it must be re-solved (or re-optimized) whenever conditions change materially within the shift.

1.6.3 – Dynamic Program (DP). A DP dispatch model treats truck assignment as a multi-stage sequential decision problem, optimising the CUMULATIVE objective (e.g. total production, or minimised total waiting time) over the remainder of the shift by considering the full state of the system (queue lengths, truck positions, remaining shovel capacity) at each decision epoch and choosing the assignment that is optimal given all possible future states, not just the immediate one. It accomplishes what LP and BP cannot: a truly optimal SEQUENCE of assignments over time that properly anticipates how today’s dispatch decision affects tomorrow’s queues, at the cost of much higher computational complexity, which is why most real dispatch systems in practice use LP for the target allocation and a fast heuristic (close to BP) for the real-time assignment that tracks it.