Question 7 of 11: Open-Pit Ore and Waste Scheduling (NW-Corner Method)

Question 2: Open-Pit Ore and Waste Scheduling (NW-Corner Method) (20 marks, optional – answered in full)

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. Ore: Phase 1 (elevation:Mt) 1970:5, 1955:9, 1940:6, 1925:3, 1910:1 (total 24 Mt); Phase 2: 1970:2, 1955:4, 1940:6, 1925:5, 1910:4, 1895:3, 1880:2 (total 26 Mt) – mined strictly Phase 1 before Phase 2, 7 Mt/yr NW-corner from year 1. Waste: Phase 1 2000:5, 1985:8, 1970:11, 1955:9, 1940:7, 1925:3 (total 43 Mt); Phase 2: 2000:2, 1985:4, 1970:5, 1955:11, 1940:8, 1925:7, 1910:3, 1895:1 (total 41 Mt) – 6 Mt in year -1, 12 Mt/yr thereafter, NW-corner.

Find. The resulting ore and waste schedule by year, and the answers to 2.1.1–2.3.1.

Approach. Apply the NW-corner rule mechanically: fill each year's fixed capacity (7 Mt ore, 12 Mt waste, except the 6 Mt year -1 start-up) from the supply list in the ORDER given (shallowest elevation first for ore; shallowest for waste), carrying any partial-year remainder into the next elevation/year exactly as a transportation-problem NW-corner allocation does.

1. Ore schedule (verifies the printed Figure 2.1.1 table). Phase 1 (24 Mt) fills years 1, 2, 3 completely (7+7+7=21 Mt) and 3 Mt of year 4's 7 Mt capacity; Phase 2 (26 Mt) then fills the remaining 4 Mt of year 4, all of years 5, 6, 7 (7+7+7=21 Mt) and 1 Mt of year 8. Total mined $=24+26=\boxed{50\text{ Mt}}$, over years 1–8, at a steady 7 Mt/yr except the tail year 8 (1 Mt).
2. Waste schedule (verifies Figure 2.2.1). Phase 1 (43 Mt) fills year -1 (6 Mt), year 0 (12 Mt), year 1 (12 Mt), year 2 (12 Mt) and 1 Mt of year 3's 12 Mt capacity; Phase 2 (41 Mt) fills the remaining 11 Mt of year 3, years 4, 5, 6 (12+12+12=36 Mt) fully, and... the running total 6+12+12+12+11+12+12+12=89, but only 84 Mt exists, so year 6 receives only 6 Mt (the tail). Total waste $=43+41=\boxed{84\text{ Mt}}$, over years -1 to 6, at a steady 12 Mt/yr from year 0 through year 5, tailing to 6 Mt in year 6.
3. Combined material movement. Summing ore + waste by year: year -1 = 6, year 0 = 12, years 1–6 = 7+12 = 19 Mt/yr (the sustained steady-state total), year 7 = 1(ore)+6(waste, tail) = 7, year 8 = 1(ore only, Phase 2 tail, since waste is already exhausted).

2.1.1 – Timelines and risk factors for period-1 ore. To deliver the first 7 Mt of ore at the END of year 1, the mill/concentrator must be commissioned and ready to receive ore no later than the start of year 1, which fixes the construction schedule backward from that date; simultaneously, the 6 Mt (year -1) and 12 Mt (year 0) waste pre-strip MUST be completed on schedule to physically expose the Phase 1 ore blocks (1970 m elevation, the first ore mined) before year 1 mining can begin – the ore schedule is entirely dependent on the waste schedule finishing on time. Factors that can break this: mill/construction delay (the more common real-world failure, per the question's own framing “while the mill is under construction”), pre-strip productivity shortfall (equipment availability, weather, blast performance) that leaves insufficient exposed ore at year-1 start, or a permitting/land-access delay to the waste dump that throttles how fast waste can physically be placed regardless of fleet capacity.

2.1.2 – How the 1970/1955 elevations produce the table. Applying the NW-corner rule to the ore list in the order printed (shallowest elevation first): the 5 Mt at 1970 m is entirely consumed by year 1's 7 Mt capacity, leaving 2 Mt of year-1 capacity still open; that 2 Mt is filled from the NEXT elevation, 1955 m (9 Mt available), leaving 7 Mt of the 1955 m block still unmined; year 2's full 7 Mt capacity is then filled entirely from the remaining 1955 m tonnage. This is exactly why the printed table shows "1970: 5" and "1955: 2" both landing in year 1 (5+2=7), and "1955: 7" landing alone in year 2 – the NW-corner method always exhausts the current supply row before moving to the next, splitting a single elevation's tonnage across two years whenever it doesn't divide evenly by the annual capacity.

2.1.3 – Stockpiling potential. The NW-corner schedule is a PLANNING guide, not a rigid diktat, so any elevation whose ore quality, accessibility or equipment availability allows FASTER exposure than the simple year-by-year draw creates a stockpiling opportunity: (a) around the Phase-1-to-Phase-2 TRANSITION (end of year 3/start of year 4), where Phase 2 access development may run ahead of the tonnage actually needed that year – early-exposed Phase 2 ore can be stockpiled rather than held underground/in-pit unmined; (b) during the high-combined-tonnage years 1–6 (19 Mt/yr total movement), if shovel/truck availability temporarily exceeds the combined ore+waste draw rate, surplus ore exposed ahead of the mill's 7 Mt/yr intake is stockpiled for later reclaim; and (c) the tail years 7–8 (1 Mt/yr each), where a stockpile built up earlier can be blended down to smooth what would otherwise be an abrupt production drop-off at mine closure.

2.1.4 – Head grade over the deposit's life. Copper porphyry and epithermal gold deposits typically carry a higher-grade, supergene-enriched (or oxide) blanket near surface, overlying lower-grade primary (hypogene/sulphide) mineralisation at depth – so Phase 1 (shallower elevations, 1970–1910 m) is expected to run at a somewhat higher AND more variable grade than the deeper Phase 2 material (1970–1880 m, extending well below Phase 1's floor), with a visible step at the Phase 1/Phase 2 transition rather than a smooth decline (Fig. 2.1.4). The mill and concentrate load-out must be designed for this variability from day one: blending stockpiles (rather than direct-feeding a single bench) to hold head grade within the flotation/leach circuit's design window, flexible concentrate storage/load-out capacity sized for the HIGHER-grade early years (when concentrate mass per tonne milled is greatest even at constant throughput), and a metallurgical/recovery model that is re-calibrated as the ore transitions from oxide/supergene (often requiring a different process route, e.g. leach vs. flotation) to primary sulphide at the Phase 2 transition.

2.1.5 – Effect of reduced shovel availability near Phase 1 completion. Phase 1 must be FULLY mined before Phase 2 begins (a hard sequencing rule stated in the source), so any shovel-availability shortfall (from poor blast fragmentation, per the question's own framing, which drives higher dig resistance, more re-handle, and more unplanned downtime) in the final Phase 1 years directly threatens the year-4 Phase 1→2 transition: the mill can run short of ore exactly at the transition point, the Phase 2 access-development schedule (which assumes Phase 1 closes out on time) slips in lock-step, and the mine may be forced either to draw down a stockpile (Question 2.1.3) to bridge the gap or to accept a temporary drop below the 7 Mt/yr target – precisely the kind of schedule risk the Phase 1/Phase 2 hard-sequencing rule is most exposed to.

2.2.1 – Waste elevations during deep-ore mining and blast-throw safety. While Phase 2 ore is drawn from its deepest elevations (1910–1880 m, years 6–8), the corresponding waste schedule (Figure 2.2.1) is still stripping HIGHER elevations (1940–1925 m and above) on the opposite/adjacent wall to maintain the pit's overall slope and access – i.e. waste blasting is routinely occurring directly ABOVE active deep-ore benches. The safety consideration is blast-generated flyrock/throw from the upper waste benches reaching personnel and equipment working the lower ore benches; this can also physically damage exposed deep ore blocks or block haul-road access, indirectly threatening the ore tonnage schedule. Safety is improved by enforcing adequate VERTICAL benching offset/catch-benches between the active waste blast and the ore benches below, tighter blast-exclusion-zone timing (no ore-bench personnel/equipment during an upper-bench blast), reduced burden/spacing or blast-hole stemming changes on benches directly above active lower workings to control throw distance, and blast-design review (timing/delay sequencing) specifically for benches with lower-bench occupancy.

2.2.2 – Truck-hours over the mine life and its effect on the overall plan. Truck-hours track total material moved (ore + waste) closely, since haul cycle time is driven far more by tonnage and cycle distance than by destination: the schedule ramps from 6 Mt (year -1) to 12 Mt (year 0) to a sustained plateau of 19 Mt/yr (years 1–6, Fig. 2.2.2), then falls to 7 Mt (year 7) and 1 Mt (year 8) as both phases tail out. A mine plan that attempts to maintain CONSTANT truck-hours (rather than accepting this ramp-plateau-taper shape) would smooth the schedule by (i) pulling some of the pre-production waste (years -1/0) forward or deferring a small amount of early Phase-1 waste into the plateau years to flatten the ramp, and (ii) blending Phase 2's tail-year waste forward into the plateau (again subject to the Phase 1-before-Phase 2 ore rule, which does NOT constrain waste sequencing the same way) so the fleet is not oversized for six years and then idle for two – i.e. the schedule's OWN combined-tonnage profile is the direct input to fleet-sizing and utilization planning.

2.2.3 – Would purchased/rented used trucks help? Yes, and the truck-hour profile (Fig. 2.2.2) shows exactly why a RENTAL (rather than purchased) fleet addition is the better fit here: the mine only needs its peak fleet size for the plateau years (1–6), with materially lower demand in the ramp-up (-1, 0) and tail-out (7, 8) years. Renting/leasing used trucks to cover just the plateau period avoids owning capital equipment that sits partly idle for a third of the mine's life, while a straight PURCHASE of the full peak fleet up front would face exactly that under-utilization problem in the ramp and tail years – the same trade-off already flagged for the auxiliary equipment needed at the dragline's capability shortfall in Question 4.7.

2.2.4 – Maximum/minimum annual stripping ratio. Stripping ratio (SR) $=$ waste tonnes / ore tonnes for each year. Year -1 and year 0 mine ONLY waste (no ore yet), so SR is undefined/infinite in those pre-production years – excluded from a like-for-like annual comparison. Among the ore-producing years: the MAXIMUM occurs where waste is still at its 12 Mt/yr plateau while ore is only 7 Mt/yr (years 1–5), $SR_{max}=12/7\approx\boxed{1.71:1}$; the MINIMUM occurs in the tail years once waste has been exhausted (year 7: 6 Mt waste/1 Mt ore $=6:1$, worse, not better – so the true minimum is actually year 8, where waste is fully exhausted, $SR_{min}=0/1=\boxed{0:1}$). Knowing this range does help maintain constant truck-hours: since SR varies year to year while the COMBINED tonnage (ore+waste) is what actually drives truck-hours, a planner who tracks SR alongside total tonnage can see that the low-SR tail years (7–8) are exactly where fleet size can be safely trimmed (or trucks reassigned to a rental return, per 2.2.3) without under-serving the ore schedule.

2.2.5 – Waste-before-ore sequencing. Yes – by construction, waste mining STARTS well before ore mining in every phase (years -1/0 waste-only pre-strip precede year 1's first ore, per the source's own start-up description), which is correct practice, not a broken rule. The rule that WOULD be broken is the reverse: ore must never be exposed/scheduled to be mined before its OVERLYING waste has been stripped clear (the fundamental "waste leads ore" sequencing rule underlying every open-pit schedule, and the same physical constraint the moving-cone/Lerchs–Grossmann pit-limit logic of Question 1.5/5.2 encodes at the block level) – nothing in this NW-corner schedule violates it, since the ore-schedule elevations are drawn only after their corresponding waste elevations are shown stripped in Figure 2.2.1.

2.3.1 – Has the simple scheduler given the planning engineer a solid basis? (bonus, 2 marks) Only partially. The NW-corner method is a useful FIRST-PASS teaching/planning tool – it guarantees a feasible schedule that respects the stated capacities and the Phase 1-before-Phase 2 rule, and it is transparent enough to sanity-check by hand (Question 2.1.2). But it optimizes nothing: it makes no reference to discounted cash flow (Question 1.2.3's front-loading argument is entirely absent), grade/blend requirements at the mill (Question 2.1.4), equipment-fleet utilization smoothing (Question 2.2.2–2.2.3), or the true Lerchs–Grossmann pit-limit/pushback logic of Question 1.5. My recommendation: use the NW-corner result as the INITIAL feasible schedule and starting point, then re-optimize it with an NPV-based mixed-integer or LP mine-scheduling model (subject to the same capacity and Phase-sequencing constraints) to pull value forward per Question 1.2.3, smooth the truck-hour profile per Question 2.2.2, and explicitly manage head-grade blend into the mill – i.e. treat this figure as a feasibility check and short-term (annual) production guide, not as the long-term (10–20 year) financial optimum.