25 Stochastic Scheduling Has Arrived - Finally!
Mark Bowater
► Leaving Mine Planning In A Better Place Than I Found It ► Developing Mining Engineers ► Improving Mine Planning Systems
On November 1st (2022) I gave the keynote presentation at the Brisbane Deswik Users Conference, the title of that talk was “Deterministic Scheduling – It Is So Last Century”. If you’ve read my book then you’ll know that I think deterministic scheduling is the root of all evil and that one of the greatest mine planning crimes is our unwavering faith in the reliability of outputs from this form of scheduling.
I spoke about one of the issues in mine planning that (sadly) gets an inadequate level of attention – risk. I highlighted how we consciously choose to introduce risk into our mining operations, such as operating with low preventative maintenance and running parts to failure, which subsequently leads to high variability in our mine planning. I believe there were many in the audience who agreed with me, but it was a presentation later in the day that I gained the most satisfaction from.
Patrick Doig and Todd Valance from Deswik gave a presentation titled - Stochastic Scheduling. Now I admit, after all my “banging on” about stochastic scheduling for so long now, there was a small element of apprehension about whether they had any findings of value, but that apprehension was small compared with my anticipation for what I might learn. And they did not disappoint, I’ll be honest, even I was blown away with the outcomes and very excited about the future.
Let’s start with the primary learnings I took away from the presentation:
Slippage
Sitting in the audience, I admit to a little fist pump when Pat and Todd put up the slide showing the chart in Figure 1. It backed up what I wrote about in both my book and Article 15, that the combination of variability and task dependencies means it is basically impossible to achieve the schedule. The figure shows the planned end of life for an underground metal mine, with both deterministic and stochastic results shown – these results are from a relatively simple, mine schedule example.
The deterministic schedule showed an end of mine life of April 2039, while the stochastic results varied between July 2040 and July 2041. The mean end date (P50) was December 2040, 20 months later than the deterministic schedule, which is a slippage of approximately 10%.
Preliminary works also seem to suggest that the slippage in a highly constrained underground mine is greater than in a highly flexible open pit mine with numerous faces to choose from. This finding obviously needs additional testing and analysis yet, but at face value seems entirely logical as maximising flexibility is one step in the process of lowering risk.
Areas of Risk
Recently I have been talking about one of the benefits of stochastic scheduling being that you can see where the areas of highest risk are in the mine plan, in other words, where the plan could go off the rails. I really like the chart shown in Figure 2 that was put together by Todd and Pat because it highlights exactly that. The chart shows the cumulative product tonnage for a number of simulations and there are two clear inflection points which are circled in red. The left hand inflection point indicates something that has happened in the schedule which in a number of cases led to a reduction in product of about 1Mt. Then in those plans which were already suffering from reduced tonnages, there is a second inflection point that leads to a variation between best and worst cases of an additional 1Mt of product.
By reviewing the schedules with the lower tonnages and comparing to the higher tonnage schedules, it is possible to identify what has happened and subsequently where an area of high risk sits in the schedule.
Recommended by LinkedIn
Critical Path
In my Article 13 on LinkedIn, I challenged the norm that mine scheduling usually doesn’t consider the critical path and asked the question as to why we don’t. Consequently, it was interesting to see the schedule critical path become a point of focus by Pat and Todd and that it had an important role to play. The tool was modified so that it was possible to report the percentage of the simulations that each task was on the critical path. Armed with this information, it was then possible to re-run a series of schedules where tasks were prioritised based on the frequency with which they were on the critical path. As shown in Figure 3, this change in priorities resulted in a lift in annual production from 910 for the original scenarios (grey) to 950 for the critical path prioritised scenarios (pink). In this example, that is an increase of 4.4% achieved purely by focussing on the “right” tasks.
In Chapter 6 of Crimes Against Mine Planning I write about how to execute a plan and provide a methodology for choosing tasks to prioritise and then how to go about focussing production efforts on those tasks. Stochastic scheduling now provides a more scientific method of selecting the key tasks to focus on in execution than the simple rules I developed previously.
An interesting additional benefit of prioritising the critical path is that the range of potential outcomes has significantly reduced. The original scenarios (grey) had a range of outcomes that varied by 20% on either side of the mean, whereas the scenarios that prioritised critical path tasks (pink) only varied by 10% on either side of the mean. That is a halving of the potential variability in outcomes and therefore a lowering of downside risk.
Improvement Opportunities
One fascinating part of the presentation was that it was evident that Pat and Todd were learning as they used the tool on varying cases and that this was leading to new questions and subsequently new developments to the tool to be able to answer those questions. Sometimes new reporting capabilities were required, sometimes it was changes to how the tool worked, and sometimes it was determining new scenarios to run. As I have always said, a good mine plan leads to more questions than answers, particularly life-of-mine plans, which should always indicate new scenarios worthy of investigation. It was great to see that happening here.
One of the outcomes from the presentation I was most excited about was that stochastic scheduling can be used for the purposes of improving the plan. To date, I have envisaged it being difficult to sell stochastic scheduling because it will produce mine plans with reduced outcomes from deterministic schedules. Undoubtedly the results will be more realistic, but still, lower nonetheless, and I could imagine the mine executives saying “why on earth do I want to spend money transitioning to a mine planning process that provides lower outcomes than the existing one? I don’t want fewer tonnes, I want more!”
But this presentation showed that stochastic scheduling can also be used as a mine plan improvement tool, as shown by the critical path analysis above. In addition, Pat and Todd used the tool to test the range of potential plan production increases that may be achieved by adding extra resources to the mine. Figure 4 shows the range of outcomes for the cases with extra resources (in purple) versus the critical path prioritised cases (in pink). Most mining companies build some form of range analysis into their financial modelling of investment decisions, stochastic scheduling enhances that capability, leading to increased confidence levels in investments.
It was fantastic to see the wide range of benefits stemming from stochastic scheduling and that it can be used to test so many areas of value at mine sites, one that I can’t wait to test is how well the Theory of Constraints works in mining. Now that we have stochastic capability, there are numerous areas to write about in this subject and I have plenty of discussions to initiate. But I’ll be doing that via my new podcast titled Mine Planning MATTERS, so keep an eye out for that.
If you need convincing that we should be switching to stochastic scheduling, then you can find the link to the video recording of my keynote here. But if you only have time to watch one video, then I would recommend watching the presentation by Todd and Pat here.
This article is one of a series of articles on various issues and topics relating to mine scheduling. If you found this article of value, then you may want to start back at the beginning of the series of articles, click here.
For quality conversations on a range of mining engineering subjects, I'd encourage you to join the free mining engineering community called The Crew where we share our knowledge and support each other, click here
General Manager Gualcamayo Mine - Director Minas Argentinas.
2yImpresionante. Gracias por compartir.
Business Analyst | Software Development & Data Analysis for the Mining & Metals Industry
2yThe finish date is just an agreement on the day when everyone will sit together and think "okay, when will we get this done?" 😂
Customer Success | Product Management | Mine Planning | Mine Scheduling | Mine Optimization
2yNPV is a great metric for relative comparison and prioritization of projects but somewhere along the way it became the end all be all in mining. As an industry we need to put more emphasis on developing and analyzing more information about mine planning and scheduling as you have pointed out both here and in the past. One of the big problems I see is related to funding technical services teams and the tools they need. Part of this is related to the fact that you don’t create any revenue when you publish a plan or create a new geo model. If it were ground engaging tools that’d be a different story.
President Director PT SMG Consultants
2yI would argue that there is an issue that I see almost universally that goes well before scheduling and that relates to Resource geologist focus on Resource model with teh objective of estimation of the Resource. We end up with models that give a fine estimate of the global Resource in terms of tonnes and grade but ar essentially useless for mine planning. We lose the granularity that exists in borehole databases and sampling behind layers of assumptions to arrive at a Resource estimate.
Aligning mental, business and engineered system models for uncertain futures.
2yWhen we created a new concept for flexible underground mines, we used mechanical cutting and a novel topology that offers great choice of faces, tolerating the increased dilution by means of underground bulk sorting and in-situ backfill. Because mechanical cutting advance rates are non-linearly dependent on rock properties, it is simply not sensible to have a deterministic schedule. So instead we created sequencing algorithms based on rules for machine dispatch. This allows us to simulate outcomes over a wide variety of stochastic variations. We are targeting resilience vs efficiency. We are probably the only people who believe in doing less exploration, extracting less precisely, and tolerating ore body ignorance. But with the right system architecture, sufficient volatility in the operating context, and urgency of metal-to-market need, we think it becomes advantageous.