1. Production Capacity of Truck and Loader Teams ©Dr. B. C. Paul 2003

2. Production Can be Limited by Either the Truck or Loader l Example 6 Cat 773 trucks work 10 hours/day 6 days/ week and 40 weeks/year 10 minutes moving cycle Loaded in 4 passes with 992 Drive by with no spot time 2.8 minutes 12.8 min total cycle

3. Calculating the Truck Production l 144,000 minutes/year at 12.8 minutes/cycle 11,250 trips at 57.98 tons/trip 652,275 tons/truck per year l Trucks breakdown Say they run 85% of the time 652,275*0.85 = 554,434 tons

4. More Truck Production l Workers not running equipment all shift Say 50 minutes/hour or 0.83 554,434*0.83 = 460,180 tons l Loader won’t work all the time Say it runs 85% of the time 0.85 460,180*0.85 = 391,153 tons

5. Finishing? Truck Production l May not utilize equipment all the time it is available Say 95% utilized of available 391,153*0.95 = 371,595 tons l Off course we know we may have to worry about trucks bunching but lets say we ignore that l For 6 trucks I could haul out 2.23 million tons per year Obviously ignoring any bunching up at the loader

6. Now Lets Look at My Loader’s Production l 144,000 minutes with 0.7 minutes/pass Loader could do 205,714 cycles/year At 14.495 tons/pass 2.982 million tons l Loader only runs 85% 2.535 million tons

7. More Loader Production l Loader Operator working 50 min/hour 2.104 Million l Utilized of Available 95% 1.998 Million tons l This of course assumes there is always a truck there to be loaded

8. Question of the Day l How did my trucks haul out 2.23 million tons of rock if the loader could only load 1.998 million tons under best conditions? l Of course the answer is that loader was limiting l Check of Over-trucked 12.8 minutes/truck cycle/2.8 minutes/loader 4.57 trucks/loader (ie 6 trucks is more than the loader can possibly handle)

9. Conclusion l When one is over-trucked it is the loader that determines production

10. How to Handle Bunching l If I have 6 trucks and 1 loader l Calculate my Match Factor 6*2.8/(1*12.8) = 1.3125 Number greater than 1 indicates over- trucked l Look up my bunching factor 0.952 Trick is that bunching is applied to the limiting part of the system (ie the loader)

11. Calculating Production l Theoretically could do 1.998 million tons/year 1,998,496 * 0.952 = 1,902,568 l What 0.952 bunching meant was that 95.2% of the time when the loader had a scoop of material it would have a truck there waiting (even over-trucked its not always there)

12. What We Haven’t Considered l I just assumed that I had 6 trucks ready to go whenever my loader was Reality is that trucks could be broken too. l Noted that all my examples so far were based on trucks with only 1 loader that was conveniently there or not there

13. How to Handle Truck Break-downs l Binomial Probability gives me the odds on any number of trucks working Not too scary with the spreadsheet to do all the work 6 trucks 37.71% 5 trucks 39.93% 4 trucks 17.62% 3 trucks 4.14% 2 trucks 0.55% Lower numbers have little chance

14. Solution Approach l I have 5 truck fleets that have some chance of happening 37.71% chance of 6 trucks to one loader This fleet could produce 1.903 Million tons per year l Find What I could produce with the other 4 fleets and what there probability is l Do a weighted average of my production rates to see what my fleet could most likely produce

15. 5 Trucks to One Loader l Match Factor 5*2.8/(1*12.8) = 1.09375 Still over-trucked ie the loader is the limit to which bunching is applied l Bunching Factor is 0.886 Note that as # trucks went down the chances that one would be waiting went down Production Loader Full Production 1.998 Million tons * 0.886 = 1.771 Million tons l Probability is 39.93%

16. 4 Trucks to 1 Loader l Calculate Match Factor 0.875 Note this is under 1 which means that trucks are now the limiting step l Bunching Factor is 0.885 l Production per Truck without bunching is 371,595 tons 371,595*0.885 = 328,862 tons/truck l For 4 trucks 1,315,000 tons Probability is 17.62%

17. 3 Trucks and 1 Loader l Match Factor 0.656 l Bunching is 0.931 applied to trucks l Production per truck is 345,955 tons/year (with 0.931 bunching) For 3 Trucks 1,038,000 tons/year with 4.14% probability

18. 2 Trucks and 1 Loader l Match Factor = 0.4375 l Bunching = 0.979 l Production/Truck = 363,792 tons/year l Two Trucks 727,582 tons/year With 0.55% Probability

19. Doing the Weighted Average l 1,903,000 * 0.3771 + l 1,771,000 * 0.3993 + l 1,315,000*0.1762 + l 1,038,000 * 0.0441 + l 727,582 * 0.0055 = l 1,703,000 tons per year is the expected production of 6 truck and 1 loader Note that probability of the loader being down was the 0.85 used in both the loader and the truck capacity