Production Capacity of Truck and Loader Teams

©Dr. B. C. Paul 2003

Production Can be Limited by Either the Truck or Loader

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

Calculating the Truck Production

144,000 minutes/year at 12.8 minutes/cycle• 11,250 trips at 57.98 tons/trip• 652,275 tons/truck per year

Trucks breakdown • Say they run 85% of the time• 652,275*0.85 = 554,434 tons

More Truck Production

Workers not running equipment all shift• Say 50 minutes/hour or 0.83• 554,434*0.83 = 460,180 tons

Loader won’t work all the time• Say it runs 85% of the time 0.85• 460,180*0.85 = 391,153 tons

Finishing? Truck Production

May not utilize equipment all the time it is available• Say 95% utilized of available• 391,153*0.95 = 371,595 tons

Off course we know we may have to worry about trucks bunching but lets say we ignore that

For 6 trucks I could haul out 2.23 million tons per year• Obviously ignoring any bunching up at the

loader

Now Lets Look at My Loader’s Production

144,000 minutes with 0.7 minutes/pass• Loader could do 205,714 cycles/year• At 14.495 tons/pass 2.982 million

tons Loader only runs 85%

• 2.535 million tons

More Loader Production

Loader Operator working 50 min/hour• 2.104 Million

Utilized of Available 95%• 1.998 Million tons

This of course assumes there is always a truck there to be loaded

Question of the Day

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?

Of course the answer is that loader was limiting

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)

Conclusion

When one is over-trucked it is the loader that determines production

How to Handle Bunching

If I have 6 trucks and 1 loader Calculate my Match Factor

• 6*2.8/(1*12.8) = 1.3125• Number greater than 1 indicates over-

trucked Look up my bunching factor

• 0.952• Trick is that bunching is applied to the

limiting part of the system (ie the loader)

Calculating Production

Theoretically could do 1.998 million tons/year• 1,998,496 * 0.952 = 1,902,568

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)

What We Haven’t Considered

I just assumed that I had 6 trucks ready to go whenever my loader was• Reality is that trucks could be broken

too. Noted that all my examples so far

were based on trucks with only 1 loader that was conveniently there or not there

How to Handle Truck Break-downs

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

Solution Approach

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

Find What I could produce with the other 4 fleets and what there probability is

Do a weighted average of my production rates to see what my fleet could most likely produce

5 Trucks to One Loader

Match Factor• 5*2.8/(1*12.8) = 1.09375• Still over-trucked ie the loader is the limit to which

bunching is applied 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 Probability is 39.93%

4 Trucks to 1 Loader

Calculate Match Factor 0.875• Note this is under 1 which means that

trucks are now the limiting step Bunching Factor is 0.885 Production per Truck without bunching

is 371,595 tons• 371,595*0.885 = 328,862 tons/truck

For 4 trucks 1,315,000 tons• Probability is 17.62%

3 Trucks and 1 Loader

Match Factor 0.656 Bunching is 0.931 applied to trucks Production per truck is 345,955

tons/year (with 0.931 bunching)• For 3 Trucks 1,038,000 tons/year with

4.14% probability

2 Trucks and 1 Loader

Match Factor = 0.4375 Bunching = 0.979 Production/Truck = 363,792

tons/year Two Trucks 727,582 tons/year

• With 0.55% Probability

Doing the Weighted Average

1,903,000 * 0.3771 + 1,771,000 * 0.3993 + 1,315,000 *0.1762 + 1,038,000 * 0.0441 + 727,582 * 0.0055 = 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