

Calculating Delivery Efficiencies
Name: Scott S.
Status: Other
Age: 30s
Location: N/A
Country: N/A
Date: N/A
Question:
I am trying to calculate delivery efficiencies for our
fleet of trucks, and we have equations to calculate cost from point A
(the terminal) to point B (the customer). That's all well and good for
two dimensional thinking. What I would like to do is to incorporate
altitude changes into the equation.
For instance, if point A is at Sea
Level, and point B is at an elevation of 1000 feet, I would like to find
the difference in cost per mile. In other words, what is the diffenence
between the cost if point A and B were both as sea level as opposed to
being 1000 feet different?
Replies:
Scott,
I really do not know of an equation which could quantify this...my suspicion
would be that fuel cost and time for the delivery would be the best way to
calculate this. Note that travel vertically will add a time component to
delivery beyond the normal horizontal travel. Because one might or might
not encounter red lights when travelling, it would be quite difficult to
specifically quantify a component due to 'vertical' travel.
If I were trying to quantify this, for example, to estimate delivery costs
and to set prices for customers, I would gather data about current
deliveries. You could record distabce between points a and b (the
horizontal component), fuel used for the delivery (this could be hard to
estimate depending on the sensitivity of your fuel gauge), and time required
for the delivery. A notation could be placed on the records to indicate a
change in elevation. By gathering this data, you could determine predicted
milespergallon while climbing and/or travelling at (approximately) the
same elevation and then set your rates based upon a elevation map for your
delivery area. As always, mathematics is only an approximation, but you
should be able to predict, for a given delivery to a particular area, what
the predicted cost would be.
Thanks for using NEWTON!
Ric Rupnik
I assume that you calculate the cost by determining a certain cost per
mile [$/mile] and multiplying by the distance from A to B.
Algebaically, you are calculating the distance from A to B by putting the
points on an XY graph, say (xB, yB) and (xA,yA) and calculating the
distance between them using the Pythagorean Theorem:
D = { (xBxA)^2 + (yByB)^2 }^1/2
To generalize this to take altitude into account you have to know the
difference in the altitude of B and A, call the altitudes zB and zA
respectively. Assign a cost per mile between zB and zA, keeping in mind that
the cost per mile will be positive if you are going 'up hill' and negative
if your are going 'down hill' . Then the distance formula just adds another
term for the difference in altitude using the Pythagorean Theorem with three
terms:
D = { (xBxA)^2 + (yByB)^2 + (zBzA)^2 }^1/2
Vince Calder
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Update: June 2012

