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Sliding scale discounts

GVP

New Member
Greetings!

A while back, someone posted a formula for calculating quantity discounts on a sliding scale... can someone point me to the posting - I have tried a search but am not sure what to look for?

Thanks
 

GVP

New Member
Thanks Brian,

That's not the one though - I seem to recall it was a mathematical formula between the highest price you would charge and the lowest?
 

bob

It's better to have two hands than one glove.
One more time...

(maximum-minimum)+minimum*area+substrates+etc.

Area is the size of the work. In my shop it's a square foot or fraction thereof.

Maximum is the maximum you'd ever charge for one unit of area. My max currently is $24.

Minimum is the least amount you'd work for per unit of area. My min currently is $6.

When I have multiple copies to make I treat them as one big job for pricing. Doing it this way builds in a reasonable quantity discount.

This particular formula generates a pleasing exponential curve that starts out at the maximum and proceeds to become asymptotic at the minimum. The larger the work the less per unit of area.
 

GB2

Old Member
Bob, forgive me but I'm not understanding your formula at all.

First, what do you apply this to and/or what is the unit of area? Is it printing? Do you apply your formula to cut vinyl, banners, dimensional painted signs, etc.? I'm assuming that your formula doesn't include materials, substrates, etc. since you seem to add them at the end but would that be the case for something like printed banners, which I think would be a prime candidate for your formula?

Second, where is the sliding scale? Your formula for your example will always be $24 for a unit of area:
($24-$6)+$6
($18)+$6
$24

This is how I would apply your formula using a maximum rate of $3 and a minimum rate of $1 for the digital printing and $3 for the banner substrate cost:

1 banner 3'x10'
($3-$1)+$1*30+$90
($2)+$1*30+$90
$3*30+$90
$90+$90
$180

10 banners 3'x10'
($3-$1)+$1*300+$900
($2)+$1*300+$900
$3*300+$900
$900+$900
$1800

This results in the same cost for 1 banner as in 10 banners, tell me what is wrong please.
 

bob

It's better to have two hands than one glove.
Bob, forgive me but I'm not understanding your formula at all.

First, what do you apply this to and/or what is the unit of area? Is it printing? Do you apply your formula to cut vinyl, banners, dimensional painted signs, etc.? I'm assuming that your formula doesn't include materials, substrates, etc. since you seem to add them at the end but would that be the case for something like printed banners, which I think would be a prime candidate for your formula?

Second, where is the sliding scale? Your formula for your example will always be $24 for a unit of area:
($24-$6)+$6
($18)+$6
$24

This is how I would apply your formula using a maximum rate of $3 and a minimum rate of $1 for the digital printing and $3 for the banner substrate cost:

1 banner 3'x10'
($3-$1)+$1*30+$90
($2)+$1*30+$90
$3*30+$90
$90+$90
$180

10 banners 3'x10'
($3-$1)+$1*300+$900
($2)+$1*300+$900
$3*300+$900
$900+$900
$1800

This results in the same cost for 1 banner as in 10 banners, tell me what is wrong please.

Perhaps I should have stated it this way...

(max-min)+(min*area)+(this and that)

The equation does not need the extra parentheses surrounding the min*area since, by convention, multiplication [and division] is performed before addition [and subtraction].

What you were doing was performing the parenthetical max-min, then performing the +min, and then doing the *area. What you should have done was the mathematically correct method of doing the parenthetical statement first then the multiplication, and finally the sum of the two.

Like this, using your rather dubious numbers...

1 banner 3'x10'
($3-$1)+$1*30+$90 ...merely a statement of the equation using actual numbers...

($2)+$1*30+$90 ..correct so far...

$3*30+$90 ...bzzzt, wrong. This should be ($2)+$30 + $90 yielding $122 not $180 by the rest of your solution.

Changing the 30 to 300 for 10 banners, when done properly yields...

($3-$1)+$1*300+$900
($2)+$1*300+$900
($2)+$300+$900
=$1202

Thus, with your totally unrealistic min and max values, the price per copy for a quantity of 10 is $120.20, not $122.00. If you were to plug in min and max values with a taste more difference you'd see a much more dramatic volume discount.
 
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