A Guide to Implementing the Theory of
P&Q Answer - Part One
How did you get on? Did you get an answer?
Many people decide to make everything required to meet market demand. So let’s work through that first. The results are tabulated for convenience.
If we work through this step by step, then the first step is to determine the contribution, or margin, or as we have called it here – throughput. This is sales price less material costs and for P this is 90 less 45 = $45. For Q it is 100 less 40 = $60.
Thereafter, it is simply a matter of multiplying out the margin by the number of units produced to the weekly throughput. The weekly throughput less the weekly operating expense gives us a weekly net profit of $1500. Not bad at all.
But let’s check things first. Let’s check that we have enough capacity to undertake the supply that we committed to.
In order to do this we must check that the total amount of time required for each resource does not exceed the total amount of time available. If you still have that rough sketch of the process on paper now would be a good time to retrieve it. Let’s start with resource A.
In order to make 100 units of P, resource A needs 100 times 15 minutes (raw material 1) and in order to make 50 units of Q, resource A needs 50 times 10 minutes (raw material 3). A total of 2000 minutes out of the 2400 available to resource A. So from the perspective of resource A, we can meet that commitment. Let’s move to resource B.
In order to make 100 units of P, resource B needs 100 times 15 minutes (raw material 2) and in order to make 50 units of Q, resource B needs 50 times 15 minutes (raw material 2) plus 50 times 15 minutes (raw material 3). A total of 3000 minutes out of the 2400 available to resource B. Oops. It seems that we have insufficient capacity on resource B to meet our commitment. Let’s check C and D.
Fortunately C only requires 1750 minutes (100 by 10 + 100 by 5 +50 by 5). D also only requires 1750 minutes (100 by 15 + 50 by 5).
Let’s tabulate that data so that it is a little clearer. The right-hand-most column is the maximum available time, and the column to its left is the sum of the time required for each resource to complete the commitment for units supplied of both P and Q.
The problem now seems to be one of how to best maximize the capacity of resource B and still derive a good profit at the end of the week.
Because we have a approached this problem from a cost point of view, then surely the best way to maximize our process would be to chose the product that has the lowest cost. If we do this in terms of raw material cost, then the answer must be Q at $40 rather than P at $45. If we do this in terms of labor cost, then the answer must also be Q at 50 minutes labor (10 + 30 + 5 + 5) rather than P at 60 minutes (15 +15 +15 +15).
As a reality check, let’s also see what the effect of maximizing selling price and margin or throughput is. The maximum selling price also favors Q at $100 rather than P at $90. The margin also favors Q at $60 rather than P at $45.
It would seem then that Q is the product to favor and any spare capacity left over after meeting market demand can be used to produce P. Let’s do the basic calculation for this.
We now want to produce 50 Q. For resource B this will require 50 times 15 minutes (raw material 2) and 50 times 15 minutes (raw material 3). A total of 1500 minutes is required for product Q. This leaves 2400 – 1500 = 900 minutes for P. P takes 15 minutes for resource B. Therefore we can make 900/15 = 60 units of P. Let’s tabulate this new condition.
Well if your eye jumped to the bottom line like mine did, you will see we are spilling red ink!
How did that happen?
We did everything that our experience told us would be useful. We chose the lowest labor cost, the lowest material cost, the highest sales price, and the highest margin. And yet based upon these rational decisions we seem to have driven our bottom line into the red.
Let’s leave this problem for the moment and return to the measurements page. Hopefully we can find out what is wrong and return to this problem later.
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(1) Goldratt, E. M. (1990) The haystack syndrome: sifting information out of the data ocean. North River Press, pp 72-78.
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