A Guide to Implementing the Theory of
P&Q Answer - Part Four
So far we have only had to contend with an internal constraint – resource B. In the previous section, part three of the P & Q answer, we had begun to elevate the constraint by making a small investment, we also had some effective subordination. We have essentially reached the stage now where the external market is the constraint. Sure, resource B is essentially fully utilized, however, it is usually easier to obtain additional capacity than it is to obtain additional sales. The question then is – what to do?
Let’s develop the argument further based on the system as developed to date and using numbers presented by Goldratt for new market composition and capital investment (1). And although our throughput rate will have increased slightly ($3.20 for P’s and $2.07 for Q’s) lets use the round figures from prior to our small change in operating times, therefore;
Like so many small businesses, we find in this case that capacity doesn’t come in small chunks. If we are going to elevate resource B and move the constraint into the market then we must purchase the full equivalent of resource B’s machinery. That is probably OK, but it comes with a price tag of $100,000. We also need a second operator for resource B. We are lucky here because an experienced operator can be had for $400 per week. Our operating expense will have to increase by this much to accommodate our new outgoing.
Being small and prudent, we are not going to rush in and make this commitment until we are certain that we have a market for the additional output – and that the additional output is worth our while.
However a new market segment has been located. This new market is either geographically or conceptually isolated from the current market – it is segmented. A point we will return to later. The market is prepared to buy 50 Q’s a week and in addition up to 100 P’s a week. Unfortunately due to the nature of the new market segment’s economy they are willing to pay (after exchange rates) only 80% of the current rate. Thus these P’s are worth $72 each to us and a Q $80.
Previously Q’s were the least desirable of our products generating $2/min on the scarce resource. Now if we sell additional P’s at $72, less the material costs of $45 a unit, we will only generate $27.
The throughput rate of additional P’s = $27 per 15 minutes or $1.80 per minute.
This is less than we currently get from Q’s!
In the reductionist/local optima approach selling below par for additional production would be rejected. However, in the systemic/global optimum approach we can understand that so long as the market is the constraint, any additional sales that exceed raw material costs will make a positive contribution to the bottom line. After all we have already “covered” our operating expenses with our previous sales. Whether the contribution is sufficient in this case to justify the additional investment needs to be determined. Let’s do that.
We have tabulated all the new data and increased operating expenses to cover the additional worker. We have twice as much time available on B as we did before.
We set out initially to capture more of the market for P because we knew that they generate 50% more throughput than Q does. However, in the process of elevating resource B we broke a constraint, and now we must locate the new constraint before any meaningful analysis can be made. In this system where the likely candidates – resource C & A – both have the same total capacity we can make a reasonable guess that resource A with 15 + 10 = 25 minutes will be more likely to be constrained than resource C with 17 + 7 = 24 minutes. Therefore let’s evaluate resource A as the constraint.
To do that we need to establish the new throughput rates. For example P would be 45/15 = $3minute – just as before. Q would be 60/10 = $6 minute.
Oops. Is that correct? The order seems to have been changed around. Q’s are now twice as profitable as P’s! Let’s tabulate this for both old P & Q’s and additional P & Q’s.
It seems surprising at first, Goldratt explains it thus; “… in the ‘cost world’ almost everything is important, thus changing one or two things doesn’t change the total picture much. But this is not the case in the ‘throughput world.’ Here, very few things are really important. Change one important thing and you must re-evaluate the entire situation.” We change one important thing here – the location of the constraint, and therefore we must re-evaluate the entire situation.
In real life the number of options the constraint can move to are limited, and often well within control. They in fact become strategic decisions based upon where it is most desirable to have the constraint.
Let’s work through the calculations step by step. Let’s sell as much as possible of the best performer using resource A and then move on to the next.
We can sell 50 *10 = 500 minutes of Q which leaves us with 2400 – 500 = 1900 minutes
We can sell 50 *10 = 500 minutes of Q’ which leaves us with 1900 – 500 = 1400 minutes
We can sell 100 * 15 = 1500 minute of P. We don’t have that much. Let’s try the other way around.
1400/15 = 93 Ps.
Let’s plug this into the table and see what we have.
Ah ha! If we make a commitment to this market, and we break our current constraint as intended by purchasing another resource B and a machine, then we will make $2785 per week – up from $540 per week at present.
So we don’t even double sales (we can’t supply the demand at all for additional P’s) and yet our profit increases (2785-540)/540 = 400%. Should we do it?
Look at it another way, payback on the capital will be 100,000/(2785-540) = 45 weeks. Less than a year. I’ll let you make your own decision.
Let’s go over what we have discovered in these 4 sections. Firstly we learnt the identity of the constraint or scarce resource when we couldn’t meet our aspirations to sell all the market demand. Such accidental acquaintance with a constraint isn’t so unusual either. Then we learnt how to best exploit the current situation by ensuring that we produced the maximum throughput per unit time on our scarce resource. Next we elevated the scarce resource a little by some incremental capital investment and our profit rose substantially. We also had to subordinate one of the non-constraint resources at the same time in order to do this. Finally we set out in search of additional market and additional capacity. We found that breaking a previous constraint can have important ramifications on our future decisions. However once we aligned those decisions with our experience in maximizing throughput we once again surprised ourselves with the increase in output that could be achieved.
The objective is to turn that knowledge into effective implementation in real life. The process is the same and the results just as effective as we shall see.
Let’s return to the measurements page.
To return to the previous page press Alt key + left arrow.
(1) Goldratt, E. M. (1990) The haystack syndrome: sifting information out of the data ocean. North River Press, pp 93-99.
This Webpage Copyright © 2003-2009 by Dr K. J. Youngman