A Guide to Implementing the Theory of
P&Q Answer - Part Three
At the end of part two of the P & Q answer we had stemmed the flow of red ink and turned a healthy profit. We did this by realizing that our previous attempts to maximize the constraint were based on our old and, as it turns out, incorrect assumptions about minimizing cost or maximizing labor. Once we realized that to effectively exploit the constraint we must maximize the throughput per unit time on the scarce resource then we were back in the black ink.
This is the situation that we found ourselves in at the end of the previous part. Let’s press on.
Many people who use the P & Q problem to illustrate exploiting a constraint don’t proceed beyond the stage that we have just reach. And yet this example is full of further potential. A number of people have developed extensions, let’s stick to the one that Goldratt uses (1).
If you look at the above table you will see that although we have maximized the throughput of our constraint, we still have unmet potential in the form of 20 Q that we can’t supply to our demanding market. Goldratt presents the following scenario;
Let’s suppose that a foreman comes and suggests that for a mere $3000 he could purchase a fixture that would increase the time taken to manufacture a high volume part from 20 minutes to 21 minutes. What is the likely response to such a suggestion?
The reaction based upon the reductionist/local optima approach is to dismiss it outright. But we should be coming to realize now that such suggestions, when viewed in the light of the systemic/global optimum approach, might be quite different – and positively different at that.
Indeed what the foreman has suggested would go a long way to fulfilling that unmet market demand for another 20 Q. What he has proposed is that the fixture will off-load some work from our constrained resource B and load it onto C. In fact the tasks concerned are on the middle or common path for raw material 2 (you might like to find that piece of paper with the logic diagram sketched on it). We off-load 1 minute from B and have to add 2 minutes to C. The end result is that the total time to process raw material 2 will increase from 20 to 21 minutes.
What will the effect be of the additional minute saved per piece on raw material 2? Currently we are producing 100 units for assembly into P, and 30 units for Q – 130 units per week. The saving then is 130 minutes on B.
It would be nice to sell these 130 minutes at the rate for P of $3/minute but for the moment we have saturated that market. We must therefore sell it at the rate for Q of $2/minute. How many additional complete Q’s can we make? 130/29 = 4
Let’s tabulate the result.
We produced an additional 4 Q’s and profit went from $300 per week to $540 per week. That is a (540-300)/300 = 46% increase. What is the payback period for our $3000 investment?
Payback = 3000/240 = 12½ weeks.
A fraction over 3 months for payback. Let’s do it.
Do you wonder if $3000 for a fixture that substantially increases profit is the product of a fertile imagination and some clever numbers? There is a very good example of just such a circumstance described by Vicky Mabin where a double nozzle was added to a small goods (ham, sausage) filling machine which reduced the time to fill by 50% with immediate gains in effective capacity at very little cost.
We have done two things here that bear further explanation. Firstly we have elevated the constraint; we have taken external investment and raised the production of the constraint. Previously, in part two of the answer, we limited ourselves to improving the constraint by exploiting it without additional investment. Secondly in this part we actually made the local performance of one task worse. The task that resource C performs on raw material 2 now takes 7 minutes rather than 5; clearly the local efficiencies for resource C have gone down. Yet this type of situation, which we will call subordination, is critical for effective implementation of theory of constraints. We will introduce the sequence that we have performed here – identify, exploit, subordinate, and elevate in the section on process of change.
Let’s reinforce subordination with an example from a furniture factory. In this particular instance the task that requires subordination is before the constraint, it is a series of sanding machines prior to the constraint which is assembly. By spending a little more time on machine sanding substantial savings in time could be made in assembly from not having to do as much finishing sanding with hand sanding machines. Unfortunately this factory still records local efficiencies – so I will let you decide which prevailed, common sense or the measurements.
Well, in our example we have managed to keep the constraint internal to the process. What happens if the constraint moves out into the market? We should investigate that possibility as well. However, first, let’s return to the measurements page.
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(1) Goldratt, E. M. (1990) The haystack syndrome: sifting information out of the data ocean. North River Press, pp 86-92.
(2) Mabin, V. J., and Gibson, J. (1998) Synergies from spreadsheet LP used with the Theory of Constraints: a case study. Journal of the operational research society, 49 pp 918-927.
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