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A Guide to Implementing the Theory of
Constraints (TOC) |
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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. 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 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. This Webpage Copyright © 2003-2009 by Dr K. J.
Youngman |
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