Thinking About Constraints, where to Focus - the P-Q Thought Experiment (from Eli Goldratt) - 1

Alan Barnard (at the 2006 TOC-ICO conference) asked the question whether the simple Throughput per Constraint Unit rule is valid if there are 2 (or more) overloaded resources. Alan used Eli Goldratt’s P-Q thought experiment for his discussion. His question is important because it is common to see businesses reduce ‘excess’ capacities to balance (or almost balance) their capacities. The practice often results in (two) or more concurrently active constraints or ‘almost’ constraints. Since 2006 I have observed several factories that wonder why output collapses below the theoretical capacity of their (almost) balanced lines.

I plan to show that the Throughput per Constraint Unit rule continues to be valid using the same P-Q thought experiment. I also want to discuss this result in relation to the real World – how companies should manage resource capacities.

I would like readers to follow Eli Goldratt’s recommendation that they solve the (P-Q) problems – before I provide my solution and before my discussion of results. A learning experience is usually greater and readers will be in a better position to discuss and critique my conclusions. If you are familiar with the thought experiment you can jump to the second part of this article.

The key part of the article comes at the end when the solution used in the P-Q thought experiment is discussed in relation to REALITY. The thought experiment should not lead managers to an easy solution. The tool (Throughput per Constraint Unit (T/Cu) is useful but always be usd thought and care. Like any paradigm it can lead a person tinto errors. Paradigms can be pitfalls!

As far as I know this thought experiment was first published in the "Haystack Syndrome" by Eli Goldratt. Eli Schrageneim takes the experiment a further few steps in his book, "Throughpt Economics". Throughput Economics should be used as a reference by all managers.

The original P-Q Thought Experiment

Goldratt frequently used this experiment as part of his presentations. Before introducing the thought experiment he usually presenedt and discussed his 5 focusing steps listed here:

1. Identify the constraint of the system.
2. Decide how to exploit the constraint.
3. Subordinate everything else to the above decision.
4. If you cannot extract any more from the constraint, elevate (expand) it.
5. If during any of the previous steps the constraint is broken (has moved to another location) go back to step 1. BUT do not let your inertia become the systems constraint!

The P-Q Company

The P-Q company is "mine". I  hired you to help me maximise my profits.

1. My factory has 4 machines (A, B, C and D). All 4 are required to producethe 2 products P and Q we sell.
2. For the purposes of the experiment the number of available hours per wek is limited to 40. (1 shift; (40 hours equals available 2400 minutes.)
3. Product P sells for 90€ per unit and Q for 100€ per unit.
4. Demand per week is 100 of P and 50 of Q – IF my factory can make all 150 units.
5. Raw materials 1 and 2 plus a purchased part are required for P (1 of each raw material and purchased part).
6. Raw materials 2 and 3 (no purchased parts) are required to produce Q (again 1 unit of 1 of each material).
7. All raw materials cost 20€ per unit. The purchased part costs 5€/unit.
8. Operating expenses (all costs other than materials and purchased parts) are 6000€ per week.
9. Raw materials and purchased parts are always immediately available.
10. All set-up times are ‘one-touch’ – set-ups take no time at all.
11. All resources are perfect – all work 8 hours per day without any breaks, my people work 8 hours without fail and without stopping.
12. Quality is perfect; I experience no losses due to defective raw materials, parts or products.
13. The graphic below shows the routing (how materials flow through my factory from raw material to finished product). The routing shows the sequence of operations each product goes through and not the layout of the factory. Clearly raw material 2 is required for both P and Q as are the operations on the B and C machines in the middle path.
14. How much money can I (should I) make per week?

Work it out – the answer can be found using what has been written so far, or you might want to use linear programming. Either way, try to understand why you decided on one or the other option to produce and sell. When you are finished, carry on to the next post.

A solution to the problem will be demonstrated in my next post.

Winter in Baie Comeau, Québec - Feb. 1954!!! Where I grew up ... shoveling a lot of snow. Streets of the town were covered with snow from November until April!