Impact of more than one Constraint -1

Alan Barnard (at the 2006 TOC-ICO conference) asked the question whether the simple Throughput per Constraint Unit rule is valid with 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) capacities. The practice often results in two) or more concurrent constraints or ‘almost’ constraints. Since 2006 I have observed several factories that wonder why their output collapses below the theoretical capacity of their (almost) balanced lines.

I plan to show that 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 should companies manage resource capacities.

I would like readers to follow Eli Goldratt’s recommendation that they solve the problems – before I provide the solution and before my discussion of results. The learning experience will be greater and readers should be better able 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 is useful but requires thought and care.

 

The original P-Q Experiment

 

Goldratt frequently used this experiment as part of his presentations. Before introducing the thought experiment he would usually present and discuss 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 company is mine. I have hired you to help me maximise my profits from the resources I have.

 

1. I have 4 machines (A, B, C and D). All 4 are required to produce my 2 products P and Q.
2. There are 40 hours of production time available per week (1 shift). (40 hours are 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 to produce P (1 of each raw material and purchased part).
6. Raw materials 2 and 3 (no purchased parts) are required to produce Q (1 of each).
7. All raw materials cost 20€ per unit. The purchased part costs 5€/unit.
8. Operating expenses (all costs other than materials and the purchased part) 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, even my people work 8 hours without fail.
12. Quality is perfect; I experience no losses due to defective 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 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 page.

 

A solution to the problem is demonstrated starting on the next page or in my next post.

Winter in Baie Comeau - Feb. 1954!!!