Theory of Constraints Bottom Line Measurements P & Q Question

A Guide to Implementing the Theory of Constraints (TOC)
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The P & Q Question Explained

The P & Q is a simple process which makes just two things; “P’s” and “Q’s.” The objective of the exercise is to make a decision as to how to best maximize the profit of this process.

We can draw the flow of the process as follows.

There are 3 raw materials and one purchased part which are used to make the two end products – P’s and Q’s. One unit each of raw materials 1 and 2 combined with one purchased part constitutes the chain for product P. One unit each of raw materials 2 and 3 constitutes the chain for product Q.

We can make the process flow more explicit by splitting out the flows for each product. Let’s do that.

For product P we have;

Raw material 1 is processed at sections A, C, & D but not at section B. Raw material 2 is processed at sections B, C, & D but not at section A. One unit each of raw materials1 and 2 along with one unit of the purchased part are combined in section D to produce one unit of product P.

Let’s look at product Q. We have;

Once again raw material 2 is processed at sections B, C, & D but not at section A. Raw material 3 is processed at sections A, B, & D but not at section C. One unit each of raw materials 2 and 3 are combined in section D to produce one unit of product Q.

Because this is a perfect system we know exactly the selling price and the actual demand, we also know the input prices. Let’s add these, keeping our chains separate to keep things as simple as possible – remembering that the chains share one physical process.

In addition to this financial information we also know exactly the time it takes to work on each material at each stage in the process. Let’s add these.

All of which makes for a rather busy diagram, but it allows us to understand better Goldratt’s shorthand method for showing this information in the form of a logic diagram.

Let’s have a look.

All the information that was in the process flow diagrams is more concisely presented in the logic diagram. It might be a good idea to quickly sketch this diagram out onto a piece of paper.

Let’s reiterate;

The selling price for P’s is $90 each and the market demand (which is accurately known to the last unit) is 100 units per week. The selling price for Q’s is $100 each and the market demand is 50 units per week.

In addition;

The operating expense for the whole process is $6000 per week. In this ideal situation resource availability is; 60 minutes per hour, 8 hours per day, 5 days per week, or 2400 minutes per week. There is never any waiting, when one step is finished; the next step is immediately ready.

Note however, there is no multitasking. Resource A, B, C, D can only do their nominated jobs. In processes where you might visualize the resources as people, then its not uncommon for managers to assume, for the purposes of this exercise, that the resources can multitask – even though in real-life they are happy for their own resources to do the same job year in – year out.

Let’s also remind ourselves that;

Profit = throughput – operating expense, and

Throughput = selling price – material costs.

Given this information, the question then is; how much profit can we generate per week from this process?

Have a go at this exercise and then, once you have an answer, any answer, return to the measurements page.

To return to the previous page press Alt key + left arrow.

References

(1) Goldratt, E. M. (1990) The haystack syndrome: sifting information out of the data ocean. North River Press, pp 64-71.