F5 Technical Article THROUGHPUT ACCOUNTING AND THE THEORY OF CONSTRAINTS, PART 2

Example 2
Cat Co makes a product using three machines – X, Y and Z. The capacity of each machine is as follows:

Machine X Y Z
Capacity per week 800 600 500

The demand for the product is 1,000 units per week. For every additional unit sold per week, net present value increases by $50,000. Cat Co is considering the following possible purchases (they are not mutually exclusive):

Purchase 1 Replace machine X with a newer model. This will increase capacity to 1,100 units per week and costs $6m.

Purchase 2 Invest in a second machine Y, increasing capacity by 550 units per week. The cost of this machine would be $6.8m.

Purchase 3 Upgrade machine Z at a cost of $7.5m, thereby increasing capacity to 1,050 units.

Required:
Which is Cat Co’s best course of action?

Answer
First, it is necessary to identify the system’s bottleneck resource. Clearly, this is machine Z, which only has the capacity to produce 500 units per week. Purchase 3 is therefore the starting point when considering the logical choices that face Cat Co. It would never be logical to consider either Purchase 1 or 2 in isolation because of the fact that neither machines X nor machine Y is the starting bottleneck. Let’s have a look at how the capacity of the business increases with the choices that are available to it.

X Y Z Demand
Current capacity per week 800 600 500* 1,000
Buy Z 800 600* 1,050 1,000
Buy Z & Y 800* 1,150 1,050 1,000
Buy Z, Y & X 1,100 1,150 1,050 1,000*

* = bottleneck resource

From the table above, it can be seen that once a bottleneck is elevated, it is then replaced by another bottleneck until ultimately market demand constrains production. At this point, it would be necessary to look beyond production and consider how to increase market demand by, for example, increasing advertising of the product.

In order to make a decision as to which of the machines should be purchased, if any, the financial viability of the three options should be calculated.

Buy Z
Additional sales = 600 – 500 = 100 units $’000
Benefit: 100 x $50,000 5,000
Cost (7,500)
Net cost (2,500)

Buy Z & Y
Additional sales = 800 – 500 = 300 units
Benefit : 300 x $50,000 15,000
Cost ($7.5m + $6.8m) (20,300)
Net benefit 700

Buy Z, Y & X
Additional sales = 1,000 – 500 = 500 units
Benefit: 500 x $50,000 25,000
Cost ($7.5m = $6.8m + $6m) (20,300)
Net benefit 4,700

The company should therefore invest in all three machines if it has enough cash to do so.

The example of Cat Co demonstrates the fact that, as one bottleneck is elevated, another one appears. It also shows that elevating a bottleneck is not always financially viable. If Cat Co was only able to afford machine Z, it would be better off making no investment at all because if Z alone is invested in, another bottleneck appears too quickly for the initial investment cost to be recouped.

I am not understanding why when finding out the net benefit of each decision we are subtracting for Buy Z *600 – 500 = 100 to find out the extra units* for additional sales that are going to come out.
Same for Buy Z and Y why subtract 800 – 500 = 300 units
And for Buy Z Y and X 1000 – 500 = 500 units.

I hope my question was clear 🙁 It’s my first time posting on the forums! 🙂