How to financially quantify optimal number of items in a release?

Question

In Don Reinertsen's book - Principles of Product Development Flow - the tradeoff between release size (number of stories) and release cost (regression test cost and release cost) is described like this:

In Ken Rubin's book - Essential Scrum - he talks about the benefits of smaller release sizes - being:

• Reduced cycle time
• Reduced flow variability
• Accelerate feedback
• Lower risk of failure
• Reduced overhead
• Increased motivation and urgency
• Reduced cost and schedule growth

He also uses the following way of describing this tradeoff:

They both talk about this in terms of a U-curve optimisation problem. The challenge is how to quantify this.

My question is: How to financially quantify optimal number of items in a release?

Answer 1

The above has the form of

cost = n*BS + m/BS 

with

• n = holding cost factor,
• m = transaction cost factor and
• BS= batch size.

You have to find the zero crossing of the first derivative for the minimum. The first derivative for the above is

n - m/(BS^2)

When setting that to zero you find

min cost = sqrt(m/n)

Now you can just set a fence around this to have an area instead of a single point.