# Limiting Factor Analysis

Limiting factor analysis is the method that we aim to maximize our production output with limiting input. The company does not have enough resource to produce unlimited output. So they have to analyze the and select the production combination to maximize the output or profit.  These factors are the reasons which put the limitation on our producton output.

Limiting factor is the scare resource within our operation that prevents us from the archive the highest output or profit. This factor will create the bottleneck in our production process.

The production input includes the following:

• Labor
• Raw material
• Machine capacity

These three resources suppose to have similar or the same capacity so that the whole factory can produce at a certain level. However, if one of them has less than the other, it will become the limiting factor for the other resource, and factory output will be limited by it.

This will be more complicated when the company produces more than one type of product, we have to calculate the limiting factor to maximize production. We may try to combine the production quantity of each product to maximize our profit.

Most of the company will decide to produce the product with a higher contribution (sale less variable cost) per unit first, then followed by the next product with a lower contribution. However, it is not always the case, please refer to the example below.

## Example

Company Z produces two types of product A & B with the standard costing as following:

Description A B
Direct Material 5 8
Direct Labor 6 10
Machine hour 3 6
Demand in October 1,000 2,000
Selling price 30 50

However, due to machine breakdown in October, the Machine can only operate 10,000 hours. There are enough material and direct labor to cover the order of both products.

Calculate the production plan, which will maximize the profit.

#### Step 1. Define the limiting factor

Description A B Total
Machine hour per unit 3 5
Demand in October 1,000 2,000
Machine hour require 3,000 12,000
Total machine hour require 15,000
Available machine hour (10,000)
Shortage 5,000

So we can see that the machine hour is the limiting factor which prevents the company from archive 3,000 units of both products A & B.

Note: we do not calculate the limiting factor of direct material and direct labor as there is no limitation provided in the example. However, in real situations, we calculate and compare all of them to check if they are the limiting factor or not.

#### Step 2. Identify the contribution per unit of the limiting factor

Description A B
Sale price 30 50
Variable cost 10 15
Contribution 20 35
Machine hour 3 6
Contribution per Machine hour 6.66 5.83

It means that both products can contribute \$6.66 and \$5.83 per machine hour respectively. So it is more profitable to produce product A which has a higher contribution per machine hour.

We noted that product B has a higher contribution per unit but has a lower contribution per machine hour (limiting factor). So producing product A is more profitable than product B. We need to allocate the machine hour to product A first, and the remaining hour will be used to produce product B.

#### Step 3. Prepare the production plan

Product Demand Machine hour require Available machine hour Remaining
A 1,000 3,000 10,000 7,000
B 2,000 12,000 7,000 0

We only have 7,000 machine hours for product B after we have spent 3,000 machine hours for product A. It will equivalent to 1,166 units (7,000h /6h per unit) of product B.

## Limitation of limiting factor analysis

This analysis Ignore the fixed cost. It assumes that the fixed will stay the same forever. However, in real life, the fixed cost may change when the products reach a certain level. We may need to rent additional space when new machines are set up.

Not applicable when multiple limiting factors exist. It will be impossible to do the analysis when there is more than one limiting factor happen at the same time.