What are Limiting Factors?
In management accounting, limiting factors refer to the constraints in availability of production resources (e.g. shortages in labor, machine hours or materials) that prevent a business from maximizing its sales.
Single Limiting Factor Analysis
If an organization manufactures more than one product and faces a shortage in the supply of a single resource (e.g. labor hours, machine hours or a material) that is required in the production of its multiple products, what quantities of its various products should be produced to maximize profits?
One option would be to determine production quantities on the basis of contribution per unit of the different products (i.e. products with higher contribution per unit shall be given preference over products with lower contribution per unit).
Prioritizing production on the basis of contribution per unit however would not maximize profits as the approach fails to take into account the contribution of various products relative to their usage of the limiting resource which shall ultimately determine the overall profit. Therefore, when facing a situation involving a single limiting factor, products should be prioritized in the production plan according to their contribution per unit of the limiting resource.
Six Step Approach
Single limiting factor problems can be solved by adopting the following six-step approach.
Step 1: Determine the maximum sales
In order to calculate whether a limiting factor exists (Step 2), we need to ascertain the maximum sales that the business can achieve ignoring any limiting factors that affect production of multiple products.
In most cases, Maximum Sales will equal to sales demand of the respective products of the company.
However, if there is any limiting factor specific to a product (i.e. the limiting factor only affects production of one product rather than multiple products) the Maximum Sales of that product should not exceed the units of production that will be achievable subject to such limitation.
See Step 1 of Example below for an illustration of this step.
Step 2: Determine the limiting factor
Here we need to establish which factor is responsible for limiting the production of its various products.
This can done by simply comparing:
a) Available units of factors
b) Units of factors required to achieve the Maximum Sales calculated in Step 1
If there is however a shortfall in more than one units of resource (i.e. multiple limiting factors), then the problem can only be solved using linear programming techniques.
Step 3: Calculate contribution per unit of output of each product
Contribution is simply selling price less variable costs.
As with most short term decisions in managerial accounting, fixed costs are non-relevant which is why the limiting factor analysis uses contribution per unit rather than profit per unit.
Step 4: Calculate contribution per unit of limiting factor for each product
This represents the contribution earned from a product for every unit of scarce resource consumed.
Step 5: Rank products in order of priority
The product with highest contribution per unit of limiting factor calculated in Step 4 shall be ranked first whereas the second highest shall be ranked second and so on.
Step 6: Calculate production quantities
Product ranking first in Step 5 would be produced up to the maximum sales subject to the availability of the limiting resource. Lower ranked products shall only be produced if the entire production requirement of higher ranked products have been met.
Following example illustrates how the 6 Steps Approach can be applied in a given scenario.
Example
ABC Watches is a manufacturer of premium hand-crafted watches.
Estimated watch sales, production and usage for the next period are as follows:
| Available Units | ABC Platinum | ABC Gold | ABC Silver | |
|---|---|---|---|---|
|
Labor |
200,000 hours |
$500 |
$400 |
$300 |
|
Platinum |
220 Kg |
$5,000 |
|
|
|
Gold |
300 Kg |
|
$4,000 |
|
|
Silver |
200 Kg |
|
|
$1,000 |
|
904L Stainless Steel |
2200 Kg |
$500 |
$400 |
$600 |
|
Variable Overheads |
|
$300 |
$100 |
$200 |
|
Total Variable Overheads |
|
$6,300 |
$4,900 |
$2,100 |
|
Fixed Overheads Absorption |
|
$100 |
$80 |
$60 |
|
Total Cost Per Unit |
|
$6,400 |
$4,980 |
$2,160 |
|
Selling Price |
|
$10,000 |
$8,000 |
$5,000 |
|
Sales Demand |
|
1,000 Units |
2,000 Units |
2,500 Units |
Calculate the production quantities that will maximize profits of ABC Watches in the following period.
Step 1: Determine the maximum sales
Platinum, Gold & Silver are not potential limiting factors for the purpose of this analysis as they do not affect the production of other products unlike steel and labor which are required in the production of all watches.
However, we need to ensure that any shortage in the availability of Platinum, Gold or Silver is accounted for when calculating the resource requirements of potential limiting factors (i.e. steel and labor) in Step 2 based on the maximum sales.
| Factor | Available Units | Maximum Output | Sales Demand | Maximum Sales |
|---|---|---|---|---|
|
|
|
A |
B |
Lower of A & B |
|
Platinum |
200 KG |
1100 units (W1) |
1000 Units |
1000 Units |
|
Gold |
300 KG |
2000 units (W2) |
2000 Units |
2000 Units |
|
Silver |
200 KG |
2000 units (W3) |
2500 Units |
2000 Units |
W1 : Platinum Watches: 220 KG / 0.2 KG* = 1100 units
*200 grams = 0.2 KG
W2: Gold Watches: 300 KG / 0.15 KG* = 2000 units
*150 grams = 0.15 KG
W3: Silver Watches: 200 KG / 0.10 KG* = 2000 units
*100 grams = 0.10 KG
Step 2: Determine the limiting factor
| Factor | Available Units | Required units | Shortfall |
|---|---|---|---|
|
Steel |
2200 KG |
2500 KG (W1) |
Yes |
|
Labor |
200,000 hours |
190,000 hrs (W2) |
No |
Steel is the limiting factor.
| W1: Steel Units required to produce maximum sales units | |||
|---|---|---|---|
|
Platinum |
500 grams x 1000 units |
= |
500 KG |
|
Gold |
400 grams x 2000 units |
= |
800 KG |
|
Silver |
600 grams x 2000 units |
= |
1200 KG |
|
Total Steel Units: |
= |
2500 KG |
|
| W2: Labor hours required to produce maximum sales units | |||
|---|---|---|---|
|
Platinum |
50 hours x 1000 units |
= |
50,000 hours |
|
Gold |
40 hours x 2000 units |
= |
80,000 hours |
|
Silver |
30 hours x 2000 units |
= |
60,000 hours |
|
Total Labor hours: |
= |
190,000 hours |
|
Step 3: Calculate the Contribution Per Unit of each product
| Product | Revenue | Variable cost | Contribution per Unit |
|---|---|---|---|
|
|
A |
B |
A-B |
|
Platinum |
$10,000 |
$6,300 |
$4,700 |
|
Gold |
$8,000 |
$4,980 |
$3,020 |
|
Silver |
$5,000 |
$2,160 |
$2,840 |
Step 4: Calculate the Contribution Per Unit of Limiting Factor of each product
| Product | Contribution per Unit | Stainless Steel per Unit | Contribution of products per unit of limiting factor |
|---|---|---|---|
|
|
A |
B |
A/B |
|
Platinum |
$4,700 |
500 grams |
$9.4 per gram |
|
Gold |
$3,020 |
400 grams |
$7.55 per gram |
|
Silver |
$2,840 |
600 grams |
$4.73 per gram |
Step 5: Rank products in their order of priority in the production plan
| Product | Contribution of products per unit of limiting factor | Rank |
|---|---|---|
|
Platinum |
$9.4 per gram |
1 |
|
Gold |
$7.55 per gram |
2 |
|
Silver |
$4.73 per gram |
3 |
Since Platinum Watches earn the highest contribution for every gram of stainless steel used, it is given first priority in the production plan followed by Gold and Silver Watches.
Step 6: Calculate the production quantities
| Product | Rank | Steel Units Available | Steel Units Required | Units to be Produced |
|---|---|---|---|---|
|
Platinum |
1 |
2200 KG |
500 KG (W3) |
1,000 |
|
Gold |
2 |
1700 KG (W1) |
800 KG (W4) |
2,000 |
|
Silver |
3 |
900 KG (W2) |
900 KG (W4) |
1500 (W5) |
1000 Platinum Watches, 2000 Gold Watches and 1500 Silver Watches should be produced to maximize profit.
Platinum and gold watches can be produced up to the level of their maximum sales. However, only 1500 Silver watches can be produced from the steel units available after the production of platinum and gold watches.
W1: 2200 KG – 500 KG = 1700 KG
W2: 1700 KG – 800 KG = 900 KG
W3: 1000 units x 500 grams per unit = 500 KG
W4: 2000 units x 400 grams per unit = 800 KG
W5: 900 KG / 0.6 KG* = 1500 units
*600 grams = 0.6 KG
Limitations
Where multiple limiting factors exist, the optimum production plan cannot be found using the method explained above. Where an organization manufactures only 2 products, simple linear programming using graphs can be applied to solve problems involving multiple limiting factors whereas in case of more than 2 products, the optimum production plan has to be determined using more complex algorithms such as Simplex.