Limiting Factor Analysis

Organisations are often faced with difficult decisions on how to organise, schedule and plan activities in such a way as to maximise returns.  A logical and methodical approach to this type of decision making can help with such problems.

Consider an organisation who manufactures three types of product, all of which use the same type of labour and materials, as follows:


Product
Retail Price
Material Costs
Labour Cost
Total Cost
Contribution*
A
$90
$20
$21
$41
$49
B
$100
$10
$28
$38
$62
C
$80
$15
$14
$29
$51


*Contribution is the sales price less the variable cost of production which contributes to the fixed costs of the business.

We are also told material cost is $5/kg and labour $7/hour.

In the coming period the management wish to maximise the contribution from production but are faced with the following constraints:

1) Sales demand for Product A is 100 units
2) Sales demand for Product B is 120 units
3) Sales demand for Product C is 160 units
4) Material is limited to 1000kg due to shortage of availability from a supplier
5) Labour has a capacity of 1150 hours due to a shortage of skilled operatives
6) A clause in the contract with a customer for Product A means 75 units must be produced and delivered otherwise a fine of $1000 will be incurred by the business


How should management proceed?

Our instincts should point our initial investigation to the fact that labour and materials are in short supply - if this were not the case then we would simply produce and deliver up to the maximum sales demand, avoiding the penalty clause and thus maximising returns.

From this we can conclude the total materials demand could be:

Maximum demand for Product A = 100 units x [$20/$5/kg] = 400kg
Maximum demand for Product B = 120 units x [$10/$5/kg] = 240kg
Maximum demand for Product C = 160 units x [$15/$5/kg] = 480kg
 
Thus, the total demand for materials is 1120kg against availability of 1000kg.

In addition, we can calculate the total maximum demand for labour:

Maximum demand for Product A = 100 units x [$21/$7/hr] = 300hr
Maximum demand for Product B = 120 units x [$28/$7/hr] = 480hr
Maximum demand for Product C = 160 units x [$14/$7/hr] = 320hr

The total maximum demand for labour is 1100hr compared with a capacity of 1150hr.

As a result of the limited material availability, we should concentrate our efforts on maximising the contribution from the materials resources.  This is achieved by producing the goods with the greatest return per kg of materials up to the maximum demand and then producing the next best product until all materials have been exhausted.

In order to do this, the contribution per limiting factor must be calculated for each of the products to identify the most 'profitable':


Product
Contribution
Materials Used
Contribution/kg of materials
Rank
A
$49
4kg
$12.25/kg
3
B
$62
2kg
$31.00/kg
1
C
$51
3kg
$17.00/kg
2


Following this analysis we can establish the first of two production schedules:


Product Manufactured
No. Made
Materials Used
Remaining Materials
Contribution /unit
Total Contribution/product
B
120 [Maximum]
240kg
760kg
$62
$7440
C
160 [Maximum]
480kg
280kg
$51
$8160
A
70 [280kg/{4kg/unit}]
280kg
0kg
$49
$3430
Total Contribution Generated
$19030


We must also consider the effect of the penalty clause regarding the non-delivery of Product A to our key customer. If we recalculate our production schedule to accommodate the 75 units required to fulfill the obligations under this contract even though this is the least 'profitable' in terms of material usage:


Product Manufactured
No. Made
Materials Used
Remaining Materials
Contribution /unit
Total Contribution/product
A
75
300kg
700kg
$49
$3675
B
120 [Maximum]
240kg
460kg
$62
$7440
C
153 [460kg/{3kg/unit}]
459kg
1kg
$51
$7803
Total Contribution Generated
$18918

Summary

Option 1  -  the company ignores the contract: contribution = $19030 - $1000 fine = $18030

Option 2  -  the company delivers the contracted products then maximises returns from the remaining materials: contribution = $18918

We would therefore conclude that the contract should be fulfilled.

Of course, this is just a simple example which can easily be made infinitely more complicated by any number of factors such as numerous contracts, many different products, delivery days etc.

There is, in addition, a large number of assumptions made in these types of working:

  • The organisation's overall aim is to maximise short term profits which can often lead to loss of goodwill and breakdown of existing relationships with customers
  • All costs and revenues are fixed regardless of quantities purchased
  • No alternative sources of material can be found from different suppliers
  • There is no product bundling or failure to deliver one product affecting demand of another
  • Estimates of sales demand are accurate
The list of non-quantifiable considerations and assumptions is not exhaustive and it is vital these issues are analysed to the best of our ability when making decisions.