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How to best use available scarce resources

In some production and distribution decisions, management may be confronted with the question of how best to allocate the firm’s limited resources. Where demand for the product is greater than the production or distribution capabilities available, a company should seek to maximise its total contribution margin from these limited resources.

Limited resources can arise from one, or a combination, of the following:

  • Shortages of raw materials or purchased goods;
  • Shortage of certain labour skills;
  • Restricted space for production, in the warehouse or in a retailing outlet;
  • Maximum machine capacities.

It may not only be on the supply side that limitations prevail. It is also quite possible that a firm will face limitations upon the amount it can produce and/or sell because of:

  • Customer demand for one or more products and/or services;
  • Government restrictions.

In such circumstances, the challenge is to obtain the maximum possible benefit from the market opportunities and the resources available.

Where there is one single constraint, it is possible to carry out an analysis to determine the best mix of products to maximise total contribution margin. At its simplest, the analysis requires the contribution margin for a product to be divided by the unit of scarce resource, i.e. limiting factor. That product or service with the highest contribution per unit of the scarce resource is the most desirable whilst the resource constraint operates. The application of the contribution per unit of scarce resource will be demonstrated with reference to T.O. Wood Ltd, where management is considering the most desirable mix of products to incorporate into their annual budget.

Market research information has produced the estimated revenues of T.O. Wood’s present products together with further estimates of two new products, P and Q. There is no revenue constraint, but there is a constraint on machine capacity of 4,800 hours and, given this constraint, management needs to know the mix of products which should be produced so they are able to maximise the total profit margin. The product data is summarised in Table 1.

Table 1 T.O. Wood Ltd – Possible alternative products

  Existing Products New Products
  X Y Z P Q
Machine hours 2,000 800 2,000 800 1,000
  £'000 £'000 £'000 £'000 £'000
Revenues 1,500 1,600 800 700 1,000
Material costs 500 400 100 200 400
Labour Costs 400 800 300 200 200
Total variable costs 900 1,200 400 400 600
Contribution 600 400 400 300 400
Cont'bn to revenues ratio 40% 25% 50% 43% 40%

Unfortunately, as we will illustrate, the current product analysis is inadequate for selecting the appropriate product mix to maximise profit. What is required, is an analysis of the contribution yielded per machine hour for each product. This is provided in Table 2, which has been used to rank the products from those which show the highest contribution per machine hour through to the lowest.

Table 2 Best use of scarce resources – Ranking

  Existing Products New Products
  X Y Z P Q
(a) Machine hours 2,000 800 2,000 800 1,000
  £'000 £'000 £'000 £'000 £'000
(b) Contribution 600 400 400 300 400
  £ £ £ £ £
Contribution per
machine hour [(b) / (a)]
300 500 200 375 400
Ranking 4 1 5 3 2

The analysis shows that Product Y, ranked first, provides the highest contribution per machine hour. Each unit requires less of the scarce resource than the other products, and it contributes £500 per machine hour.

The ranking, illustrated in Table 2, provides the order which will result in the best use of scarce machine hours. Given the total constraint of 4,800 hours and the selection of Product Y, which requires 800 hours, the remaining 4,000 hours would be allocated to products Q, P and X. This allocation to the four products does not exhaust the 4,800 hours available, and 200 hours still remain available. This 200 hours spare capacity could be used to ease production scheduling, or it might be used to produce a proportion of Product Z.

You will have doubtless noted by selecting the product mix using contribution per machine hour, Product Z with the highest contribution revenues ratio is the least desirable. Whilst it may produce the largest effect on contribution for a given increase in revenues, it suffers from being inefficient in terms of machine hour use. Hopefully, you will be thinking why not buy or lease a new machine or investigate subcontracting production. This line of thinking is entirely appropriate, as is questioning whether T.O.Wood should focus more heavily on Product Y. However, your attention would not have been so readily directed at these questions without the analysis we have outlined.

Assuming that the 200 hours are retained to ease production scheduling, the following revised product income statement shows the results of maximising total contribution per machine hour available.

Table 3 Product contribution and total profit statement

  Existing Products New Products
  Y Q P X Total
Machine hours 800 1,000 800 2,000 4,600
  £'000 £'000 £'000 £'000 £'000
Revenues 1,600 1,000 700 1,500 4,800
Material costs 400 400 200 500 1,500
Labour Costs 800 200 200 400 1,600
Total variable costs 1,200 600 400 900 3,100
Contribution 400 400 300 600 1,700
Fixed Costs         1,000
Profit         700

Where more than one constraint exists, the problem will be reliant upon operations research methods, like linear programming, for its solution. Such techniques are beyond the aims of these introductory blogs.

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