Performance management: Ian Janes shows how to solve a problem featuring a minimum demand constraint resulting from the existence of a contract with a penalty clause.

AuthorJanes, Ian
PositionStudy notes

My previous article on decision-making concepts (November/December 2009) showed that a decision should be taken with ' reference to the relevant costs and benefits relating directly to it. In particular, it showed that the contribution per unit of scarce resource can be used to prioritise production in cases where there are insufficient quantities of one material.

Let's now extend the analysis to cover a situation where there is a minimum demand constraint owing to the existence of a contract containing a penalty clause for any failure to fulfil its obligations. Suppose that the Scarsprey Company manufactures three types of kettle: Basic, Deluxe and Super. The maximum market demand, budgeted unit contribution and resource requirements of each of these products are shown in table 1. The kettles are made from an advanced heat-resistant material that gives the firm a competitive advantage. An e-mail from the purchasing manager has informed us that, because of a problem with the supplier, it should be assumed that the year's supply of this special material is limited to 28,000kg. We can also assume that, since Scarsprey operates just-in-time production methods, opening and closing inventory levels are zero. The sales director has already accepted an order for 1,000 Deluxe kettles that, if not fulfilled, would incur a financial penalty of $2,000. This order is included in the Deluxe's maximum market demand figure.

We need to work out whether Scarsprey should go ahead and satisfy the contract and then prioritise production in the normal way or whether it should consider breaching the contract and incurring the penalty.

First, let's look at the situation that would occur if the firm were to fulfil the contract by considering once again the issue of prioritising production. From table 1 we can see that Basic kettles would have a contribution of $8.00 [Division Sign] 2.00kg=$4.00 per kg of special material; Deluxe kettles would have a contribution of $3.00 per kg; and Super kettles would have a contribution of $3.50 per kg. This means that the order of production priority would be Basic first, Super second and Deluxe third.

Of course, there is a more pressing priority if we are determined to satisfy the contract: the company must make the 1,000 Deluxe kettles before using the rest of the special material to make Basic kettles, then Super kettles and then-if there's any material left-more Deluxe kettles (see table 2).

The contribution resulting from...

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