The decision is then made on the basis of the lowest regret, which in this case is the large order with the maximum regret of $200, as opposed to $600 and $450 for the small and medium orders.

### Decision trees

The final topic to be discussed in this first article is the use of decision trees to represent a decision problem. Decision trees provide an effective method of decision-making because they:

- clearly lay out the problem so that all options can be challenged
- allow us to fully analyse the possible consequences of a decision
- provide a framework in which to quantify the values of outcomes and the probabilities of achieving them
- help us to make the best decisions on the basis of existing information and best guesses.

A comprehensive example of a decision tree is shown in Figures 1 to 4, where a company is trying to decide whether to introduce a new product or consolidate existing products. If the company decides on a new product, then it can be developed thoroughly or rapidly. Similarly, if the consolidation decision is made then the existing products can be strengthened or reaped. In a decision tree, each decision (new product or consolidate) is represented by a square box, and each outcome (good, moderate, poor market response) by circular boxes.

The first step is to simply represent the decision to be made and the potential outcomes, without any indication of probabilities or potential payoffs, as shown in Figure 1.

The next stage is to estimate the payoffs associated with each market response and then to allocate probabilities. The payoffs and probabilities can then be added to the decision tree, as shown in Figure 2. The expected values along each branch of the decision tree are calculated by starting at the right hand side and working back towards the left recording the relevant value at each node of the tree.

These expected values are calculated using the probabilities and payoffs. For example, at the first node, when a new product is thoroughly developed, the expected payoff is:

Expected payoff = (0.4 x $1,000,000) + (0.4 x $50,000) + (0.2 x $2,000) = $420,400

The calculations are then completed at the other nodes, as shown in Figure 3. We have now completed the relevant calculations at the uncertain outcome modes.

We now need to include the relevant costs at each of the decision nodes for the two new product development decisions and the two consolidation decisions, as shown in Figure 4.

The payoff we previously calculated for ‘new product, thorough development’ was $420,400, and we have now estimated the future cost of this approach to be $150,000. This gives a net payoff of $270,400.

The net benefit of ‘new product, rapid development’ is $31,400. On this branch, we therefore choose the most valuable option, ‘new product, thorough development’, and allocate this value to the decision node.

The outcomes from the consolidation decision are $99,800 from strengthening the products, at a cost of $30,000, and $12,800 from reaping the products without any additional expenditure.

By applying this technique, we can see that the best option is to develop a new product. It is worth much more to us to take our time and get the product right, than to rush the product to market. And it’s better just to improve our existing products than to botch a new product, even though it costs us less.

**Written by a member of the Performance Management examining team**