The AB Charity is planning its annual campaign to raise money. This year, three alternative methods are being considered: (i) street collections, (ii) a television advertising campaign and (iii) a direct-mail appeal. After using simulation to assess the risk associated with the alternatives the charity's managers have opted for a direct-mail appeal.

The direct-mail appeal will involve sending out 343 000 letters to selected people. To encourage donation these will include a free ballpoint pen displaying the charity's logo and people not replying after three weeks will receive a reminder. While the fixed costs of the campaign and the cost of sending out each letter and reminder are known for certain, the charity's managers have had to estimate probability distributions for the following four factors:

(a) The percentage of people who will reply to the first letter in the North (N), Central (C) and South (S) regions of the country, respectively.

(b) The average donation of those replying to the first letter in each of these regions.

(c) The percentage of people who will reply to the reminder in each of the three regions.

(d) The average donation of those replying to the reminder in each of the regions

Probability distributions have been estimated for the different regions because their different economic conditions are likely to have a major effect on people's propensity to donate to the charity.

Figure 12.6 shows the cumulative probability distribution of net returns (i.e., the total value of donations less the cost of running the direct-mail appeal). It can be seen that there is approximately a 20% probability that the net returns will be negative, causing the charity to lose money. In the simulation the possible losses extended to nearly $150 000.

The managers of the charity are keen to take action to reduce this risk, but are not sure where their actions should be directed. Figure 12.7 shows a tornado diagram for the appeal. The numbers at the ends of the bars show what are thought to be the highest and lowest possible values for each factor. For example, the possible average donation in the North is thought to range from $2 to $17.