EXERCISES
1. Draw a decision tree for the bid for services example.
2. In the clinic renovation example, what if management thinks that the likeli¬hood of current demand remaining is 30%, the likelihood of a moderate increase is 25%, and the likelihood of a large increase is 45%? What should they do, according to the expected total payoff?
Clinic Renovation
An ambulatory can clinic administrator is trying to decide whether to renovate to accommodate possible increased demand. The manager could plan a major renova¬tion costing $700,000 that would allow 50 patients per day to be served, or a minor renovation costing $225,000 that would allow 35 patients a day to be served. The final alternative is to do nothing, thus keeping the status quo by not renovating. This continues the existing capacity of accommodating the current 20 patients per day, but no more. Presently the clinic earns $75 per patient served. Assume that the clinic is open 300 days per year and that management wants to cover the costs of the renova¬tion from first-year earnings.
To begin quantitatively analyzing our decision options, we first go back to the three decision steps listed previously. The first step is to state the alter¬natives. These are to do nothing, undergo a minor renovation, or undergo a major renovation. The second step is to determine the future states of the world. These are the unknowns in our decision. Here they are the estimates of future demand. Because our decisions limit future capacity, we will use these limits as estimates of future demand. Thus, let us describe the potential for 20 patients per day, 35 patients per day, or 50 patients per day to be served, defined by current capacity, capacity given a minor renovation, and capacity given a major renovation.
There are three alternatives and three possible states of the world. This means that there are nine possible outcomes. These are listed in Table 10-3. The third step is to determine the payoffs for each of the potential outcomes.
Earnings are based upon patients served; therefore, part of the payoff involves earnings. For each state of the world of future demand, there are different potential maximum patients who can be seen. Each of these brings in revenue of $75. This amount is then multiplied by the 300 days the clinic is open yearly to calculate the total revenue per year. The maximum revenue generated in each state of the world can be seen in Table 10-4.
Table 10-4 Potential Monetary Payoffs by States of the World
| Future demand forecasts (patients per day) |
Payment per patient |
Day open |
Total yearly payment |
| 20 |
$75.00 |
300 |
$450,000.00 |
| 35 |
$75.00 |
300 |
$787,500.00 |
| 50 |
$75.00 |
300 |
$1,125,000.00 |
In addition to revenue, however, clinic renovations cost money that must be charged against these earnings. Remember that doing nothing carries no renovation expense, whereas minor and major renovations cost $225,000 and $700,000 respectively. Table 10-5 lists the revenue, cost, and payoff for each decision alternative.
It is important to remember that the potential demand is uncertain. The clinic does not know for certain whether the demand will continue to be 20, 35, or 50 patients per day. It is quite possible that if a major renovation is undertaken, only 35 patients per day show up or are booked. At this point in this example, one management approach would be to use expert opinion or mathematical forecasting to predict the future demand and base the subsequent analysis upon the "certainty" associated with the forecast. Such insight may help determine how probable future demand might be and could assist in choosing an alternative.
Another approach is to assume that all states of the world are equally likely to occur. In this example doing so would mean that the probability of current demand (20 patients per day) would be 0.3333, moderate demand (35 patients per day) would be 0.3333, and high demand (50 patients per day) would be 0.3333, thus setting them equal.