A shipping company that primarily operates only one vehicle must decide whether to use Model 1 or Model 2. In Model 1, there are two zones A and B for delivery and pick-up, while in Model 2 also there are two zones for delivery and pick-up but they are different and named C and D.
Model 1: Deliveries picked up in zone A have destinations in zone A with a probability of 0.2 and the same in zone B with the remaining probability. These deliveries earn a profit of $12.
Model 1: Deliveries picked up in zone B have destinations in zone B with a probability of 0.8 and the same in zone A with the remaining probability. These deliveries earn a profit of $8.
Model 2: Deliveries picked up in zone C have destinations in zone C with a probability of 0.1 and the same in zone D with the remaining probability. These deliveries earn a profit of $15.
Model 2: Deliveries picked up in zone D have destinations in zone D with a probability of 0.5 and the same in zone C with the remaining probability. These deliveries earn a profit of $7.
1) If the average profit is the metric for selecting the model, determine which model is better.
2) If the metric is Average Profit minus times the Variance in Profits, then which model is better? Use a value of 0.2 for theta.