Question

Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.

Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.

As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.

Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).

Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.

Ram's statistically minded friend Rocky feels that Ram should not use just one criterion to decide on a plan. "Decision making has to bring in all the criteria together. That is what makes a decision sound," Rocky said.

"How do I do that?" Ram asked. "Simple," said Rocky. "Give a weight to each criterion, multiply the value of each criterion by its weight, and add up the products for each option."

Rocky explained with an example: "For each option there are two criteria, the probability of not making it to the wedding and the travel time. The probability of not reaching on time is 1 minus the probability of reaching on time. Say you hate the thought of missing the wedding after all this effort, so give that criterion a weight of 80%. You also want to keep the travel time low, so give that a weight of 20%. For each option, add up (value of each criterion times its weight) and compare the totals across options. Pick the option with the lowest total."

"That simple?" Ram asked. "Well, it is, for a start," Rocky admitted.

Q128. As the foggy winter conditions continue, flights out of Delhi remain uncertain and unreliable. Using Rocky's elementary decision-making framework, which of the following itineraries should Ram adopt?

• A. Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by bus; Jaipur to Ajmer by train
• B. Delhi to Bharatpur by taxi; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by flight; Jaipur to Ajmer by train
• C. Delhi to Bharatpur by train; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by train; Jaipur to Ajmer by train
• D. Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by train; Jaipur to Ajmer by train

Hint:

Scale each itinerary's travel time against the longest travel time in the group before combining it with the failure probability using Rocky's eighty-twenty weighting.

Answer 1

The Correct Option is C

Step 1: Recall Rocky's scoring method.
Rocky's approach takes two criteria for each itinerary, the probability of not reaching on time, and the total travel time, gives the first a weight of eighty percent and the second a weight of twenty percent, multiplies each value by its weight, adds the two products together, and picks the itinerary with the lowest total.

Step 2: Work out the failure probability for each itinerary.
Multiplying each leg's on time probability and subtracting from one gives the chance of failure. Train, taxi, bus, train comes to about 0.627. Taxi, train, flight, train comes to about 0.570. Train, train, train, train comes to about 0.453. Train, taxi, train, train comes to about 0.484.

Step 3: Bring the travel times onto the same scale.
The total hours are 45, 30, 38 and 40 for the four itineraries respectively. Since probability already sits on a scale from zero to one, the travel times need to be brought onto a comparable scale too, so each is expressed as a fraction of the longest travel time in the group, 45 hours. That gives 45 divided by 45 equals 1.0, 30 divided by 45 equals about 0.667, 38 divided by 45 equals about 0.844, and 40 divided by 45 equals about 0.889.

Step 4: Combine both criteria with Rocky's weights.
For train, taxi, bus, train: 0.8 x 0.627 plus 0.2 x 1.0, which comes to about 0.70. For taxi, train, flight, train: 0.8 x 0.570 plus 0.2 x 0.667, which comes to about 0.59. For train, train, train, train: 0.8 x 0.453 plus 0.2 x 0.844, which comes to about 0.53. For train, taxi, train, train: 0.8 x 0.484 plus 0.2 x 0.889, which comes to about 0.56.

Step 5: Pick the lowest total.
The all train itinerary comes out with the lowest combined score of the four, since its clearly higher reliability on every single leg outweighs its somewhat longer total travel time once both criteria are weighed together the way Rocky describes.

Final Answer:
Delhi to Bharatpur by train, Bharatpur to Jodhpur by train, Jodhpur to Jaipur by train, Jaipur to Ajmer by train.