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

Rocky's rule is to weigh the probability of not reaching on time at eighty percent and the total travel time at twenty percent, multiply each by its weight, add the two together for every itinerary, and go with whichever total comes out lowest.

1. Train, taxi, bus, train: The failure chance is about 0.627, and the travel time of 45 hours is the longest of the four, the maximum against which the others get compared. Combining both gives a score of about 0.70, the weakest of the group.
2. Taxi, train, flight, train: The failure chance is about 0.570, and the travel time is only 30 hours, a good deal shorter than the rest. Scaled against the 45 hour maximum and combined with the failure chance, the score comes to about 0.59.
3. Train, train, train, train: Every leg by train pushes the failure chance down to about 0.453, the lowest of the four, while the travel time of 38 hours is only moderately higher than the flight based option. Once scaled and combined, this gives the lowest score of the group, about 0.53.
4. Train, taxi, train, train: The failure chance here is about 0.484, with a travel time of 40 hours, giving a combined score of about 0.56, higher than the all train option.

Since Rocky's weighting leans heavily toward avoiding failure, at eighty percent of the total score, the itinerary with the lowest failure chance keeps its edge even though it is not the fastest of the four.

Let's summarize:

• Scaling travel time against the longest option in the group puts it on the same footing as the zero to one probability scale.
• The all train itinerary has the lowest failure chance of the four by a clear margin.
• Once both criteria are combined using Rocky's eighty-twenty weighting, the all train itinerary comes out on top.

So Ram should adopt the itinerary Delhi to Bharatpur by train, Bharatpur to Jodhpur by train, Jodhpur to Jaipur by train, and Jaipur to Ajmer by train.