Question

Transrail is bidding on a project that it figures will cost $400,000 to perform. Using a 25% markup, it will charge $500,000, netting a profit of $100,000. However, it has been learned that another company, Rail Freight, is also considering bidding on the project. If Rail Freight does submit a bid, it figures to be a bid about $470,000. Transrail really wants this project and is considering a bid with only a 15% markup to $460,000 to ensure winning regardless of whether or not Rail Freight submits a bid.

a) Do a profit payoff table from Transrail's point of view

b) For this payoff table find Transrail's optimal decision using (1) the pessimistic approach, (2) the optimistic approach, and (3) minimax regret approach.

c) If Rail Freight is known to submit bids on only 25% of the projects it considers, what decision should Transrail make?

d)Given the information in (c), what is EVPI?

Answer 1

Answer:

Given that,

Transrail is bidding on a project that it figures will cost $400,000 to perform. Using a 25% markup, it will charge $500,000, netting a profit of $100,000.

However, it has been learned that another company, Rail Freight, is also considering bidding on the project. If Rail Freight does submit a bid, it figures to be a bid about $470,000.

Transrail really wants this project and is considering a bid with only a 15% markup to $460,000 to ensure winning regardless of whether or not Rail Freight submits a bid.

(a).

Do a profit payoff table from Transrail's point of view:

Profit payoff table from Transrail's point of view.

Decision Alternative	Railfreight doesn't bid	Railfreight bids
Bid $460000	60,000	60,000
Bid $500000	100000	0

(b).

For this payoff table find Transrail's optimal decision using (1) the pessimistic approach, (2) the optimistic approach, and (3) minimax regret approach:

(i).

Optimistic Approach -Maximax:

As per the optimistic approach, we determine the maximum payoff of each alternative and then select the alternative whose maximum payoff is the maximum of all of them.

Transrail should bid $5,00,000 to maximize its profit under optimistic approach.

Decision Alternative	Railfreight doesn't bid	Railfreight bids	Max of row
Bid $460000	60,000	60,000	60,000
Bid $500000	100000	0	1,00,000 (Recommended decision)

(ii).

Conservative Approach - Maximin:

As per conservative approach, we find out the maxminimum apyoff of each alternative then select the alternative whose minimum payoff is the maximum of all of them.

Transrail should bid 4,60,000 to maximize its profit under conservative approach.

Decision Alternative	Railfreight doesn't bid	Railfreight bids	Min of row
Bid $460000	60,000	60,000	60,000 (Recommended decision)
Bid $500000	100000	0	0

(iii).

Minimax regret approach:

Regret value of each decision alternative is computed by subtracting the value of particular decision from the maximum value of the corresponding state.

Decision corresponding to the minimum regret value is selected out of the averages or sum of values corresponding to each decision.

Transrail should bid $460000 to maximize its profit while minimizing regret.

Decision Alternative	Railfreight doesn't bid	Railfreight bids	Min of row
Bid $460000	40,000	0	40,000 (Recommended decision)
Bid $500000	0	60,000	60,000

(c).

If Rail Freight is known to submit bids on only 25% of the projects it considers, what decision should Transrail make:

Payoff table under uncertainty:

In this case, it is given that there's a 25% probability of Railfreight bidding on the project. We calculate the EMV based on these probabilities And select the decision with the highest EMV. Decision B (bid 5,00,000) has the highest payoff.

Transrail should bid $4,60,000 to maximize its profit.

Decision Alternative	Railfreight doesn't bid	Railfreight bids	Min of row
Bid $460000	60,000	60,000	60,000
Bid $500000	100000	0	75000 (Recommended decision)

(d).

Given the information in (c), what is EVPI:

EVP:

As expected value for a bid of 5,00,000 is greater than that for bidding 4,60,000, Transrail should bid 5,00,000.

A spy is worth up to15,000 the difference between expected values.