Question

SciTools Incorporated, a company that specializes in scientific instruments, has been invited to make a bid on a government contract. The contract calls for a specific number of these instruments to be delivered during the coming year. The bids must be sealed (so that no company knows what the others are bidding), and the low bid wins the contract. SciTools estimates that it will cost $5000 to prepare a bid and $95,000 to supply the instruments if it wins the contract. On the basis of past contracts of this type, SciTools believes that the possible low bids from the competition, if there is any competition, and the associated probabilities are those shown in the table below. In addition, SciTools believes there is a 30% chance that there will be no competing bids.

Lowest competing Bid	Probability
Less than $115,000	0.2
Between $115,001 and $120,000	0.4
Between $120,001 and $125,000	0.3
Greater than $125,000	0.1

Based on the data in the table above, SciTools will limit its choices for bids to $115,000, $120,000, and $125,000.

a) Draw a decision tree for this scenario

b) Solve this decision tree using EMV

c) Draw the risk profiles for all decision strategies

d) Draw the cumulative risk profile for this scenario. Is there dominance?

e) Construct a tornado diagram for this scenario, if we assume the following ranges for the

variables:

a. Probability of no competing bids: 0 to 0.6

b. Cost to supply the instruments: $85,500 to $105,400

c. Bid cost: $4,500 to $5,500

Answer 1

Ans:

On the off chance that SciTools offers $115,000, its EMV is $12,200. Nonetheless, SciTools will not procure a benefit of $12,200. It will procure $15,000 or it will lose $5000. The EMV of $12,200 speaks to as it were a weighted normal of these two conceivable qualities.

SciTools has two essential techniques: submit a bid or do not submit a bid. In the event that SciTools presents an offer, then it must choose the amount to offer. In view of the cost to SciTools to set up the offer and supply the instruments, there is unmistakably no reason for offering under $100,000 –SciTools wouldn't make a benefit regardless of the possibility that it won the offer. (Really, this isn't thoroughly valid. Looking ahead to future contracts,

SciTools may make a low offer just to "get in the diversion" and pick up involvement. Notwithstanding, we won't consider such a plausibility here.Although any offer sum over $100,000 may be viewed as, the information in the table above propose that SciTools may restrict its decisions to $115,000,

$120,000, and $125,000.

The organization first settles on an offering choice, then watches what the opposition offers, in the event that anything,

lastly gets a result. The collapsing back process is equal to the figurings of EMVs in (6).

There are frequently equal approaches to structure a choice tree. One option for this case is

demonstrated as follows.

The organization first chooses whether to offer by any stretch of the imagination.

In the event that the organization does not make an offer, the benefit is a certain $0.

Something else, the organization then chooses the amount to offer. Take note of that if the organization chooses to offer,

it brings about a beyond any doubt cost of $5000, so this cost is put under the Bid branch.

Once the organization chooses the amount to offer, it then watches whether there is any opposition.

In the event that there isn't any, the organization wins the offer without a doubt and makes a relating benefit.

Something else, if there is rivalry, the organization in the end finds whether it wins or loses the

offered, with the comparing probabilities and adjustments.

Take note of that these adjustments are put beneath the branches where they happen in time. Likewise, the

combined settlements are put at the closures of the branches. Each aggregate result is the total of all

adjustments on branches that prompt to that end hub.

The collapsing back strategy is to some degree more mind boggling than it was for the littler tree.

To show, the EMVs over a chose few of these hubs are figured as takes after:

Hub 7: EMV = 20000(0.40) + (?5000)(0.60) = $5000 (utilizes money related qualities from end hubs)

Hub 4: EMV = 20000(0.30) + (5000)(0.70) = $9500 (utilizes financial incentive from an end hub

what's more, the EMV from hub 7)

Hub 2: EMV = max(12200, 9500, 6100) = $12,200 (utilizes EMVs from hubs 3, 4, and 5)

Hub 1: EMV = max(0, 12200) = $12,200 (utilizes financial incentive from an end hub and EMV

from hub 2)

The outcomes are the same, paying little heed to whether you utilize the table of EMVs created in (6), the

littler choice tree, or the bigger one, since they all compute the same EMVs in comparable ways.