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 Table 9.2. In addition, SciTools believes there is a 30% chance that there will be no competing bids. What should SciTools bid to maximize its EMV?

Objective To develop a decision model that finds the EMV for various bidding strategies and indicates the best bidding strategy.

Table 9.2: Data for Bidding Example

Low Bid

Probability

Less than $115,000

0.2

Between $115,000 and $120,000

0.4

Between $120,000 and $125,000

0.3

Greater than $125,000

0.1

The company has probably done a thorough cost analysis to estimate its cost to prepare a bid and its cost to manufacture the instruments if it wins the contract. (Actually, even if there is uncertainty in the manufacturing cost, the only value required for the decision problem is the mean manufacturing cost.) The company's estimates of whether, or how, the competition will bid are probably based on previous bidding experience and some subjectivity. This is discussed in more detail next.

Let's examine the three elements of SciTools's problem. First, SciTools has two basic strategies: submit a bid or do not submit a bid. If SciTools submits a bid, then it must decide how much to bid. Based on the cost to SciTools to prepare the bid and supply the instruments, there is clearly no point in bidding less than $100,000-SciTools wouldn't make a profit even if it won the bid. (Actually, this isn't totally true. Looking ahead to future contracts, SciTools might make a low bid just to "get in the game" and gain experience. However, we won't consider such a possibility here.) Although any bid amount over $100,000 might be considered, the data in Table 9.2 suggest that SciTools might limit its choices to $115,000, $120,000, and $125,000.3

The next element of the problem involves the uncertain outcomes and their probabilities. We have assumed that SciTools knows exactly how much it will cost to prepare a bid and how much it will cost to supply the instruments if it wins the bid. (In reality, these are probably only estimates of the actual costs, and a follow-up study could perform a sensitivity analysis on these quantities.) Therefore, the only source of uncertainty is the behavior of the competitors-will they bid, and if so, how much?

From SciTools's standpoint, this is difficult information to obtain. The behavior of the competitors depends on (1) how many competitors are likely to bid and (2) how the competitors assess their costs of supplying the instruments. Nevertheless, we assume that SciTools has been involved in similar bidding contests in the past and can reasonably predict competitor behavior from past competitor behavior. The result of such prediction is the assessed probability distribution in Table 9.2 and the 30% estimate of the probability of no competing bids.

The last element of the problem is the value model that transforms decisions and outcomes into monetary values for SciTools. The value model is straightforward in this example. If SciTools decides not to bid, its monetary value is $0-no gain, no loss. If it makes a bid and is underbid by a competitor, it loses $5000, the cost of preparing the bid. If it bids B dollars and wins the contract, it makes a profit of B minus $100,000-that is, B dollars for winning the bid, minus $5000 for preparing the bid and $95,000 for supplying the instruments. For example, if it bids $115,000 and the lowest competing bid, if any, is greater than $115,000, then SciTools wins the bid and makes a profit of $15,000.

Question: The optimum choice for the company is to bid $115,000 for an expected return of $12,200. What other considerations should be made before the company decides to bid?