Spreadsheet Demonstration Bidding Simulation

Bidding simulation Winston 12.2 The Rogers Construction Company is trying to decide whether to make a bid on a construction project. Rogers believes it will cost the company $10,000 to complete the project (if it wins the contract), and it will cost $350 to prepare a bid. Four potential competitors are going to bid against Rogers. The lowest bid will win the contract (and the winner will then be given the winning bid amount to complete the project). Based on past history Rogers believes that each competitor’s bid has a triangular distribution with low and high extremes 10,000a and 10,000b

Bidding simulation Winston 12.2 (cont’) and most likely value 10,000c. That is, each competitors bid is at least a times Rogers’s cost. For this particular example, we will assume that a=1, b=3, and c=1.3. These four competitors’ bids are also assumed to be independent of one another. If Rogers decides to prepare a bid, then it has decided that its bid amount will be a multiple of $500 in the range from $10,500 to $15,000. The company wants to use simulation to determine which strategy to use in order to maximize its expected profit.

Bidding simulation Basic problem Rogers Company wants to bid for a project against four competitors Low bid wins the contract Competitors’ bids are uncertain until after Rogers has made its bid

Bidding simulation Uncertainties Each competitor’s bid is uncertain Each is modeled with a triangular distribution with parameters “minimum,” “most likely,” and “maximum” Each parameter is a multiple of Rogers’ cost to complete project If you haven’t done so yet, review the section in Chapter 12 on generating random numbers from a triangular distribution. Although this distribution is intuitive and often useful, the procedure for generating random numbers from it (with Excel’s built-in functions) is fairly complex.

Bidding simulation Monetary inputs Costs to Rogers include Cost to prepare bid Cost to complete project (if it wins bid) If Rogers wins the bid, it receives the bid amount

Bidding simulation Decision to make Rogers must to decide whether to submit a bid, and if so, what its bid amount should be Decision criterion: maximize the expected profit

Building the spreadsheet model (See Excel “Steps 1-3” sheet) Step 1: Enter all inputs Steps 2, 3: Generate random bids for the four competitors Go through steps for generating triangularly distributed random numbers

Building the spreadsheet model (See Excel “Steps 4-6” sheet) Step 4: Enter the company’s possible decisions (including the “no bid” decision) Step 5: Use an IF function to see whether Rogers is the low bidder Step 6: Calculate its profit This will be a loss if it prepares a bid and then doesn’t win the contract

Building the spreadsheet model (See Excel “DataTable” sheet) Create a data table to replicate Rogers’ profit Possible decisions are along the top Replication numbers are along the side For each possible decision calculate summary measures (at least averages and standard deviations) over all replications This data table might be a bit confusing. It is really a one-way table (with column input cell any blank cell) with multiple outputs (one for each possible decision along the top). So there is no row input cell. Note how we have used the TRANSPOSE function to transpose a column of profits into the row (in gray) at the top of the data table.

Building the spreadsheet model (See Excel “Averages”, “Stdevs” sheets) Create bar charts for the averages and standard deviations from the data table Bid of around $12,000 to $13,000 appears to maximize average profit Standard deviations tend to increase for larger bids (more risk) These graphs are “live” (press F9 key) Highest peak on “Averages” graph changes This is a good example to illustrate how the decision that maximizes the objective (average profit) can change from one set of replications to another. Go to the “Averages” sheet and repeatedly press the F9 key. The “optimal” bid keeps changing!