Download Preparation for Tuesday, Nov. 25

BA 312/Decision Models/Professor Nau
Preparation for Tuesday, November 25
Start reading Chapter 12 and the Crystal Ball handout. (If you bought your own copy of Crystal
Ball, browse through the manual.) As your first exercise in using Crystal Ball, try building a
more realistic model of the competitive bidding problem we analyzed earlier. Recall that in this
problem an electrical company ("you") is bidding on a contract to wire a building. Your cost to
perform the work is estimated to be $45K, you are considering a bid in the range of $50-70K,
and there are two other competitors who are also going to be submitting bids in the same general
range. If your bid is lowest, you win the contract, and your profit is the difference between the
amount you bid and your cost of $45K. You may recall that a decision tree was a somewhat
awkward model for this problem: it seemed somewhat unrealistic to consider only a small
number of discrete bid levels for all the bidders, and even so, the tree was rather bushy.
To model this problem via simulation, set up a worksheet as shown below. Enter your cost and
the values of your competitor's bids as data cells at the top of the worksheet. In a column below,
enter a list of possible bid values for yourself from 50K to 70K in increments of 1K. In the next
column over, enter a formula to compute an indicator of whether you win the contract, given
your bid level and the bid levels of your opponents. The formula should return the value 1 if
your bid is less than or equal to the minimum of your two opponent's bids, otherwise 0. In the
next column over, enter a formula to compute your profit. (There are various ways you can write
the profit formula using references to the "you win" formula. The basic logic is that your profit
is the difference between your bid and your cost IF you win the contract, otherwise it is zero.)
Your formulas should use absolute or relative cell references as appropriate so that they can be
copied into the rest of the cells in the same column) At this point, you should have a model that
can be used for "what if" analysis in which different values are entered for your competitor's bids
and/or your cost, and the model will compute whether you would win the contract and what your
profit would be for various amounts you might bid. An example is shown below: if your
competitors bid $55K and $60K respectively, then you would win the contract and earn a profit
of $5K if you bid $50K, you would win and earn a profit of $10K if you bid $55, and you would
lose and earn a profit of zero if you bid $56K.
Competitive bidding problem
Your cost
$45
Comp. #1 bid
$55
Comp. #2 bid
$60
Your bid You win?
$50
1
$51
1
$52
1
$53
1
$54
1
$55
1
Profit
$5
$6
$7
$8
$9
$10
$56
$57
$58
$59
Etc. down to 70
0
0
0
0
…
$
$
$
$
…
Now comes the fun part: open this spreadsheet file using Crystal Ball, and specify that the two
competitors' bid cells are "Assumptions." (Select each of these cells in turn, hit the "Define
Assumption" button on the Crystal Ball toolbar, and choose an appropriate probability
distribution from the "gallery" that appears.) Let's suppose that you are pretty sure that
competitor #1 will bid close to 60K, whereas competitor #2 is a new entrant in the market whose
bid is much more uncertain. To reflect these assumptions, specify that competitor #1's bid is a
triangular random variable with minimum, most probable, and maximum values of 50K, 60K,
and 70K, respectively. Specify that competitor #2's bid is a uniform random variable with
minimum and maximum values of 50K and 70K. (Thus, both competitor's bids are assumed to
be between 50K and 70K, but competitor #2's bid is equally likely to be anywhere in this
interval, whereas competitor #1's bid is most likely to be around 60K.)
Once the assumptions have been defined, try hitting the "Single Step" button on the Crystal Ball
toolbar a few times. (This is the rightmost of the "VCR buttons" in the middle of the toolbar.)
You should see random values appear for your competitor's bids, and the you-win and profit
cells in your model should change accordingly. Each time you hit the single-step button, you are
performing a single random trial of your model--i.e., you are randomly simulating one possible
"future." The idea of Monte Carlo simulation is to generate LOTS of random trials, keep track of
the statistics of the outputs of your model, and use the statistics as estimates of the probabilities
and expected values. For example, the average (mean) of the you-win cell over many trials is
the probability that you will win with a given bid level, and the average of the profit cell over
many trials is the expected value of the profit at a given bid level.
Next, define the "Forecasts" (outputs) for which you wish to collect statistics. Highlight the
column of you-win cells and hit the "Define Forecasts" button (the 2nd button on the toolbar).
Just click "OK" on each of the windows that appears. Then do the same thing for the profit
column. (Note: it is important to do this one column at a time--i.e., define the column of youwin cells as one set of forecasts, and then define the column of profit cells as another set of
forecasts. This will ensure that the you-win cells appear consecutively and the profit cells appear
consecutively in the reports that follow later.)
To test that your assumptions and forecasts are defined correctly, click the "Select Assumptions"
button--you should see the competitors' bids cells highlighted. Then click the "Select Forecasts"
button--you should see the columns of you-win and profit cells highlighted.
Now you are ready to run your model. Hit the "Run Preferences" button and check to see that
the number of iterations (trials) is set to a moderately large value--at least 1,000. Then hit the
"Start simulation" button (which looks like the "play" button on a VCR) on the toolbar. You
should see a lot of interesting stuff appear on the screen while your model runs. (Later you can
adjust the "Run Preferences" and "Forecast Windows" tools to control what you see while the
model runs.)
At the end of the run, hit the "Extract Data" button and choose the "Statistics" report. The
summary statistics of your forecast cells will then be written to a separate worksheet. There you
can study--and if you wish, plot--how the probability of winning and the expected profit vary
with the bid level. (The main statistics of interest here are the mean values.) Which of the profit
cells has the highest mean value, and what bid level does it correspond to? This is evidently the
optimal bid….