SIMULATION – PART I Introduction to Simulation and Its Application to Yield Management. For this portion of the session, the learning objectives are: Receive an introduction to the technique of Simulation . Learn the meaning of Yield Management .
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SIMULATION – PART IIntroduction to Simulationand Its Application toYield Management
Yield Management encompasses a wide variety of techniques, such as maximizing profit by determining how to adjust the prices of “seats” as it gets closer and closer to the date/time when customers will use the “seats”. In this course, we will not consider this technique.
A common practice in Yield Management is overbooking, that is, confirming more reservations than the number of “seats” available.
To illustrate how simulation can be applied to Yield Management, we will use an example of airplane overbooking.
EXAMPLE
To illustrate both simulation and the airplane overbooking problem, we will consider the example below.
NOTE: As indicated in Cell A13, we will temporarily assume that the maximum allowable number of confirmed reservations is 127.
Below is a complete summary of our example’s given data:
SIMULATING DEMAND
USING A TABLE OF RANDOM NUMBERS
Random Numbers Corresponding to Demand
Demand for Confirmed Reservations
The Binomial Probability Distribution
Example 1: Flipping a Coin
Example 2: “No Shows”
SIMULATION THE NUMBER OF “NO SHOWS”
USING A TABLE OF RANDOM NUMBERS
As examples,
# of “No Shows” =
# of “No Shows” =
# of “No Shows” =
SPREADSHEET FOR SIMULATION
The following pages provide a summary of how to use Crystal Ball to analyze the Airplane Overbooking Problem.
OVERVIEW OF CRYSTAL BALL
Copy Data
Paste Data
Run Preferences
New Menu Selections
Forecast Charts
Create Report
Define
Forecast
Start Simulation
Define
Decision
Stop Simulation
Single Step
Define
Assumption
Reset Simulation
Defining Assumption Cell A18: the Demand for Confirmed Reservations
The demand for confirmed reservations is a so-called Custom Probability Distribution.
It would be too time-consuming to manually enter the Custom Probability Distribution displayed in the Cell Range R11:S60.
Fortunately, Crystal Ball provides a way to “read in” the 50 values and the associated probabilities.
To do so, we proceed as summarized on the next slide.
First click on Cell A18, next click the Define Assumption icon, then click Custom, and finally click OK. After doing so, the dialog box to the right appears. In this dialog box, first enter the Assumption Cell’s name as “Demand”, and then click LoadData.
After doing so, the dialog box to the right appears. In this dialog box, enter the Cell Range R11:S60, and then click OK.
After doing so, the dialog box to the right appears, in which the Custom Probability Distribution has been “read in”. Click OK to return to the spreadsheet.
Defining Assumption Cell A20: the Number of “No Show” Reservations
After temporarily assuming that the maximum allowable of confirmed reservations is set to 127, after defining the two Assumption Cells in Cells A18 and A20, and after defining the Forecast Cell in Cell A27, we obtain the following spreadsheet:
Our goal is to determine what value in Cell A13 will maximize the mean of Cell A27.
This slide and the following three slides display spreadsheets resulting from “debugging” the model by repeatedly clicking on the Single Step icon until four distinct types of scenarios are obtained.
Scenario 1: Demand > Supply & Bumping Occurs
Scenario 2: Demand > Supply & No Bumping Occurs
Scenario 3: Demand < Supply & Bumping Occurs
Scenario 4: Demand < Supply & No Bumping Occurs
Now that we are confident that the spreadsheet has been properly constructed, we are ready to run the simulation.
Recall that our goal is to determine the optimal value for the Maximum Number of Reservation to Confirm, that is the value for Cell A13 that maximizes the mean of the total contribution (to overhead and profit)
Although time-consuming, one way to do this would be to run the simulation 35 times, first with Cell A13 =115, then with Cell A13 =116, …, and finally with Cell A13 =149. After doing so, we could then choose the value that maximized the mean of the total contribution.
Wouldn’t it be nice if Crystal Ball could automate this process for us?
In fact, Crystal Ball can do so through its Decision TableTool.
The next slide illustrates how to use the Decision TableTool.
Using Crystal Ball’s Decision TableTool
Step 1. To define the Decision Cell, first click cell and then click the Define Decision icon. The dialog box below will pop up. Within this box, enter a descriptive name for the decision and enter its lower & upper limits; then click on the radio button for Discrete and enter the Step. Finally click on OK.
Step 2. Choose the Run, Tools, Decision Table menu selection. The dialog box below (#1 of 3) will pop up. Within this box, highlight one of the Forecast Cells to be the Target Cell (i.e., the Forecast Cell whose mean value you want to optimize). Then click Next.
Step 3. In the resulting dialog box (#2 of 3), move the Decision Variable from “Available” to “Chosen” (i.e., from left to right) by first highlighting the decision variable and then clicking “>>”. Finally, click Next.
Step 4. In the resulting dialog box (#3 of 3), first enter the number of trials for each simulation and then click Start.
Crystal Ball’s Decision Table Tool yields Rows 1-3 in the spreadsheet below. By clicking in Cell A1 on Forecast Charts, you can view any of the 35 Forecast Charts, including the one corresponding to the maximum Total Contribution, which can then be pasted into the spreadsheet.