DECISION MODELING WITH MICROSOFT EXCEL Copyright 2001 Prentice Hall Publishers and Ardith E. Baker DISCRETE EVENT SIMULATION SIMULATION Chapter 10 Part 1

DISCRETE EVENT SIMULATION INTRODUCTION Typically, simulation refers to a specific class of ______models involving the detailed observation of a complex _____________system over time. Continuous simulation models involve _________ variables that change more or less continuously with time (such as those models in Chapter 9). Discrete event simulation is applied whenever individual items are ________and in which abrupt or ___________changes in the timing of events is the norm.

________event simulation models can be used to delve into the fine details of complex systems with many_____________. However, discrete event simulation ________can become extremely complex to build and analyze. Discrete event simulation models are most commonly used to create _________operational systems representing demands among activities requiring ________resources over time.

A single server ________situation will be used to illustrate a discrete event simulation. EXAMPLE 1 A SIMULATION MODEL IN EXCEL We will illustrate the building of such models using a _____________simulation package called Extend. Extend can be used for both ___________ simulation and discrete event simulation. We will investigate the relative __________of an airport car rental business (Hervis) by modeling the movement of ___________through the rental office.

Customers arrive in an airport van and queue up, _________– first serve, for service at the rental counter. Eventually, a given customer moves to the head of the ______and, when the rental clerk is free, will receive service that consists of Finally, customers depart, collect their rental car and drive away. filling out the ________forms choosing the rental options receiving some driving____________ etc.

Consider the following data giving the relative __________distribution of customer arrivals in any given 5-minute block of time throughout a typical 24-hour day. Let’s simulate a week of _______operations and segment time into 5-minute blocks. We assume that it will always take exactly 5 minutes to serve a waiting_________.

Because 7*24*60/5 = 2016 time blocks (exceeding the 256-column __________in Excel), the time blocks will be modeled in rows. To build the Hervis model in Excel, first label the ____________by using the Fill Series option from the Edit menu.

Next, create a probability distribution table: Cell K8 computes the expected number of customer arrivals.

The computer will be driven by _________drawn probabilities, which in turn will determine the number of customers arriving in any 5-minute time________. The _______function will draw a random fraction greater than or equal to 0 and less than 1, one for each of the 2016 time blocks. Set the Tools – Options – Calculation option to ________to avoid drawing new random numbers each time the worksheet is changed.

Place the =RAND() formula in cell B5 and copy it down to cell B2020 to create all 2016 random fractions. Next, create a _______probability table based on the =RAND() formulas (the inputs). The number of customer arrivals, as__________, are computed by =VLOOKUP() formulas.

Column D formulas compute the number of customers in ______and being served. Column E formulas compute the number of customers receiving rental counter _________as being the ________of the number in line and the number of rental counter stations in C2. Column F computes the number of customers remaining _________at the end of the 5-minute block.

The initial results show that on the average, ½ customer _________in each 5-min. block (or 1 customer every 10 minutes). It always takes only one 5-min. interval to serve a customer, thus, the rental counter is _______only ½ the time on average. However, during peak times, you could have 9 customers awaiting_______, leading to a delay of 45 minutes for the 9 th customer. To __________this wait, we could add another rental station. We can use this model to evaluate the _______of adding another rental station, thus allowing up to two waiting customers to receiver service _________________.

Below is the revised model for 2 rental stations. The revised statistics indicate that the ________ number of customers delayed falls from an average of.499 to an average of _____.

EXAMPLE 2 A SIMULATION MODEL IN EXTEND The use of Excel for discrete event simulation suffers from two primary ________________: 1. For reasonably sized models, the resulting Excel spreadsheet quickly fills up with cells occupied with___________. 2. Discrete event simulation models in Excel do not ______well.

Where Excel falls short in handling _______event simulation models, Extend has the modeling capability to: 1. Scale to ________time grids and longer planning horizons. 2. __________the model representation to avoid generating large spreadsheets that are cumbersome to manipulate and debug. 3. Easily ___________and generate results. 4. Develop an environment that _________ the latest in graphic user interfaces to facilitate easy model building and self- documentation.

Extend’s models for discrete event simulation are _______oriented and are built using predefined building blocks. A ____is Extend’s object for specifying an action, process, accumulation, statistical summary, or other object for creating the____________. The blocks are _______together by drawing lines to form a ________of interrelated activities. __________ (e.g., customers) flow through the connected network of blocks while Extend gathers __________on their movements.

Links connect blocks: two accommodate item ______and output, and two accommodate value input and output. These links provide the _____that allow items to flow through the model’s blocks. These links appear as small ________on the edge of each block. These links pass data and ___________ about items between blocks. These _____appear as connectors on each parameter values and for reviewing its results after a __________run.

Each block in Extend has a dialog _________for specifying parameter values and for reviewing its _______after a simulation run. Here is an Extend Activity, Delay ______typically used to hold an item for an amount of time and then ________it to the next block.

BUILDING THE HERVIS SIMULATION MODEL Open the Simulation Setup dialog by selecting Simulation Setup from the Run menu. Here, you can specify __the simulation will run and for________. For most purposes, start with the default start time of 0. The Number of runs option can be left at 1.

Now, because Hervis models the rental car minute – by – minute for a week, click on the Global time units button and select the minutes option. Hervis will run the simulation for a week of simulation time (24*7*60 = 10,080 minutes). Enter into the End simulation at time field and click OK.

Choose New Model from Extend’s File menu to open a __________window. To add a block to the model window: 1. Open the library containing Extend’s predefined_______, if necessary.

2. Add the desired block to the model by selecting it from the_________-. 3. Click-drag to move the block to its desired ________in the model window.

4. Connect its _____and output connectors to other blocks. In order to copy a __________Extend block into a model, the library in which that block _______ must be open. For the Hervis modeling in this chapter, open the Generic, Discrete Event, Plotter, and Stats libraries.

To open the Discrete Event library, choose Open Library … from Extend’s Library menu. Locate the _____subdirectory and select Discrete Event library (DE.lix) and click OK. Now, open the ________(GENERIC.lix), Plotter (PLOTTER.lix) and Stats (STATS.lrx) libraries.

To add a block to a______, click on the Library menu and select the name of the library that holds the ________block. A _________ menu of the different types of blocks in the library will appear. To the right of this menu a list of the names of the blocks will appear. Selecting the desired block will put a ______of the block in the Extend window.

For discrete event simulation modeling, Extend always requires an ___________block from the Discrete Event library to be placed as the ______ block in the model window. This block, with an _______of a wall clock, determines its stopping conditions and handles the details of event__________. Normally, there is no _________to the Executive block, and once placed, can be ignored.

The Hervis model begins with the arrival of an airport van carrying rental-car customers. This is represented by Extend’s Generator block. Add a Generator block from the Generators submenu of the Discrete Event library.

Double-click on the block to open the ________ dialog. Select a _________distribution with a parameter setting of 5 and minutes as the Time Units. Also, label the block___________.

Each time a van arrives, it contains a _______ number of customers (a batch). By default, Extend’s Generator block creates a ______of size one. This can be ____________by providing another number via the V value input____________. In this case, we want the batch size to be a _______number of customers between 0 and 3.

Specify the random number of customers in the Input Random Number block. Go to the Inputs/Outputs menu in the GENERIC.lix library and add the Input Random Number block.

Label the block # of Customers and click OK. Double click to open the dialog. Select Empirical Table and Discrete and enter the data shown in the previous table.

Add a _________by double-clicking on the white background. Type Customers Come from Airport Van in the resulting edit field. Blocks are ___________together through their connectors by connection lines. To connect the blocks, position the mouse cursor over one of the___________. When the cursor changes to a pen, click-drag it to the other_____.

Now, connect the _____value connector to the V input connector. This allows ___________to flow from the output of the Input Random Number block to the V input __________of the Generator block. When you release the pen/cursor, a _______ will appear, connecting the two blocks. This connection will _________an arrival of a batch of items (customers) varying from 0 to 3 in size according to the previous_______________.

Now, in order to have the batch of customers queue First in, First Out (FIFO) in front of the rental station, add a Queue, FIFO block from the Queues menu of the DE.lix library.

Use the cursor-pen as before and connect the _____connector from the Queue, FIFO block to the output _________of the Generator block. This allows the customers in the batch to join the_____. Double-click on the _____to open it. Enter a label for the block.

Note that the __________lines over which items (customers) flow among blocks are ______while the connection lines among blocks providing information (______) are thin solid lines. Also note that items (customers) produced by a _________block are pushed out immediately and must have someplace to go in the model. This usually requires a direct connection from a Generator block to one of Extend’s _________or Resource blocks. Otherwise the Generator block may lose items, giving __________results.

In the original Hervis model, the rental clerk will delay each __________for 5 minutes to complete the car rental transaction. You can introduce this delay in the Activity, Delay block. However, this block only allows for one _________. Therefore, use the Activity, Multiple block from the Activities menu of the DE.lix library.

Items leave the simulation model via Extend’s Exit block found on the Routing menu of the DE.lix library.

Another useful block is the Plotter, Discrete Event block found in the PLOTTER.lix library. This block captures _______and plots up to four variables during the simulation run.

The variables to be collected and plotted are determined by connecting the Plotter, Discrete Event block’s connectors to the appropriate ____ connectors of other blocks in the model. The Utilization of the Rental Station and the customer__________, W, is captured from the Queue, FIFO block.

RUNNING THE MODEL Click on the Run - Run Simulation pull-down menu or on the Run Simulation button to begin the simulation. When the simulation begins, Extend will: 1. Display a _________at the bottom of the screen based on the designated settings. (Note that results may differ due to the ___________in the simulation data for customer batch size.)

2. Open a window for the plotter to ______________report its variables, server utilization and waiting time. Note how the wait time in line _____ in discrete units of 5 minutes. The max. wait was 35 min. The avg. ________ was 50%. This implies that the station will be busy ½ the time on avg. The avg. utilization is __________in early time periods but settles to its long run average value.

To manipulate the graph, click on the Trace Properties icon at the top of the graph. This will bring up the Trace Lines Properties window. Each of the plotter _______ occupies two rows: the properties of the variable’s ___________and the properties of the variable.

Note that a variable’s time stamp can have only its ____________format changed. Click on the model’s Queue, FIFO block and Activity, Multiple block to open their _________ dialog windows. Next, click on the Results tab to reveal the simulation run _________for each block.

To see what the effect of adding an ________ sales clerk, double-click on the Activity, Multiple block and change the Maximum Number in Activity from 1 to 2. Now, rerun the _______________to produce the following results.

The average utilization of 2 servers tends to be 25%.

The max. queue length drops to 4 with the max waiting time of 5 min.

EXAMPLE 3 - HERVIS CAR RENTAL MODEL EXPANDED Now, Hervis knows the airport vans experience traffic delays and don’t always arrive exactly every 5 minutes. To model this, modify the original Extend model to allow for a range of __________ times for airport vans from 3 minutes to 7 minutes, with the ___________ interarrival time being 5 minutes.

Note that a ___________distribution is used for simplicity. So far, we have assumed that it always takes exactly 5 minutes for the clerks to complete the car rental contract. To add some _________to this, add another Input Random Number block.

Go to the Library pull-down menu and choose Generic.lix – Inputs/Outputs – Input Random Number block.

Double-click on the block and specify the __________via an Exponential distribution with a mean of 5. Connect the block’s output connector to the _____ connector of the Activity, Multiple block. By keeping the _______of each distribution the same, the avg. queue length and waiting time will not be_________.

Rerun the model to produce the following results:

The added variability ___________the max. wait substantially and the max. _____length slightly. The avg. wait is also longer and the avg. queue length _______ dramatically. These results show that adding variability alone to the distributions _______the average performance as well as increasing performance ________.

Now, run the simulation again to see if adding another rental clerk to the model will have a dramatic improvement. Double-click on the Activity, Multiple block and change the Maximum Number in Activity from 1 to 2 and click OK. Click on the Run Simulation icon to start the simulation.

Here is the resulting graph: Remember, results will differ due to the random effects.

The avg. wait of.7 minutes and max. wait of 19 minutes look more reasonable.

End of Part 1 Please continue to Part 2