DECISION MODELING WITH MICROSOFT EXCEL Copyright 2001 Prentice Hall DISCRETE EVENT SIMULATION SIMULATION Chapter 10 Part 2.

DECISION MODELING WITH DECISION MODELING WITH MICROSOFT EXCELMICROSOFT EXCEL

Copyright 2001Prentice Hall

DISCRETE EVENTDISCRETE EVENT SIMULATIONSIMULATION

Chapter 10Chapter 10

Part 2Part 2

EXAMPLE 4 – HERVIS CAR EXAMPLE 4 – HERVIS CAR RENTAL MODEL REVISITEDRENTAL MODEL REVISITED

Based on the previous results, Hervis came Based on the previous results, Hervis came up with an idea of pulling some of the car up with an idea of pulling some of the car service people off the car lot to staff more service people off the car lot to staff more rental stations whenever the queue of rental stations whenever the queue of customers became large.customers became large.In this way, the staffing of the rental In this way, the staffing of the rental stations would increase to three or even stations would increase to three or even four clerks whenever a peak in customer four clerks whenever a peak in customer demand occurred.demand occurred.To model this dynamic change in behavior in To model this dynamic change in behavior in Extend, we would need a way to alter the Extend, we would need a way to alter the value in the value in the Maximum Number in ActivityMaximum Number in Activity field of the field of the Activity, MultipleActivity, Multiple block dialog block dialog during the simulation. during the simulation.

To do this, double-click the To do this, double-click the Queue, FIFOQueue, FIFO block to display its dialog window. For block to display its dialog window. For explanations, click on the explanations, click on the HelpHelp button. button.

The The LL value value output output connector connector reads out the reads out the queue length queue length throughout throughout the the simulation simulation run.run.The The CC connector can be used to input a connector can be used to input a capacity value that overrides the number capacity value that overrides the number recorded in the recorded in the Maximum Number in Maximum Number in ActivityActivity field. field.

What is needed is a way to convert the What is needed is a way to convert the LL value from the value from the Queue, FIFOQueue, FIFO block into the block into the desired number of rental stations and feed desired number of rental stations and feed that dynamic number into the that dynamic number into the CC connector connector of the of the Activity, MultipleActivity, Multiple block during the block during the simulation.simulation.Extend’s Extend’s Conversion TableConversion Table block is similar to block is similar to Excel’s VLOOKUP in that it will map the Excel’s VLOOKUP in that it will map the input input LL values to the output values to the output CC values. values.

To open the To open the Conversion TableConversion Table block, click on block, click on GENERIC.lix - Math - Conversion TableGENERIC.lix - Math - Conversion Table..

Connect the Connect the LL value value output connector of output connector of the the Queue, FIFOQueue, FIFO block to the block to the Conversion Table’s Conversion Table’s input connector.input connector.

Next, connect the Next, connect the Conversion Table’s Conversion Table’s output connector to output connector to the the CC value of the value of the Activity, MultipleActivity, Multiple block.block.

The text box shows Hervis’ proposed The text box shows Hervis’ proposed decision rule for increasing the number of decision rule for increasing the number of rental station clerks. rental station clerks.

Double-click on the Double-click on the Conversion TableConversion Table block block to open its dialog window. to open its dialog window.

Choose Choose SteppedStepped under under the the Table is:Table is: option.option.

A value of 4 for A value of 4 for y outy out is assigned to values is assigned to values of of xx in greater than 6. This places a cap on in greater than 6. This places a cap on the maximum number of rental clerks. the maximum number of rental clerks.

Click on the Click on the Run SimulationRun Simulation icon. icon.

These values These values (0 - 30 for (0 - 30 for x inx in and 1 - 4 for and 1 - 4 for y y outout) represent ) represent the proposed the proposed decision rule.decision rule.

Here is the resulting graph.Here is the resulting graph.

Remember, results will differ due to the Remember, results will differ due to the random effects.random effects.

Now, compare the following results for the Now, compare the following results for the Queue, FIFOQueue, FIFO block: block:

2 Clerks2 ClerksUp to 4 Clerks during Up to 4 Clerks during

peak periodspeak periods

Compare the following results for the Compare the following results for the Activity, MultipleActivity, Multiple block: block:

2 Clerks2 ClerksUp to 4 Clerks during Up to 4 Clerks during

peak periodspeak periods

To verify these results, we could run the To verify these results, we could run the simulation many more times. However, it simulation many more times. However, it would be difficult to compare each set of would be difficult to compare each set of results. results. Extend’s Extend’s Queue StatsQueue Stats block, will collect block, will collect queuing statistics from multiple runs of a queuing statistics from multiple runs of a simulation model.simulation model.

Using this, we can systematically assess the Using this, we can systematically assess the influence of the model’s inherent influence of the model’s inherent randomness on a performance measure.randomness on a performance measure.

Open this block by Open this block by going to the going to the

Library – Open Library – Open Library Library menu and menu and choosing choosing Stats.lrxStats.lrx from the resulting from the resulting

dialog.dialog.

Now, open the Now, open the Queue StatsQueue Stats block and place block and place it anywhere in the Extend model window.it anywhere in the Extend model window.

Double-click on the Double-click on the Queue StatsQueue Stats block to block to open its dialog window:open its dialog window:

To tabulate the results of multiple runs, To tabulate the results of multiple runs, select the select the Append new updatesAppend new updates and and Update Update at end of simulationat end of simulation options. options.

Now, go to Now, go to Run – Simulation SetupRun – Simulation Setup dialog dialog and change the and change the Number of runsNumber of runs to say, 20. to say, 20.

This instructs Extend to make 20 This instructs Extend to make 20 independent runs of the model, tabulating independent runs of the model, tabulating the queuing statistics from each run into the queuing statistics from each run into the the Queue StatsQueue Stats block. block.

Clicking on the Clicking on the Run Simulation Run Simulation icon will now icon will now cause the model to automatically run 20 cause the model to automatically run 20 times.times.

After starting the simulation, a status bar After starting the simulation, a status bar and small graph will appear on the bottom and small graph will appear on the bottom of the screen, from which you can monitor of the screen, from which you can monitor the progress of the simulations. the progress of the simulations.

After the runs are finished, double-click on After the runs are finished, double-click on the the Queue StatsQueue Stats block to open the dialog block to open the dialog and review the results.and review the results.

These results confirm that increasing the These results confirm that increasing the number of clerks will not help the model.number of clerks will not help the model.

Clicking on the Clicking on the Confidence IntervalConfidence Interval button button in this dialog will further summarize the in this dialog will further summarize the results giving 95% confidence intervals.results giving 95% confidence intervals.

EXAMPLE 5 – FINAL HERVIS EXAMPLE 5 – FINAL HERVIS CAR RENTAL MODELCAR RENTAL MODEL

Now, return to the original 2 clerk rental Now, return to the original 2 clerk rental station policy.station policy.

Instead of increasing the number of clerks Instead of increasing the number of clerks at the rental station, let’s consider serving at the rental station, let’s consider serving only two types of customers:only two types of customers:

Those who desire smaller compact cars Those who desire smaller compact cars (Economy cars)(Economy cars)

Those who desire larger, more powerful Those who desire larger, more powerful cars (Deluxe cars)cars (Deluxe cars)

Assume that 70% of customers will opt for Assume that 70% of customers will opt for economy cars and the balance for deluxe economy cars and the balance for deluxe cars.cars.The challenge is to decide how many of each The challenge is to decide how many of each type of car to have available at the type of car to have available at the beginning of the week to avoid car beginning of the week to avoid car shortages during the week and ultimately shortages during the week and ultimately customer dissatisfaction.customer dissatisfaction.

Past data on car rentals shows:Past data on car rentals shows:

Economy car customers rent their car Economy car customers rent their car for between one and two days.for between one and two days.

Deluxe car customers rent their cars Deluxe car customers rent their cars typically for two days plus or minus a typically for two days plus or minus a half day.half day.

Since the time interval for economy car Since the time interval for economy car rentals is fairly evenly distributed, we can rentals is fairly evenly distributed, we can approximate the distribution as being approximate the distribution as being Uniform.Uniform.For deluxe car renters, a Normal For deluxe car renters, a Normal distribution for the rental times is a good fit distribution for the rental times is a good fit to the data, with a standard deviation of ½ to the data, with a standard deviation of ½ a day.a day.

We will use Extend’s Hierarchical blocks to We will use Extend’s Hierarchical blocks to minimize visual complexity. This will allow minimize visual complexity. This will allow us to create models made up of submodels us to create models made up of submodels (logical groupings of Extend blocks).(logical groupings of Extend blocks).

To do this, select all of the blocks except To do this, select all of the blocks except the the Executive Executive and and ExitExit blocks and choose blocks and choose the the Make Selection Hierarchical Make Selection Hierarchical item on the item on the ModelModel menu. menu.

A dialog will A dialog will appear in which appear in which you can specify a you can specify a name for the new name for the new super-block.super-block.

Enter the name and click on Enter the name and click on Make H-BlockMake H-Block to create the super-blockto create the super-block..

You can double-click on the super-block to You can double-click on the super-block to expand it into a new window and add a expand it into a new window and add a label.label.

Now, begin building the expanded model in Now, begin building the expanded model in place of the original place of the original ExitExit block, so that block, so that customers flowing out of the Rental Office customers flowing out of the Rental Office submodel will enter the rental car lot of the submodel will enter the rental car lot of the simulated model.simulated model.Delete the Delete the Exit Exit block in the Extend model block in the Extend model and add two new blocks: and add two new blocks:

This block uses an Empirical Table to This block uses an Empirical Table to assign a 0 value (to signify an economy assign a 0 value (to signify an economy car rental) with probability .7 and a 1 car rental) with probability .7 and a 1 value (deluxe car rental) with value (deluxe car rental) with probability .3.probability .3.

This block splits the stream of This block splits the stream of customers to one of two output customers to one of two output connectors based upon the value connectors based upon the value present at its Select connector.present at its Select connector.

Input Random Number Input Random Number block block

Select DE Output Select DE Output block block

To insert the To insert the Input Random Number Input Random Number block, block, go to go to Library – GENERIC.lix – Inputs/Outputs Library – GENERIC.lix – Inputs/Outputs – Input Random Number– Input Random Number..

Double-click on this icon to open the Double-click on this icon to open the respective dialog.respective dialog.

Choose Choose Empirical TableEmpirical Table as the as the DistributionDistribution..

Specify the values which signify whether an Specify the values which signify whether an economy or deluxe car is rented and the economy or deluxe car is rented and the respective probabilities.respective probabilities.

Give the block a Give the block a label.label.

To insert the To insert the Select DE Output Select DE Output block, go to block, go to Library – DE.lix – Routing – Select DE Library – DE.lix – Routing – Select DE OutputOutput..

Double-click on this icon to open the Double-click on this icon to open the respective dialog.respective dialog.

The incoming customer is directed to the The incoming customer is directed to the top (“a” connector) output if the random top (“a” connector) output if the random number at its Select connector is 0 and is number at its Select connector is 0 and is directed to the bottom (“b” connector) directed to the bottom (“b” connector) output if the random number at its Select output if the random number at its Select connector is 1.connector is 1.

A Resource Pool is a variable thatA Resource Pool is a variable thatindicates how many of a named indicates how many of a named

constrained resource (e.g., Deluxe cars) are constrained resource (e.g., Deluxe cars) are available.available.

Connect the blocks accordingly:Connect the blocks accordingly:

Now, introduce a Now, introduce a Resource PoolResource Pool block from block from the the DE.lixDE.lix library, library,

Double click on the Double click on the Resource PoolResource Pool block to block to open its dialog window.open its dialog window.

Initialize the resource pool of Deluxe Cars to Initialize the resource pool of Deluxe Cars to 100, based on the weekly maximum demand 100, based on the weekly maximum demand for deluxe cars.for deluxe cars.

Insert a special form of a queuing block, a Insert a special form of a queuing block, a Queue, Resource PoolQueue, Resource Pool block (from block (from DE.lix – DE.lix – QueuesQueues).).

The item is then released and the count in The item is then released and the count in the pool is decremented, thus in effect, a the pool is decremented, thus in effect, a deluxe car is assigned to the customer.deluxe car is assigned to the customer.

Note that the Note that the Resource PoolResource Pool block is a block is a globally accessible variable, tracking the globally accessible variable, tracking the number of deluxe cars on hand in this case, number of deluxe cars on hand in this case, and has no drawn connections to other and has no drawn connections to other bocks.bocks.

The The Queue, Resource Pool Queue, Resource Pool block will hold block will hold items (deluxe car customers) until the items (deluxe car customers) until the specified number of Resource Pool units specified number of Resource Pool units from the Deluxe Cars pool are available from the Deluxe Cars pool are available (one in this case). (one in this case).

Now that a deluxe customer has received a Now that a deluxe customer has received a deluxe car, we must model the rental deluxe car, we must model the rental interval until it is returned. interval until it is returned.

We will do this using the We will do this using the Activity, Multiple Activity, Multiple block and a new block and a new Input Random Number Input Random Number block.block.Specify a Specify a normal normal distribution distribution with a mean with a mean of 2 days of 2 days (2880 (2880 minutes) and minutes) and standard standard dev. of .5 dev. of .5 days (720 days (720 minutes).minutes).

The capacity of the The capacity of the Activity, MultipleActivity, Multiple block block defaults to a large number, 1000, to assure defaults to a large number, 1000, to assure that no items would be stopped from that no items would be stopped from entering this block.entering this block.

After the rental time random delay, the car After the rental time random delay, the car is returned to the deluxe car pool to be is returned to the deluxe car pool to be available for re-renting by the available for re-renting by the Release Release Resource PoolResource Pool block (from the block (from the DE.lix – DE.lix – ResourcesResources menu) menu)..

Now, model the economy car customers Now, model the economy car customers similar to the deluxe car customers.similar to the deluxe car customers.

Add another Add another Resource PoolResource Pool block and set block and set the initial capacity to 140.the initial capacity to 140.

Add another Add another Queue, Resource PoolQueue, Resource Pool block to block to assign economy cars from the pool, if assign economy cars from the pool, if available.available.

Next, add an Next, add an Activity, MultipleActivity, Multiple block, block, Input Input Random NumberRandom Number block and a block and a Release Release Resource PoolResource Pool block to return the economy block to return the economy car to its pool.car to its pool.

Finally, insert an Finally, insert an Exit (4) Exit (4) block (from block (from DE.lix – DE.lix – RoutingRouting menu) to allow both streams of menu) to allow both streams of customer types to exit the model.customer types to exit the model.

To preserve customer goodwill, let’s To preserve customer goodwill, let’s implement a policy of upgrading an implement a policy of upgrading an economy car to receive a deluxe car, if economy car to receive a deluxe car, if possible, in the event no economy cars are possible, in the event no economy cars are available.available.Open the Open the Queue, Resource PoolQueue, Resource Pool block’s block’s dialog window for the economy car.dialog window for the economy car.

Specify Specify Car TypeCar Type under under pool name:pool name: by by clicking on the edit field and entering it in clicking on the edit field and entering it in the resulting dialog.the resulting dialog.

Extend will start at the top of the Extend will start at the top of the Pool namePool name list and attempt to assign a car from the list and attempt to assign a car from the Economy CarEconomy Car pool. pool.

If that pool is empty, it will go to the If that pool is empty, it will go to the Deluxe Deluxe CarCar pool and assign a deluxe car if pool and assign a deluxe car if available.available.Otherwise, it will hold the customer until Otherwise, it will hold the customer until one of either car type becomes available. one of either car type becomes available.

During the simulation run, economy car During the simulation run, economy car customers assigned a car from one of the customers assigned a car from one of the two pools will have the name of that pool two pools will have the name of that pool carried with them as a carried with them as a Car TypeCar Type attribute attribute for later reference.for later reference.

In the In the Release Release Resource PoolResource Pool block, block, the returned rental the returned rental car is credited to car is credited to whatever pool name whatever pool name was used earlier and was used earlier and carried by the carried by the attribute attribute Car TypeCar Type..

The The Input Random Input Random NumberNumber block shows block shows

the random rental the random rental time (from 1440 to time (from 1440 to

2880 minutes) from 2880 minutes) from a Uniform a Uniform

distribution, for an distribution, for an economy car economy car

customer.customer.

Now, to complete the model, add Now, to complete the model, add Queue Queue StatsStats (from (from STATS.lrxSTATS.lrx), ), HelpHelp (from (from GENERIC.lix - Inputs/OutputsGENERIC.lix - Inputs/Outputs) and ) and Plotter, Plotter, Discrete EventDiscrete Event (from (from PLOTTER.lixPLOTTER.lix) blocks. ) blocks.

An An Activity StatsActivity Stats block (from block (from STATS.lrxSTATS.lrx) has been ) has been added to record added to record statistics for the statistics for the Activity delay blocks Activity delay blocks just as the just as the Queue Queue Stats Stats block does for block does for the Queue blocks.the Queue blocks.

After running the simulation (with initial After running the simulation (with initial resource pools of 140 economy cars and 100 resource pools of 140 economy cars and 100 deluxe cars), double click on the deluxe cars), double click on the Plotter, Plotter, Discrete EventDiscrete Event block to view the graph block to view the graph below:below:This line represents the number of This line represents the number of Economy cars being rented during the Economy cars being rented during the week.week.

This line represents the number of This line represents the number of Deluxe cars being rented during the Deluxe cars being rented during the week.week.

This is the This is the number of number of

Economy Car Economy Car customers customers arriving on arriving on

the lot to the lot to find it empty find it empty of any car to of any car to

rent.rent.

This is the This is the number of number of Deluxe Car Deluxe Car customers customers arriving on arriving on

the lot to the lot to find it empty find it empty

of deluxe of deluxe cars.cars.

The graph indicates (by the thick line The graph indicates (by the thick line traces) that the initial car pool sizes are traces) that the initial car pool sizes are grossly inadequate for customer demands.grossly inadequate for customer demands.

The The Queue Stats Queue Stats and and Activity StatsActivity Stats windows windows confirm this conclusion.confirm this conclusion.

For example, after 20 simulation runs, the For example, after 20 simulation runs, the 95% confidence interval for the average 95% confidence interval for the average wait by a deluxe car customer was 140 wait by a deluxe car customer was 140 ++ 49 49 minutes.minutes.

In order to improve on the wait time in this In order to improve on the wait time in this model, we need to increase the pool size. model, we need to increase the pool size. Let’s experimentally increase each pool’s Let’s experimentally increase each pool’s initial size by about 15%, increasing the initial size by about 15%, increasing the Deluxe Cars pool to 115 and the Economy Deluxe Cars pool to 115 and the Economy cars pool to 160 and the re-run the cars pool to 160 and the re-run the simulation.simulation.

This increase in pool size shows much This increase in pool size shows much improvement as illustrated by the average improvement as illustrated by the average and maximum wait time.and maximum wait time.

In order to reduce the maximum wait time, In order to reduce the maximum wait time, change the initial resource pools to 170 change the initial resource pools to 170 Economy Cars and 125 Deluxe Cars and re-Economy Cars and 125 Deluxe Cars and re-run the simulation.run the simulation.

These results are even better. It seems These results are even better. It seems though, that waiting times may be sensitive though, that waiting times may be sensitive to small underestimates in the to small underestimates in the distributions’ parameter assumptions and distributions’ parameter assumptions and that much more simulation analysis is that much more simulation analysis is needed.needed.