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Problem 1 (a)

According to the explanations, we can know that the probabilities and pricing of different customers. So in order to estimate the expected profit per game, I made the estimation by the following steps:

1) Use the Excel to list the probability to sell to student, quantity of ticket, different pricing strategy, unit cost of the ticket, revenue and profit, etc.

2) Use Excel build-in function to produce a random. According to the problem, number of tickets she will be able to sell 24 hours before the game time is between 11 and 20 with equal probability of 0.10. So I use the build-in function “Insert Function”, select “Discrete” and “RiskIntUniform” to get the mean number of random between 11 and 20.

3) And then I use Excel build-in function “IF()” to select the number between RANDOM and 15 as the number of sold during the day. The formula is “IF(RANDOM > 15, 15, RANDOM). And then calculate the number of ticket sold to student group.

4) Select the sheet stands for “Total profit” and click “Add Output”, rename it, click OK. Enter the Iterations as 1000 and simulation as 1 and then click “Start Simulation”. The graph will be shown below.

So the maximum expected profit per game is $2250, the minimum expected profit

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per game is $1350 and the mean expected profit per game is $2025.(b)Experiment (by trial and error) with model to determine the optimum number of tickets Susan should buy for every game so as to maximize her expected profit per game?

Using the method of “ by trial and error”, I change the number of ticket on hand and then run the simulation each time to get the different mean number(which are shown above)So it’s obviously to see that when the number of ticket on hand is 17, the profit can reach the maximum number.

Problem 2

Run the simulation for 5000 minutes and keep statistics on the number in each queue and utilization of each machine and average time a part spent in the system.The average number of parts in Machine1 process queue: 0.94867

The average number of parts in Machine2 process queue: 2.2922

The average number of parts in Machine3 process queue: 0.89644

Utilization of Machine 1: 59.013%

Utilization of Machine 2: 74.462%

Utilization of Machine 3: 73.444%

Average time a part spent in the system: 75.946minutes

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Problem 3

(a) The utilization of servers (tellers) is 98.836%;The number of lost customers is 98;Customer flow time is 179.55 seconds.

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(b)The new model will be shown below: The utilization of servers (tellers) is 98.443%The number of lost customers is about 95Customer flow time is 257.72 seconds.

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Appendix [Problem 2(mod/exp); Problem 3(a) (mod/exp); Problem 3(b) (mod/exp)]

Problem 2.MOD

; Model statements for module: AdvancedTransfer.Route 2 (Route 2);4$ ROUTE: EXPO( 2 ),SEQ;

;;; Model statements for module: AdvancedTransfer.Station 2 (Machine 2);

5$ STATION, Machine 2;73$ DELAY: 0.0,,VA:NEXT(6$);

;;; Model statements for module: BasicProcess.Process 2 (Process 2);6$ ASSIGN: Process 2.NumberIn=Process 2.NumberIn + 1: Process 2.WIP=Process 2.WIP+1;77$ QUEUE, Process 2.Queue;76$ SEIZE, 2,VA: Resource 2,1:NEXT(75$);

75$ DELAY: Optime 2,,VA;74$ RELEASE: Resource 2,1;122$ ASSIGN: Process 2.NumberOut=Process 2.NumberOut + 1: Process 2.WIP=Process 2.WIP-1:NEXT(7$);

;;; Model statements for module: AdvancedTransfer.Route 3 (Route 3);7$ ROUTE: EXPO( 2 ),SEQ;

;;; Model statements for module: AdvancedTransfer.Station 3 (Machine 3);

8$ STATION, Machine 3;127$ DELAY: 0.0,,VA:NEXT(9$);

;;; Model statements for module: BasicProcess.Process 3 (Process 3);9$ ASSIGN: Process 3.NumberIn=Process 3.NumberIn + 1: Process 3.WIP=Process 3.WIP+1;131$ QUEUE, Process 3.Queue;130$ SEIZE, 2,VA: Resource 3,1:NEXT(129$);

129$ DELAY: Optime 3,,VA;128$ RELEASE: Resource 3,1;

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176$ ASSIGN: Process 3.NumberOut=Process 3.NumberOut + 1: Process 3.WIP=Process 3.WIP-1:NEXT(10$);

;;; Model statements for module: AdvancedTransfer.Route 4 (Route 4);10$ ROUTE: EXPO( 2 ),SEQ;

;;; Model statements for module: AdvancedTransfer.Station 4 (EXIT SYSTEM);

11$ STATION, EXIT SYSTEM;181$ DELAY: 0.0,,VA:NEXT(12$);

;;; Model statements for module: BasicProcess.Dispose 1 (Dispose);12$ ASSIGN: Dispose.NumberOut=Dispose.NumberOut + 1;182$ DISPOSE: Yes;

Problem 2.EXPPROJECT, "Unnamed Project","MAYING",,,No,Yes,Yes,Yes,No,No,No,No,No,No;

ATTRIBUTES: timein,DATATYPE(Real): Optime 1,DATATYPE(Real): Optime 2,DATATYPE(Real): Optime 3,DATATYPE(Real);

VARIABLES: Create.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Process 1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Process 2.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"),DATATYPE(Real): Dispose.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Process 3.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Process 2.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"): Process 1.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"),DATATYPE(Real): Process 3.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"),DATATYPE(Real): Process 2.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Process 1.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"): Process 3.NumberIn,CLEAR(Statistics),CATEGORY("Exclude");

SEEDS: 1,2333,No: 2,3333,No: 3,1234,No;

QUEUES: Process 1.Queue,FIFO,,AUTOSTATS(Yes,,): Process 2.Queue,FIFO,,AUTOSTATS(Yes,,): Process 3.Queue,FIFO,,AUTOSTATS(Yes,,);

PICTURES: Picture.Airplane: Picture.Green Ball: Picture.Blue Page:

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Picture.Telephone: Picture.Blue Ball: Picture.Yellow Page: Picture.EMail: Picture.Yellow Ball: Picture.Bike: Picture.Report: Picture.Van: Picture.Widgets: Picture.Envelope: Picture.Fax: Picture.Truck: Picture.Person: Picture.Letter: Picture.Box: Picture.Woman: Picture.Package: Picture.Man: Picture.Diskette: Picture.Boat: Picture.Red Page: Picture.Ball: Picture.Green Page: Picture.Red Ball;

RESOURCES: Resource 1,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,AUTOSTATS(Yes,,): Resource 2,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,AUTOSTATS(Yes,,): Resource 3,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,AUTOSTATS(Yes,,);

STATIONS: EXIT SYSTEM,,,EXIT SYSTEM,AUTOSTATS(Yes,,): Machine 1,,,Machine 1,AUTOSTATS(Yes,,): Machine 2,,,Machine 2,AUTOSTATS(Yes,,): Machine 3,,,Machine 3,AUTOSTATS(Yes,,);

SEQUENCES: Sequence 1,Machine 1,,,,Optime 1=NORM(6,1,2)&Machine 2,,,,Optime 2=NORM(10,2,2)&Machine 3,,,,Optime 3= NORM(10,2,2)&EXIT SYSTEM: Sequence 2,Machine 2,,,,Optime 2=NORM(9,2,2)&Machine 3,,,,Optime 3=NORM(5,1,2)&Machine 1,,,,Optime 1=NORM(4,1,2)& EXIT SYSTEM: Sequence 3,Machine 1,,,,Optime 1=NORM(12,2,2)&Machine 3,,,,Optime 3=NORM(7,1,2)&Machine 2,,,,Optime 2=NORM(5,2,2)& Machine 3,,,,Optime 3=NORM(4,1,2)&EXIT SYSTEM;

REPLICATE, 1,,MinutesToBaseTime(5000),Yes,Yes,,,,24,Minutes,No,No,,,Yes,No;

ENTITIES: Entity 1,Picture.Report,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Yes,,);

ACTIVITYAREAS: EXIT SYSTEM,0,,AUTOSTATS(Yes,,): Machine 1,0,,AUTOSTATS(Yes,,): Machine 2,0,,AUTOSTATS(Yes,,): Machine 3,0,,AUTOSTATS(Yes,,);

Problem 3(a).MOD;;; Model statements for module: BasicProcess.Create 1 (Car Arrive);

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5$ CREATE, 1,SecondstoBaseTime(0.0),Entity 1:SecondstoBaseTime(EXPO( 55,1 )):NEXT(6$);

6$ ASSIGN: Car Arrive.NumberOut=Car Arrive.NumberOut + 1:NEXT(0$);

;;; Model statements for module: BasicProcess.Decide 1 (Decide 1);0$ BRANCH, 1: If,NQ(Process 1. Queue)<3,9$,Yes: Else,10$,Yes;9$ ASSIGN: Decide 1.NumberOut True=Decide 1.NumberOut True + 1:NEXT(1$);

10$ ASSIGN: Decide 1.NumberOut False=Decide 1.NumberOut False + 1:NEXT(3$);

;;; Model statements for module: BasicProcess.Process 1 (Process 1);1$ ASSIGN: Process 1.NumberIn=Process 1.NumberIn + 1: Process 1.WIP=Process 1.WIP+1;14$ QUEUE, Process 1.Queue;13$ SEIZE, 2,VA: Resource 1,1:NEXT(12$);

12$ DELAY: NORM( 90, 12),,VA;11$ RELEASE: Resource 1,1;59$ ASSIGN: Process 1.NumberOut=Process 1.NumberOut + 1: Process 1.WIP=Process 1.WIP-1:NEXT(2$);

;;; Model statements for module: BasicProcess.Dispose 1 (Dispose 1);2$ ASSIGN: Dispose 1.NumberOut=Dispose 1.NumberOut + 1;62$ DISPOSE: Yes;

;;; Model statements for module: BasicProcess.Record 1 (LOST);3$ COUNT: LOST,1:NEXT(4$);

;;; Model statements for module: BasicProcess.Dispose 2 (Dispose 2);4$ ASSIGN: Dispose 2.NumberOut=Dispose 2.NumberOut + 1;63$ DISPOSE: Yes;

Problem 3(a).EXPPROJECT, "Unnamed Project","MAYING",,,No,Yes,Yes,Yes,No,No,No,No,No,No;

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VARIABLES: Dispose 2.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Car Arrive.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Process 1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Dispose 1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Decide 1.NumberOut True,CLEAR(Statistics),CATEGORY("Exclude"): Process 1.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"),DATATYPE(Real): Decide 1.NumberOut False,CLEAR(Statistics),CATEGORY("Exclude"): Process 1.NumberIn,CLEAR(Statistics),CATEGORY("Exclude");

QUEUES: Process 1.Queue,FIFO,,AUTOSTATS(Yes,,);

PICTURES: Picture.Airplane: Picture.Green Ball: Picture.Blue Page: Picture.Telephone: Picture.Blue Ball: Picture.Yellow Page: Picture.EMail: Picture.Yellow Ball: Picture.Bike: Picture.Report: Picture.Van: Picture.Widgets: Picture.Envelope: Picture.Fax: Picture.Truck: Picture.Person: Picture.Letter: Picture.Box: Picture.Woman: Picture.Package: Picture.Man: Picture.Diskette: Picture.Boat: Picture.Red Page: Picture.Ball: Picture.Green Page: Picture.Red Ball;

RESOURCES: Resource 1,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,AUTOSTATS(Yes,,);

COUNTERS: LOST,,,,DATABASE(,"Count","User Specified","LOST");

REPLICATE, 1,,SecondsToBaseTime(14400),Yes,Yes,,,,24,Seconds,No,No,,,Yes,No;

ENTITIES: Entity 1,Picture.Report,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Yes,,);

Problem 3(b).MOD;;; Model statements for module: BasicProcess.Create 1 (Car Arrive);

7$ CREATE, 1,SecondstoBaseTime(0.0),Entity 1:SecondstoBaseTime(EXPO( 55,1 )):NEXT(8$);

8$ ASSIGN: Car Arrive.NumberOut=Car Arrive.NumberOut + 1:NEXT(0$);

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;;; Model statements for module: BasicProcess.Decide 1 (Decide 1);0$ BRANCH, 1: If,NQ(Process 1. Queue)<3,11$,Yes: Else,12$,Yes;11$ ASSIGN: Decide 1.NumberOut True=Decide 1.NumberOut True + 1:NEXT(1$);

12$ ASSIGN: Decide 1.NumberOut False=Decide 1.NumberOut False + 1:NEXT(5$);

;;; Model statements for module: BasicProcess.Process 1 (Process 1);1$ ASSIGN: Process 1.NumberIn=Process 1.NumberIn + 1: Process 1.WIP=Process 1.WIP+1;16$ QUEUE, Process 1.Queue;15$ SEIZE, 2,VA: Resource 1,1:NEXT(14$);

14$ DELAY: Normal(90,12),,VA;13$ RELEASE: Resource 1,1;61$ ASSIGN: Process 1.NumberOut=Process 1.NumberOut + 1: Process 1.WIP=Process 1.WIP-1:NEXT(2$);

;;; Model statements for module: BasicProcess.Dispose 1 (Dispose 1);2$ ASSIGN: Dispose 1.NumberOut=Dispose 1.NumberOut + 1;64$ DISPOSE: Yes;

;;; Model statements for module: BasicProcess.Decide 2 (Decide 2);5$ BRANCH, 1: With,(50)/100,65$,Yes: Else,66$,Yes;65$ ASSIGN: Decide 2.NumberOut True=Decide 2.NumberOut True + 1:NEXT(3$);

66$ ASSIGN: Decide 2.NumberOut False=Decide 2.NumberOut False + 1:NEXT(6$);

;;; Model statements for module: BasicProcess.Record 1 (LOST);3$ COUNT: LOST,1:NEXT(4$);

;;; Model statements for module: BasicProcess.Dispose 2 (Dispose 2);

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4$ ASSIGN: Dispose 2.NumberOut=Dispose 2.NumberOut + 1;67$ DISPOSE: Yes;

;;; Model statements for module: BasicProcess.Process 2 (Process 2);6$ ASSIGN: Process 2.NumberIn=Process 2.NumberIn + 1: Process 2.WIP=Process 2.WIP+1;69$ DELAY: Normal(180,48),,VA;116$ ASSIGN: Process 2.NumberOut=Process 2.NumberOut + 1: Process 2.WIP=Process 2.WIP-1:NEXT(0$);Problem 3(b).EXP

PROJECT, "Unnamed Project","MAYING",,,No,Yes,Yes,Yes,No,No,No,No,No,No;

VARIABLES: Dispose 2.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Decide 2.NumberOut False,CLEAR(Statistics),CATEGORY("Exclude"): Car Arrive.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Process 1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Process 2.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"),DATATYPE(Real): Dispose 1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Process 2.NumberIn,CLEAR(Statistics),CATEGORY("Exclude"): Decide 1.NumberOut True,CLEAR(Statistics),CATEGORY("Exclude"): Process 1.WIP,CLEAR(System),CATEGORY("Exclude-Exclude"),DATATYPE(Real): Process 2.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"): Decide 2.NumberOut True,CLEAR(Statistics),CATEGORY("Exclude"): Decide 1.NumberOut False,CLEAR(Statistics),CATEGORY("Exclude"): Process 1.NumberIn,CLEAR(Statistics),CATEGORY("Exclude");

QUEUES: Process 1.Queue,FIFO,,AUTOSTATS(Yes,,);

PICTURES: Picture.Airplane: Picture.Green Ball: Picture.Blue Page: Picture.Telephone: Picture.Blue Ball: Picture.Yellow Page: Picture.EMail: Picture.Yellow Ball: Picture.Bike: Picture.Report: Picture.Van: Picture.Widgets: Picture.Envelope: Picture.Fax: Picture.Truck: Picture.Person: Picture.Letter: Picture.Box: Picture.Woman: Picture.Package: Picture.Man: Picture.Diskette: Picture.Boat: Picture.Red Page: Picture.Ball: Picture.Green Page: Picture.Red Ball;

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RESOURCES: Resource 1,Capacity(1),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,AUTOSTATS(Yes,,);

COUNTERS: LOST,,,,DATABASE(,"Count","User Specified","LOST");

REPLICATE, 1,,SecondsToBaseTime(14400),Yes,Yes,,,,24,Seconds,No,No,,,Yes,No;

ENTITIES: Entity 1,Picture.Report,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Yes,,);