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Subject: ENGG953

Assignment 2: Simulation Based Decision-Making

Purpose:

To gain knowledge and approaches to solving given problems using discrete event simulation.

Learning objectives covered:

2. Understanding of the uses and limitation of decision models and simulation techniques.

3. Working knowledge of the basic tools for modelling decisions in engineering

management.

5. Working knowledge of basic simulation methods (discrete event simulation modelling).

6. Capability to identify possible modelling and simulation approaches that might be

suitable for specific engineering management problems (MS Excel, SimQuick and

Crystal Ball) investigation.

Tasks

Problem 1 (20 marks)

A gasoline station near a shopping mall has two self-serve pumps and one full-serve pump that

services only handicapped customers, which is 10% of the calling population. Customers arrive at a

rate of 1.6 customers per minute (that is, the arrival time interval follows exponential distribution).

Service times have discrete distributions as follows:

Assignment 2: Simulation Based Decision-Making

Purpose:

To gain knowledge and approaches to solving given problems using discrete event simulation.

Learning objectives covered:

2. Understanding of the uses and limitation of decision models and simulation techniques.

3. Working knowledge of the basic tools for modelling decisions in engineering

management.

5. Working knowledge of basic simulation methods (discrete event simulation modelling).

6. Capability to identify possible modelling and simulation approaches that might be

suitable for specific engineering management problems (MS Excel, SimQuick and

Crystal Ball) investigation.

Tasks

Problem 1 (20 marks)

A gasoline station near a shopping mall has two self-serve pumps and one full-serve pump that

services only handicapped customers, which is 10% of the calling population. Customers arrive at a

rate of 1.6 customers per minute (that is, the arrival time interval follows exponential distribution).

Service times have discrete distributions as follows:

Self-serve | Full-serve | ||

Time (minute) | Probability | Time (minute) | Probability |

2.5 | 0.1 | 3.0 | 0.2 |

3.3 | 0.5 | 4.2 | 0.3 |

4.0 | 0.3 | 5.3 | 0.4 |

5.0 | 0.1 | 6.0 | 0.06 |

7.0 | 0.04 |

Tasks:

1) Draw a simulation flow diagram for this problem. (5.0 marks)

2) Simulate this system for an eight-hour period using excel and answer the following questions:

(10 marks)

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Spring 2020 – ENGG953 – Tieling Zhang

(1). What percentage of customers is lost?

(2). How many customers are served based on your simulation?

(3). Calculate the average waiting time per customer for self-serve service and full-serve service.

3) How might you improve this system if necessary and show evidence? (5.0 marks)

Problem 2 (20 marks)

The UN Association in Poverty Service (UNAPS) is going to reserve a number of tickets for a

concert held in Sydney Opera House in December 2019. Based on a survey on its members, UNAPS

believes the number of tickets requested is normally distributed with a mean of 500 and a standard

deviation of 100. The UNAPS can reserve tickets now (six months prior to the concert) for $120

each; however, for any tickets quested beyond the reserved now, the cost will be at the regular price

of $200. The UNAPS guarantees the ticket price of $120 to its members. If its members request

fewer than the number of tickets it reserves, the UNAPS must pay the concert organiser for the

difference with a discount, at $80 for each remaining ticket reserved one week before the concert.

Tasks:

1) Determine whether the UNAPS should reserve 400, 450, 500, 550, 600 or 650 tickets in

advance to realize the lowest total cost using Crystal Ball. (10 marks)

2) Can you determine a more exact number or a small range of the number of tickets to reserve

to minimize the cost? (10 marks)

Problem 3 (20 marks)

A baker is trying to figure out how many dozens of bagels to bake each day. The probability

distribution of the number of customers entering the shop each day is as follows:

60% of the people entering the shop purchase bagels. Customers order 1, 2, 3 or 4 dozens of bagels

according to the following distribution:

Number of customers/day | Probability |

5 | 0.35 |

6 | 0.30 |

7 | 0.25 |

8 | 0.10 |

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Spring 2020 – ENGG953 – Tieling Zhang

Bagels sell for $8.00 per dozen. They cost $4.00 per dozen to make. All bagels not sold at the

end of the day are sold at half-price at a local grocery store.

Tasks:

1) Use MS Excel to develop a Monte Carlo simulation model to determine the optimal

number of bagels (in dozens) to bake each morning. State your assumptions. (10 marks)

2) Comment on the optimal number of simulations required for your model to reach a

steady state. (5 marks)

3) Estimate the daily profit. (5 marks)

Problem 4 (25 marks)

A new car registration and license issuing process for NSW Roads and Maritime Services

(RMS) is being tested in Wollongong city. During the peak demand hours of 10:00 am to 1:00

pm, there is one customer arriving in average every 4 minutes, according to an exponential

distribution.

Typically, 30% of the customers want to register their cars (only), 40% want to renew

their licenses (only), and 30% want to do both (register their cars and renew their licences). The

process is as follows:

Each customer gets into a line (with a maximum of 20 people allowed in that line).

| Once the customer reaches the counter, he/she informs a clerk at the counter what he/ she needs. |

distribution with a mean time of 1.0 minute and a standard deviation of 0.5 minutes.

The clerk at the counter gives each customer a number and shows him/her where to sit

(there is plenty of room for customers to sit and wait).

Those who want to do both (register their cars and renew their licences) get their licence

renewed first.

There are specific officers dedicated to particular tasks, either licensing or registration:

o Sharon is the officer dedicated to process licence renewals and

o Peter is the officer dedicated to process car registrations.

| Sharon processes a licence according to a normal distribution with a mean of 5.0 minutes and a standard deviation of 1.0 minute. |

Dozens of bagel ordered/Customer | Probability |

1 | 0.30 |

2 | 0.40 |

3 | 0.20 |

4 | 0.10 |

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Spring 2020 – ENGG953 – Tieling Zhang

Peter processes a registration according to a uniform distribution with a minimum of 5.0

minutes and a maximum of 9.0 minutes.

Complete the following tasks:

1) Draw a flow diagram for the above process. (5 marks)

2) Develop a simulation model using SimQuick software for the peak time period (3-hour

time period); perform 400 simulations to determine: (12 marks)

• The overall average waiting time in the process for customers;

• the number of customers served during the 3-hour time peak period;

• the number of customers who have already seen the clerk at the counter but waiting to be

served at the end of the 3-hour peak period;

• the utilisation of these three employees, i.e.

o The clerk at the counter

o Sharon

o Peter

If the management is considering adding a new trained officer, Monica, who can renew licences

as well as process car registration. Monica’s approach is to keep an eye on both the registration

and licencing queues and then serves the next person in the longer queue. The amount of time

that Monica processes either a licence renewal or a car registration can be approximated by the

following distribution

Time taken by Monica to process either a licence or registration for a car, y (min) | 3 | 4 | 5 | 6 | 7 |

Probability, f(y) | 0.15 | 0.30 | 0.25 | 0.20 | 0.10 |

1) Use SimQuick simulation model to decide whether or not the management team should

employ Monica. (4 marks)

2) How best should the Marie’s time be utilised if the management team decides to employ

her? (4 marks)

Problem 5 (15 marks)

In a processing plant, it is known that the quality of finished product is a function of the temperature

and pressure at which the chemical reactions take place.

It is to model the quality, Y, of a product as a function of temperature, x1 (F), and the pressure

x2 (psi) at which it is produced.

Five inspectors independently assign a quality score (%) to each sample and the quality, Y, is

evaluated by averaging the five (5) scores. The resultant data is given in the data table below.

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Spring 2020 – ENGG953 – Tieling Zhang

Temperature, x1 (F) | Pressure, x2 (psi) | ||||||||

30 | 50 | 70 | |||||||

300 | 52.5 | 58.4 | 55.5 | 92.3 | 90.3 | 91.2 | 74.65 | 73.5 | 71.2 |

400 50 | 64.3 | 61.6 | 64.3 | 89.8 | 92.5 | 96.6 | 70.9 | 68.3 | 72.0 |

500 | 46.6 | 48.9 | 46.6 | 69.6 | 72.8 | 73.6 | 38.7 | 42.7 | 45.8 |

:

1) Specify algebraically the complete second order model for the data. (5 marks)

2) Use JMP to determine the best model. (5 marks)

3) Produce two bivariate plots: Product quality versus temperature (x1) and product quality

versus pressure (x2). Describe the shape of each graph and comment on what this

indicates about the adequacy of the possible linear model

Y = b + b1 x1+ b2 x2 + . (3 marks)

4) From the model obtained in 2), what temperature and/or pressure would you recommend?

(2 marks)

Learning Guides

In order to complete the assignment tasks, you need to review Weeks 6 ~12 materials covered in

class and posted into the Moodle. You must also read Chapter 14 of the prescribed textbook

“Introduction to Management Science” by Bernard W. Taylor. While you are reading, you need

to understand or answer the following questions:

1) What is Monte Carlo simulation?

2) What are the basic steps of Monte Carlo simulation?

3) How to draw a process map (a flow diagram) and how to construct a simulation model?

4) What is discrete event simulation process?

5) Learn the solution process of a simulation model using a software tool such as Excel,

SimQuick and Crystal Ball for Windows.

6) Learn, practise and gain skills to reformulate a real problem into a simulation process.

7) Practise and gain skills to get solution of a complicated problem using Excel, SimQuick

Crystal Ball, or other simulation tools which you are familiar with.

8) Consider how to make a decision given the simulation results.

9) Learn and gain the skills to interpret the solution results to the people who do not have

professional knowledge in engineering management.

10) What is one-Way ANOVA and what is two-Way ANOVA?

11) How to conduct ANOVA using JMP?

12) How to verify a model and how to interpret the model in ANOVA?

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Spring 2020 – ENGG953 – Tieling Zhang

NOTE:

• This is an individual assignment.

• You must submit your solution report in WORD or PDF format.

• This assignment is due by electronic submission into ASSIGNMENT 2 drop box in the

subject eLearning site. You must submit all files, including process map(s) and your answers

to all questions. When you submit, you can upload the zipped folder including all files

together.

• The due date is indicated in the subject outline.

• For additional information and assistance, contact Tieling Zhang by email:

tieline@uow.edu.au or phone: +02 4221 482