TIỂU LUẬN formulate a linear programming model and write down the mathematical model for this problem

Calculate the forecasting demand using Weighted Moving Average Method, with the weighted factor of 0,40; 0,20; 0,40.. Calculate the forecast using 3-month average method.. The following

ĐẠI HỌC UEH TRƯỜNG KINH DOANH KHOA KINH DOANH QUỐC TẾ - MARKETING

TIỂU LUẬN

BỘ MÔN KHOA HỌC QUẢN TRỊ NGUYỄN PHƯƠNG UYÊN

Giảng viên: Nguyễn Thị Hồng Thu

Mã lớp học phần: 21C1BUS50306804 Sinh viên: Nguyễn Phương Uyên

Khóa – Lớp: K46 - FTC01 MSSV: 31201024693

TP Hồ Chí Minh, ngày 24 tháng 11 năm 2021

ENDORSEMENT

I hereby declare that the data and research results in this thesis are my own construction,

processing, not copied from any articles of any other organizations and individuals

TABLE OF CONTENT PART I: LINEAR PROGRAMMING PROBLEM

1 Formulate a linear programming model and write down the mathematical model for

this problem 6

2 Way to solve this problem using QM and SOLVER 8

3 If the company want to maximize revenue while ignoring client preferences and consultant compatibility, will the solution in b change or not ? 9

4 Create a sensitivity report Find out about the shadow price in this case ? 10

5 If consultant A and E change their hourly wage from $155 to $200 (A) and from $270 to $200, will the solution change ? 15

6 If the capacity for consultant B and E for every project now minimum start from three instead of 1 or 2, will the shadow price change ? 16

PART II: DECISION MAKING PROBLEM 1 Draw a decision tree to help Petrolimex choose what’s best for the profit 21

PART III: FORECASTING 1 Calculate the forecasting demand using Weighted Moving Average Method, with the weighted factor of 0,40; 0,20; 0,40 26

2 Calculate the forecast using 3-month average method 27

3 Calculate the forecast using last-value method 27

4 Explain 3 methods of forecast Which one is better and more accurate ? 28

PART 1: LINEAR PROGRAMMING PROBLEM

UDT is a consulting firm that develops e-commerce project, systems and websites for its clients It has six available consultants and eight clients project is under contract The consultants have different technical abilities and experience, and as a result, the company charges different hourly rates for its services Also, the consultant’s skill are more suited for some projects than others, and clients sometimes prefer some consultants over others The suitability of a consultant for a project is rated according to a 5-point scale, in which 1 is the worst and 5 is the best The following table shows the rating for each consultant for each project, as well as the hours available for each consultant and the contracted hours and maximum budget for each project :

Project Consultant Hourly

The company wants to know how many hours to assign each consultant to each project in order

to best utilize their skill while meeting clients needs

a Formulate a linear programming model and write down the mathematical model for this problem

b Solve this problem using QM and SOLVER

c If the company want to maximize revenue while ignoring client preferences and consultant compatibility, will this change the solution in b ?

d Create a sensitivity report What is the shadow price in this case ?

e If consultant A and E change their hourly wage from $155 to $200 (A) and from $270 to

$200, will the solution change ?

f By exprerience, consultant B and E is getting better at their ability, which mean their capacity for every project now minimum start from 3 instead of 1 or 2, will the shadow price change ?

***

a.) Formulate a linear programming model and write down the mathematical model for

this problem

In order to formulate a linear programming model for this problem, we have to start with

defining the decision variables

*These variables are defined below:

Hence let Hi: the hour used by each consultant (i=A,B…F)

HWi: the hourly wage for each consultant (i=A,B F)

HAi: the hour available for each consultant (i=A,B F)

WPj : the wage per hours of each project (j=1,2 8)

PHj: the contracted hours for every project (j=1,2, 8)

CBJ: the contract budget for every project (j=1,2 8) Then

Hij: the hour used by each consultant for every project where (i=A,B…F) and (j=1,2 8)

*The constraint is calculated:

⚫ The total sum of the hours used by each consultant for every project is smaller than or equal

the hours available for each consultant

⚫ The contracted hours for every project is equal the sum of the hour used by each consultant

for every project

⚫ The wage per project is equal the total sum of hourly wage of each consultant times the

hours used by each consultant for every project In addition, the wage per project is smaller than or equals the the contract budget for every project

b Solve the problem using Excel and QM

+ Using Excel Solver

+ Using QM (in file NguyenPhuongUyen QM1)

c If the company want to maximize revenue while ignoring client preferences and

consultant compatibility, will the solution in b change?

If the company want to maximize revenue while ignoring client preferences and consultant

compatibility, the solution in b changewill change, as the new total profit would be $597200 but

it will affect the customer preferences and the compatibility of the consultant highly

d Create a sensitivity report (file Sensitivity Report d) The shadow price in this case is

shown below:

Microsoft Excel 16.0 Sensitivity Report

Worksheet: [Book1-3-2.xlsx]Sheet1

Report Created: 11/22/2021 9:58:57 AM

Variable Cells

Final Shadow Constraint

e If consultant A and E change their hourly wage from $155 to $200 (A) and from $270 to

$200, will the solution change?

If consultant A and E change their hourly wage from $155 to $200 (A) and from $270 to $200,

the solution will change accordingly,as the new total rate is 13195, and the total profit is

502092.59

f By exprerience, consultant B and E is getting better at their ability, which mean their

capacity for every project now minimum start from 3 instead of 1 or 2, will the shadow

price change

If consultant B and E is getting better at their abilities and their capacity for every project now

minimum start from 3 instead of 1 or 2, the shadow price will change accordingly

Microsoft Excel 16.0 Sensitivity Report

Worksheet: [Book1-3.xlsx]Sheet1

Report Created: 11/17/2021 4:09:41 PM

Variable Cells

$C$21 Wage per project = 90000 0.008333333 90000

$D$21 Wage per project = 71625 0 80000

$E$21 Wage per project = 65100 0 110000

$F$21 Wage per project = 70825 0 90000

$G$21 Wage per project = 49000 0 65000

$H$21 Wage per project = 69000 0 85000

$I$21 Wage per project = 50000 2.05998E-18 50000

$J$21 Wage per project = 54000 0 55000

PART 2: DECISION MAKING

Petrolimex Gas station are soon going to open a new dealership They have 3 offers : from a local gas company, from a provider and from a big gas corporation The success of each type

of dealership will depend on how much gasoline is going to be available during the next few years The profit of each type of dealership, giving the availability of gas, is shown in the following payoff table (unit : million VND) Draw a decision tree to help Petrolimex choose what’s best for the profit

Dealership Gasoline Shortage 60% Gasoline Surplus 40%

***

*Step by step on how to draw a decision tree to help Petrolimex choose what’s best for the profit

(file Decision Making)

a Using Weighted Moving Average Method, with the weighted factor of 0,40; 0,20; 0,40

What is the forecasting demand

b Using 3-month average method, calculate the forecast

c Using last-value method, calculate the forecast

d Explain 3 methods of forecast Which one is better and more accurate according to you?

You can explain however you want

***

a) Using Weighted Moving Average Method, with the weighted factor of 0,40; 0,20; 0,40

the forecasting demand is:

b) Using 3-month average method, calculate the forecast

c) Using last-value method, calculate the forecast

d) Explain three method of forecast

* 3-Month Average Method: The 3 -month average forecasting method provides a middle

ground between the last-value and averaging method by using the average of the monthly sales

for the three most recent months as the forecast for the next month For example, a three-month

moving average forecast for the supermarket in the 4th month is being calculated by:

Forecast = 25 + 24+ 28 = 25,666666667

3

*Last-Value Method: The last-value forecasting method is calculated simply by using the last

month’s sales as the forecast for the next month For example, the last-value method forecast for

the supermaket in the 2nd month is being calculated by

Forecast = 25

* Weighted Moving Average Method: The weighted average is employed when there is a need

importance on recent data Therefore in this case, the 0.4 will be placed on the most recent

value (3th month) , the 0,2 on the next most recent (2nd month) and so on For example, we can

now calculate the weighted moving average method for the 4th month using the given weights

0.4; 0.2; 0.4:

Forecast = 0.4*28 + 0.2*24 + 0.4* 25 = 26

+ Which method is better and more accurate according to you?

- The key factor in choosing a forecasting method is how stable the time series is and the value

of MAD It is known that

+ Last-value method is suitable for a time series that is so unstable that even the next-to-last

value is not considered relevant for forecasting the next value In this last-value forecasting

problem, MAD =2,6

+ Averaging method: Suitable for a very stable time series where even its first few values

are considered relevant for forecasting the next value In this 3-month average method,

MAD = 1.555555556

+ Weighted moving-average method: Suitable for a moderately stable time series where the last

few values are considered relevant for forecasting the next value In this weight moving-average

method, MAD = 1.66666667

-> In this case, It is clear that 3-month average method is the best method among the three

since it has the lowest MAD (1.56 <1.67 <2.6) and it is suitable for a very stable time series (

the monthly demand of a water bottle extracted from a supermarket )

THE END _