(TIỂU LUẬN) 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 4.. By exprerience, consultant B and E is getting better at their ability, which mean their capacity for e

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

TIỂU LUẬN

BỘ MÔN KHOA HỌC QUẢN TRỊ

NGUYỄN PHƯƠNG UYÊN

TP Hồ Chí Minh, ngày 24 tháng 11 năm 2021

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

TIỂU LUẬN Môn học: Khoa học quản trị (Management Sciene)

Giảng viên: Nguyễn Thị Hồng Thu

TABLE OF CONTENT PART I: LINEAR PROGRAMMING PROBLEM

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

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

6 If the capacity for consultant B and E for every project now minimum start from

PART II: DECISION MAKING PROBLEM

1 Draw a decision tree to help Petrolimex choose what’s best for the profit 21PART III: FORECASTING

1 Calculate the forecasting demand using Weighted Moving Average Method, with the

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 forsome 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 andmaximum budget for each project :

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 equalthe hours available for each consultant

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

$C$21 Wage per project =

$D$21 Wage per project =

$E$21 Wage per project =

$F$21 Wage per project =

$G$21 Wage per project =

$H$21 Wage per project =

$I$21 Wage per project =

$J$21 Wage per project =

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 is502092.59

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

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%

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 forthe supermaket in the 2nd month is being calculated by

Forecast = 25

to place more importance on some periods over others In most cases, we place more

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 cannow calculate the weighted moving average method for the 4th month using the given weights0.4; 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-lastvalue is not considered relevant for forecasting the next value In this last-value forecastingproblem, MAD =2,6

+ Averaging method: Suitable for a very stable time series where even its first few valuesare 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 lastfew values are considered relevant for forecasting the next value In this weight moving-averagemethod, 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 )

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