final assignment business modeling and applications

FINAL ASSIGNMENT

Subject code: 22C1BUS50320202

Course: Business Modeling and Applications Lecturer: Dr Ha Quang An

Student

20 December 2022, Ho Chi Minh City

The name of the subject Management Science

The class: IBC05

Subject CODE: 21C1BUS50304002

Name of the student:

Name of Instructor: Dr Quang-An Ha

PB se oi 7i 8n 12

2.1 In the initial case, which brick kiln should DuoCera use, and whhy? cv seseerseee 13 2L L1 1111111 HH HH TT T111 11111111 HT HT 11111111111 111111111111 T111 H1 11111111 11111 10g 15 E200 17

ENDORSEMENT

I hereby declare that this is my personal final thesis and 1s under the scientific guidance of MSc Ha Quang An The research contents in my topic "Management Science - Final individual project" are honest and developed by student alone, not copied from any other organizations and individuals The data in the tables for analysis, comments and evaluation are personally collected and summarized from the topic and calculated through the specified software If I find any fraud, I will take full responsibility for the content of my essay

Tuesday, December 20, 2022

Author (signed)

UEH

UNIVERSITY LECTURE'S COMMENT

1 Linear programing

Two recent graduates at UEH decided to open a ceramic tile kiln after seeing, learning and being inspired by business trip The foundation of DuoCera Brick was born, with the first kiln being opened in Dong Nai, a location deemed with easy access to clay sources, various vehicles at many sizes and equipments to facilitate production Although the steps to create the finished product are simple and easy to understand, they require thoughtfulness and care in production — including cutting, firing, and glazing

The two of you decided to manufacture two products of glazed tiles commonly used in bathrooms and laundry rooms — small and colorful tiles called Mosaic There are 2 types of Mosaic: large type - 1 color and small type - multicolor Both types of bricks are produced once in batches of 100 bricks Each large batch of bricks needs 18 minutes to make and cut the mold, while the small bricks only need 15 minutes for | batch DuoCera has 60 hours/week available for cutting After separating the brick from the mold, the next step is firing the brick Each large batch of bricks requires 0.27 hours and the small batch needs 0.58 hours - 105 hours per week After the brick is fired, the brick will be covered with enamel to preserve the surface Each batch of large bricks requires 0.16 hours to glaze while the small ones only need 0.20 hours - the company will work 40 hours per week for the glaze process

In terms of raw materials, each batch of large bricks requires 32.8 kg of clay and 20 kg for a small batch of bricks - each week there are 6 tons of clay to be processed

Each batch of large bricks is sold for VND 4,700,000, and each batch of small bricks is sold for

VND 5,900,000 DuoCera needs to know how many bricks to produce to fit the plan

1 Set up an algebraic model - which clearly states the Solution, Problem Objective, and Constraints

2 Solve with SOLVER 3 Conclusion

4, Sensitivity analysis — what is the Shadow Price of this problem?

5 DuoCera sees small bricks selling well and doing well so they are trying to produce only small bricks So under what conditions should DuoCera produce ONLY SMALL Brick?

6 Because of some technical issues, the brick kiln had to be cut down by 3 hours/week — that 1s,

only 37 hours a week instead of 40 hours like the original So has DuoCera's production plan changed?

STEP 1: IDENTIFY THE PROBLEM

After reading the topic, 1 can abstract the need of DuoCera Brick:

DuoCera Brick wants to produce 2 kinds of product: large brick and small brick These 2 kinds of brick have different requirements to produce The company wants to optimize the production to maximize the total revenue And the question for me is that “How manny large and small bricks Should be produced each week to maximize profits?”

STEP 2: FORMULATE LINEAR PROGRAMMING MODEL

Based on the three key questions needed to be answer to begin the process of using the spreadsheet

to fomulate a mathmatical model:

What are the decisions to be made? > The decision to be made are the number of large and small bricks should be produced each week

What are the constraints on these decisions? > The constraints on these decisions are that the number of hours and materials can not exceed the number of those available resources

What is the overall measure of performance for these decisions? > The overall measure of performance for these decision is the total revenue per week form the 2 products

To easily solve this problem, 1 will use some characters:

¢ Number of Large Mosaic Batch: (L) ® Number of Small Mosaic Batch: (S) ® Number of Large Mosaic Brick: (LBr) ¢ Number of Small Mosaic Brick: (SBr) 1 The algebric model

Solution: The number of Large and Small Brick to produce per week ® LB=? (IL =100LB)

¢ SB=? (1S = 100SB)

Problem objective: Maximize the total revenue

Total revenue = 4,700,000L + 5,900,000S

Constraints: The limitation of thoses resources (time, material)

Constraint Formula

2 | Firing the brick (hours) = 0,27L + 0,585 <= 105 3 | Glazing (hours) =0,16L + 0,28 <= 40 4 | The requirement of clay (kg) = 32,8L + 208 <= 6000

Apply these answers to the worksheet:

1 Linear programing

To solve this problem easily, 1 will define name like this:

New Filter Y Name Value Refers To Scope Comment G =|Number_of_batch """} ='Q1'!$C$11:$D$11 Workbook @=)Total_revenue_V 0 ='Q1'!$G$11 Workbook

x

To: O max © Min © value of ) By Changing Variable Cells:

Subject to the Constraints:

$F$6:§FS9 <= §H§6:$HS9 a Add

Change Delete Reset All v Load/Save

a Make Unconstrained Variables Non-Negative

Method:

Solving Method

Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear Select the LP Simplex engine

for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth

The final answer will be:

| 1 Linear programing

Used Available and cut the mold 55.67010309 <= 60

So i will roundup the number to make the presentation looks neater:

e The number of large bricks: 56,7 * 100 = 5670 bricks 8

® - The number ofsmall bricks: 154,7 * 100 = 15467 bricks l also caculate it in the excel:

So:

The total number of bricks to produce to fit the plan: 21134.021

4 Sensitivity analysis — what is the Shadow Price of this problem?

100 bricks

[

I can easily expert a sensitive report by using Solver Access the Excel file attachment for a more detailed and complete view Sensitivity analysis reveals how the optimal solution changes when the model's coefficients are changed You can generate a sensitivity report once the Solver has found a

solution

Microsoft Excel 16.0 Sensitivity Report

Worksheet: [TL0OTT_KHOT_ IBC05_ Trần Bình Phương Linh_31211021077.xlsx]Q1

Report Created: 12/16/2022 8:47:55 PM

Variable Cells

Cell Name Value Cost Coefficient Increase Decrease $C$11 Number of batch Large brick 56.70103093 0 20000 1953448.276 $D$11 Number of batch Small Brick 154.6391753 0 5900000 4196296.296 25000

Constraints

Final Shadow [Constraint Allowable Allowable Cell Name Value Price Increase Decrease $FS6 Make and cut the mold (hours) Used 55.67010309 0 1E+30 4.329896907 SFS7 Firing the brick (hours) Used 105) 103092.7835 11 8.4

SFS8 Glazing (hours) Used 40 29201030.93 40 1.577464789 3.793103448

SFS9 The requirement of clay (kg) Used 4952.57732 0 1E+30 1047.42268

The shadow price reflects how the “total revenue” can be increased or decreased if we change the right hand values (resources available) by one unit

According to the Sensitivity Analysis:

¢ The shadow price in firing the brick is 103092.7835 It means if we increase or decrease the

constraint right hand side in the allowable range, the total revenue will increase or decrease

103092.7835 VND by each increased or decreased time used (hour)

¢ The shadow price in glazing is 29201030.93 It means if we increase or decrease the

constraint right hand side in the allowable range, the total revenue will increase or decrease

29201030.93 VND by each increased or decreased time used (hour)

5 DuoCera sees small bricks selling well and doing well so they are trying to produce only small bricks So under what conditions should DuoCera produce ONLY SMALL Brick? CASE 1: DuoCera should produce only small brick when the new revenue is higher or equal to the revenue when they produce both types of bricks

It means:

New revenue > 1,178,865,979 (VND)

© 4,700,000L + 5,900,000S 2 1,178,865,979 (VND)

= 5,900,000S 2 1,178,865,979 (VND) (L= 0 beacause the demand of the the topic is that they only

produce small bricks) = S > 199.8077931 = 200

Conclusion: if DuoCera wants to produce only small brick, DuoCera must produce at least 200 batches of small bricks and meet the following requirements:

¢ Time for making and cutting mold 2 0.3*0 + 0.25*200 = 50 (hours) ¢ Time for firing the brick 2 0.27*0 + 0.58*200 = 116 (hours) ¢ Time for preserve the surface =0.16*0 + 0.2*200 = 40 (hours) ¢ Requirement of clay = 32.8*0 + 20*200 = 4000 (kg)

CASE 2: Sensitivity Report can be used to find the allowable range of unit sales of 2 small and large brick products

Conclusion: When we change Rs from 5,900,000 to 10,096,296.3, it is easy to see that the optimal solution of R] returns to 0 So when the brick price is less than 10,096,296.3, DuoCera should only

produce small bricks

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CASE 3: Using “THE 100 PERCENT RULE FOR SIMULTANEOUS CHANGES IN OBJECTIVE FUNCTION COEFFECIENTS”

Suppose that the price of small bricks is better than large bricks For instance:

Price of large bricks decrease from 4,700,000 to 3,000,000

xf DOE 4,700,000 — 3,000,000 EE I= o Percentage of allowable decrease is 100 | 1,953,448.257 | 87.03%

Price of smaall bricks increase from 5,900,000 to 7,000,000

— I have listed 3 cases and these are all the conditions that DuoCera should produce only small

bricks

6 Because of some technical issues, the brick kiln had to be cut down by 3 hours/week — that

is, only 37 hours a week instead of 40 hours like the original So has DuoCera's production plan changed?

I change the time from 40 hours to 37 hours in excel:

Make and cut the mold (hours) 0.3 0.25 55.67010309 <= 60

Firing the brick (hours) 0.27 0.58 105 < 105

Number of batch 56.701031|154.63918| [Total revenue (VNĐ) |1,178,865,979.38|

1 Linear programing

Large brick [Small Brick

Unit price (VND) 4,700,000 | 5,900,000

Make and cut the mold (hours) 0.3 0.25 47.43556701 <= 60

Number of batch I 11.85567 | 175.51546 | [Tetalrevenue (vụr) |1ØS1282886 60) |

-

We can see that something has changed here:

® The time for making and cutting the mold decreases from 55,7 hours/week to 47,4 hours/week

¢ The time for firing the brick does not change

¢ The time for glazing decreases from 40 hours/week to 37 hours/week

e The number of LARGE brick batch decreases from 56,7 to 11,9 batch e The number of SMALL brick batch increases from 154,6 to 175,5 batch

¢ The total revenue decreases from 1178865979 VND to 1091262887 VND

— So DuoCera's production plan does not change too much when we cut down by 3 hours/week 2 Decision making

DuoCera plans to launch a small batch of Mosaic bricks with beautiful colors on the market for VND 5,900,000 The production of this type of brick is being done in Dong Nai with a fixed cost to

open a brick kiln of about 300,000,000 VND In addition, this batch of bricks can be processed at

the joint factory in Vinh Long with a fixed cost of only 120,000,000 VND/month According to the growth report of the ceramic tile industry in 2022, the Strong growth rate for the ceramic tile industry is about 62% - ie DuoCera is expected to be able to sell with | year sales of about 6000 bricks, while if the ceramic tile industry going slow, DuoCera at average can only sell about 3000 lots of bricks and called it Moderate growth The production cost of bricks is calculated as below:

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Strong market growth Moderate market growth DUng Nai 2.500.000 3.000.000

VVnh Long 2.300.000 2.300.000

1 In the initial case, which brick kiln should DuoCera use, and why?

2 DuoCera decided to ask for the advice of an external reality survey company to analyze customer product needs The table below is the survey results After the survey, businesses find 2 observations: customers will have a more favorable view of the product - that is, the number of customers will tend to buy more - and customers will have a skeptical view - ie the number of customers will tend to buy less:

Favorable Skeptical Strong market growth 60% 40%

Moderate market growth 20% 80%

Should DuoCera take a survey if it's free? And if there is a fee, from how much does it cost

DuoCera won't accept surveys?

2.1 In the initial case, which brick kiln should DuoCera use, and why?

DuoCera will choose which brick kiln gives them greater profits We have that:

e §6Profit = Revenue — Total cost

e Total cost = Fixed cost + Variable cost

And the variable cost in this problem is the production cost of bricks e Revenue = Expected sales * Unit revenue

e Fixed cost of Vinh Long per year = 120,000,000 * 12=1,440,000,000

e Variable cost = Cost per batch * Prior probability * Unit Revenue

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