set up an algebraic model which clearly states the solution problem objective and constraints

Thus, DuoCera only produces small bricks when it is possible to change their capacity at least to 50 hours for cutting, 116 hours for firing, 40 hours for glazing and have more than 4000

COLLEGE OF BUSINESS

SCHOOL OF INTERNATIONAL BUSINESS - MARKETING

FINAL INDIVIDUAL PROJECTBUSINESS MODELING AND APPLICATIONS

LE THI HA VI

Ho Chi Minh City, December 19 2022th

UEH UNIVERSITYCOLLEGE OF BUSINESS

UEH UNIVERSITY COLLEGE OF BUSINESS

Business Models & Applications

Final Individual Project

The name of the subject

Business Models & Applications

December, 2022, Ho Chi Minh City

SCHOOL OF INTERNATIONAL BUSINESS – MARKETING

1.4 Sensitivity analysis – what is the Shadow Price of this problem? 6

1.5 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? 7

1.6 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? 9

2 Decision making 10

2.1 In the initial case, which brick kiln should DuoCera use, and why 10

2.2 Should DuoCera take a survey if it's free? And if there is a fee, how much doesit cost DuoCera won't accept surveys? 11

3 Network Distribution 14

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I declare that this thesis has been composed solely by myself and that it has not beensubmissed by any other organizations and individuals Except where states otherwise byreference or acknowledgment, the work presented is entirely my own If any fraud isdiscovered, I will accept full responsibility for my essay’s content.

December 19, 2022Signature

Algebraic symbols

L = number of the large type batches of bricks to be produced per weekS = number of the small type batches of bricks to be produced per weekR = total revenue per week from the two products, in VND

Relevant data

DuoCera Brick Product-Mix

Units Revenue

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In addition, because of the limit of materials:32.8L + 20S ≤ 6000

1.2.Solve with SOLVER

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The optimal solution is to produce 56.7010309278351 batches of large type per week and154.639175257732 batches of small type per week.

DuoCera needs to produce quantity of brick as follows:Numer of batch (Large type & Small Type ) * 100• Large Type = 56.70 *100 = 5670 Bricks• Small Type = 154.64*100 = 15464 Bricks

Thus, DuoCera needs to produce 5670 bricks of large type and 15464 bricks of small typeto fit the plan.

1.4.Sensitivity analysis – what is the Shadow Price of this problem?Microsoft Excel 16.0 Sensitivity

Worksheet: [Book3]Sheet1Report Created: 12/15/2022 1:42:22 PM

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Variable Cells

Units Produced Large type

Units Produced Small type

Materials Clay Used

7 Cutting Hour Used

3.793103448The shadow price remains (0; 0; 103092,7836; 29202030,93)

It means

The shadow price in the firing process = 103 092,7835 VND

So, if we change the constraint on the right side of the permissible range, the total revenue will change by 103 092,7835 VND for each modified in time used (hour)The shadow price in Glazing process = 29 201 030,93 VND

So, if we increase or decrease the constraint right-hand side in the allowable range,the total revenue will increase or decrease by 29 201 030,93 VND by each increased or decreased time used (hour)

1.5.DuoCera sees small bricks selling well and doing well so they are trying toproduce only small bricks So under what conditions should DuoCeraproduce ONLY SMALL Brick?

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DuoCera should produce only small bricks when the new revenue is higher or equal to the old revenue (when producing types of bricks)

In addition, the new plan is to produce only small bricks so L = 0T = New revenue

It means

T ≥ 11788659795900000S ≥ 1178865979S ≥ 200

Thus, if DuoCere want to produce only small brics, they must produce at least 200 batches of small bricks

meet the following constrains:

Available Hour of Cutting process ≥ 0,25 x 200 ≈ 50Available Hour of Firing process ≥ 0,58 x 200 ≈ 116Available Hour of Glazing process ≥ 0,2 x 200 ≈ 40Available Clay ≥ 32,8 x 200 ≈ 4000

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Thus, DuoCera only produces small bricks when it is possible to change their capacity at least to 50 hours for cutting, 116 hours for firing, 40 hours for glazing and have more than 4000 kg clay.

1.6.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?

To see what happens when the brick kiln had to be cut down by 3 hours/week, you need to substitute the new number in cell G9 and run Solver again

Results

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So, DuoCera's production plan has changed to 1185 bricks of large type 17551 bricks of, small type and the total revenue changed to 1091 262 887 VND to fit the new capacity.

2 Decision making

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

The decision is whether 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) or processed at the joint factory in Vinh Long (with a fixed cost of only 120,000,000 VND/month) This decision is represented in the decision tree by a decision node with two branches For each decision, there are two outcomes: strong growth (62% probability) or moderate growth (38% probability) This is represented in the decision tree by event nodes with two branches

Profit = [(Revenue of each batch – Cost of each batch) Number of batches of bricks] – Fixed cost

If the Dong Nai factory is used and growth is strong, the profit would be:[(5,9 – 2,5)6000] – 300 = 20100 (milion VND)

If the Dong Nai factory is used and growth is moderate, the profit would be [(5.9 – 3)3000] – 300 = 8400

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The expected payoff of the Dong Nai factory would be20100 x 0,62 + 8400 x 0,38 = 15654

If the Vinh Long factory is used and growth is strong, the profit would be [(5.9 – 2.3)6000] – 1440 = 20160

If the Vinh Long is used and growth is moderate, the profit would be[(5,9 – 2,3)3000] – 1440 = 9360

The expected payoff of Vinh Long factory would be20160 x 0,62 + 9360 x 0,38 = 16056

The resulting solved decision tree is shown below The decision to produce in Vinh Long has a higher expected profit of 16056 million VND.

2.2.Should DuoCera take a survey if it's free? And if there is a fee, how much does it cost DuoCera won't accept surveys?

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

Possible Findings from a Survey

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Favorable: customers will have a more favorable view of the product; the number of customers will tend to buy more.

Skeptical: customers will have a skeptical view; the number of customers will tend to buy less.

To use either finding to calculate the posterior probability of each state of nature, it is necessary to estimate the probability of obtaining this finding for each state of nature.

P (finding | state) = Probability that the indicated finding will occur, given that the state of nature is the indicated one

P (favorable I strong growth) = 0,6P (skeptical I strong growth) = 0,4P (favorable I moderate growth) = 0,2P (skeptical I moderate growth) = 0,8Recall that the prior probabilities are

P (strong growth) = 0,62P (moderate growth) = 0.38

The joint probability is determined by the following formula.P(state and finding) = P(state) P(finding | state)P(Strong and Favorable) = 0,62 x 0,6 = 0,372P(Strong and Skeptical) = 0,62 x 0.4 = 0,248P(Moderate and Favorable) = 0,38 x 0,2 = 0,076P(Moderate anf Skeptical) = 0,38 x 0.8 = 0,304

Find each probability of just a particular finding without specifying the state of nature Since any finding can be obtained with any state of nature, the formula for calculating theprobability of just a particular finding is

P(finding) = P(State 1 and finding) + P(State 2 and finding)P(Favorable) = 0,372 + 0,076 = 0,440

P(Skeptical) = 0,248 + 0,304 = 0,552

Thus, there is a 44,8% chance that the survey will indicate a favorable attitude and a 55,2% chance that the survey will indicate a skeptical attitude toward the product.

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Finally, we now are ready to calculate each posterior probability of a particular state of nature given a particular finding from the survey The formula involves combining the joint with the unconditional probabilities underneath the diagram as follows.

P (state I finding)=P(state finding∧ )P(finding)P(Strong I Favorable) = 0,83

P(Strong I Skeptical) = 0,45P(Moderate I Favorable) = 0,16P(Moderate I Skeptical) = 0,55

Given a favorable attitude, the probability of strong growth increases to 83%, and moderate growth to 17% Given a skeptical attitude, the probability of strong growth sinks to 45%, and moderate growth to 55%.

The revised decision tree is shown below It begins with an event node with two branchesfor the two possible outcomes of the survey After the survey results are known, there is adecision of whether to open a new factory in Dong Nai, or process at the joint factory in Vinh Long, represented by a pair of branches.

Finally, after the decision is made, there will either be strong or moderate growth This is represented by event nodes with two branches and uses the posterior probabilities given the results of the survey

If the survey indicates a favorable attitude toward the product, they should processit at the joint factory in Vinh Long

If the survey indicates a skeptical attitude toward the product, they also should process it at the joint factory in Vinh Long

The expected profit is 16.058.690.000 VND

The expected value of experimentation is the expected payoff with the information minusthe expected payoff without the information

With the survey information, the expected payoff is 16058,59 million VND.Without the survey information, the expected payoff is 16056 million VND.Thus, the expected value of experimentation in part b is 2,59 million VND

So, DuoCare should take a survey if it’s free

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survey before it would no longer be worthwhile to conduct.

3 Network Distribution

This is a shortest-path problem To set up a spreadsheet model, first list all of the arcs as shown in B4:C18, along with their distance (F4:F19) Then list all of the nodes as shown in H4:H15 along with each node's supply or demand (K4:J15) We are sending one unit from Ho Nai, Dong Nai to Phan Rang (Start), and Ninh Thuan (End), so the supply is 1 atStart and the demand is 1 at End Every other node has demand 0 because if you enter thenode, you must also leave it.

The changing cells are whether or not to include an arc on the route These are shown in OnRoute (D4:D18) below If one unit is shipped through an arc, it must mean they traveled along that route.

For each node, calculate the net flow as a function of the changing cells This can be done using the SUMIF function In each case, the first SUMIF function calculates the flow leaving the node and the second one calculates the flow entering the node For example, consider the Start node (H4) SUMIF(From,H4,OnRoute)sums each individual entry in OnRoute (the changing cells in D4:D18) if that entry is in a row where the entry in From (B4:B18) is the same as in H4 are rows 4 and 5, the sum in the OnRoute column is only over these same rows, so this sum is D4+D5

The goal is to minimize the total distance of the route The cost is the SUMPRODUCT ofthe Distance with OnRoute, or Total distance = SUMPRODUCT(OnRoute,Distance) This formula is entered into Total_Distance (E20).

The Solver information and solved spreadsheet are shown below.14

OnRoute (D4:D18) indicates whether that arc should be included in the route The optimalroute is to go B – E – F – H – J or Dong Nai – Bau Ham – Tan Nghia – Tan Hai – Suoi Da – Ca Na – Ninh Thuan

The minimum Total_Distance (E20) is 220.

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1 Frederick S Hillier and Mark S Hillier (2019 – sixth edition) Introduction to Management Science A Modeling and Case Studies Approach with Spreadsheets2.Dr Ha Quang An (2022) Lecture slides of Business Models & Applications Subject

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