Case Study - Extend Your enjoyment Welcome to Cunningham Gudgal Golf Resort
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Part 1: Action Plan - Describe the process you will undertake to transform the business problem into a set of mathematical equations using the four steps approach.
1. Identify the decision variables - the unknown values that the model seeks to determine.
2. Identify the objective function - the quantity to be minimised or maximised.
3. Identify all appropriate constraints - limitations, requirements, or other restrictions that are imposed on any solution, either from practical or technological considerations or by management policy.
4. Write the objective function and constraints as mathematical expressions.
Answer - Action Plan
A. Decision model to meet management plan
B. Decision model to meet shareholders' request
C. Decision models incorporating three options for the exclusive clubhouse golf course model.
Requirements for standard and exclusive clubhouses
|
Standard Clubhouse
|
Exclusive Clubhouse
|
|
Land size for clubhouse
|
2 hectares
|
4 hectares
|
|
Cost of clubhouse plus parking
|
$3,50,0000
|
$6,00,0000
|
|
Budget
|
$20 million
|
$20 million
|
|
Land available
|
42 hectares
|
42 hectares
|
|
Number of holes
|
18
|
18
|
|
Total par
|
70-72
|
70-72
|
|
Straight par 5
|
At least 1
|
At least 1
|
|
Dogleg par 5
|
At least 1
|
At least 1
|
|
Straight par 4
|
At least 2
|
At least 2
|
|
Dogleg par 4
|
At least 2
|
At least 2
|
|
Long par 3
|
At least 1
|
At least 1
|
|
Short par 3
|
At least 1
|
At least 1
|
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A. Decision Model to Meet Management Plan
Let us assume,
The number of Straight par 5 holes is given by A5
The number of Straight par 4 holes is given by A4
The number of Dogleg par 5 holes is given by B5
The number of Dogleg par 4 holes is given by B4
The number of Long par 3 holes is given by L3
The number of Short par 3 holes is given by S3
These are the decision variables. The values of whose values are to be determined using the decision model.
The company wants to construct Cunningham Gudgal Golf Resort at Charters Towers with an aim to make it one of the most attractive venues and successful resorts for golfers all over the world. To progress in this direction the company needs to know what are thing that allure golfers towards a venue. They used golf course enjoyment which measures the golfer's enjoyment and satisfaction with the golf course design, the difficulty of the holes on the course and the available facilities. Using a recent international survey on golfers and golf course design, the company derives the total golf course enjoyment index function (Z), which the company wants to maximize with the choice of the decision variables as defined above and through construction of a standard clubhouse.
The golf course enjoyment of the golfers is the objective function which the company wants to maximize
Z= 2A5+ 1.5A4+ 1.5 B5+ 2B4+ 1.75L3 + 2.25S3
This objective function will be maximized subject to a list of constraints. It is given that an international standard 18-hole golf course should have no more than no more than 4 par 5's. this can be translated into the following inequality.
A5+B5≤4.............................................................(1)
Next, it should have no more than 14 par 4's. This is converted into the following inequality.
A4+B4≤14.............................................................(2)
The course should have no more than 4 par 3's which can be written as the following inequality.
L3+S3≤4...................................................................(3)
The condition that total number of holes must be exactly 18 is represented using the following equation.
A5+A4+B5+B4+ L3+S3 = 18..........................................(4)
There has been a stipulation that the total par must be between 70 and 72.
70≤5A5+4A4+5B5+4B4+3L3+3S3≤ 72..............................(5)
The total acreage must be between 36 and 42 hectares, which is represented by the following inequality.
36≤3A5+ 2B4+3.5B5+ 2.5B4+L3+0.75S3≤42........................(6)
Now, it has been mentioned that the total cost of the project must be within the budgeted $20 million. This information can be represented as:
1000000A5+ 750000A4+1500000B5+ 900000B4+600000L3+ 650000S3+ 3500000≤20000000
Or, 100A5+75A4+150B5+90B4+60L3+65S3≤1650.............(7)
Finally, it has mentioned in the condition that the golf course should have at least one straight par 5 hole, which is expressed as:
A5 ≥1............................................................................(8)
The golf course should have at least two straight par 4 holes, which is expressed as:
A4≥2...............................................................................(9)
The golf course should have at least one Dogleg par 5 hole, which is expressed as:
B5≥1................................................................................(10)
The golf course should have at least two Dogleg par 4 holes, which is expressed as:
B4≥2.................................................................................(11)
The golf course should have at least one Long par 3 hole, which is expressed as:
L3≥1..................................................................................(12)
The golf course should have at least one Short par 3 hole, which is expressed as:
S3≥1...................................................................................(13)
B. Decision model to meet shareholders' request
The shareholders' request is constriction of an exclusive clubhouse. Using all the previously defined specification the decision model is created as follows.
The golf course enjoyment of the golfers is the objective function which the company wants to maximize
Z= 2A5+ 1.5A4+ 1.5 B5+ 2B4+ 1.75L3 + 2.25S3+4
Subject to
A5+B5≤4....................................................................(1)
A4+B4≤14....................................................................(2)
L3+S3≤4.......................................................................(3)
A5+A4+B5+B4+ L3+S3 = 18.....................................(4)
70≤5A5+4A4+5B5+4B4+3L3+3S3≤ 72........................(5)
36≤3A5+ 2B4+3.5B5+ 2.5B4+L3+0.75S3≤42...............(6)
100A5+75A4+150B5+90B4+60L3+65S3≤1400...............(7)
A5≥1...............................................................................(8)
A4≥2...............................................................................(9)
B5≥1................................................................................(10)
B4≥2.................................................................................(11)
L3≥1..................................................................................(12)
S3≥1...................................................................................(13)
The only difference here is the inequality (7), which has been modified as per the budget and cost of the project.
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C. Decision Models Incorporating Three Options for The Exclusive Clubhouse Golf Course Model.
Option 1: The size of exclusive clubhouse is reduced to 3 hectares.
So far as the cost of building a clubhouse of size 3 hectares is concerned, it comes to
$ [3,50,0000+ (6,000,000-3,50,0000)/2] = $4,750,000
The decision model is given as follows:
The golf course enjoyment of the golfers is the objective function which the company wants to maximize
Z= 2A5+ 1.5A4+ 1.5 B5+ 2B4+ 1.75L3 + 2.25S3+4
Subject to
A5+B5≤4....................................................................................(1)
A4+B4≤14..................................................................................(2)
L3+S3≤4.....................................................................................(3)
A5+A4+B5+B4+ L3+S3 = 18...................................................(4)
70≤5A5+4A4+5B5+4B4+3L3+3S3≤ 72........................(5)
36≤3A5+ 2B4+3.5B5+ 2.5B4+L3+0.75S3≤42..........................(6)
100A5+75A4+150B5+90B4+60L3+65S3≤1525..........................(7)
A5≥1...............................................................................(8)
A4≥2...............................................................................(9)
B5≥1................................................................................(10)
B4≥2.................................................................................(11)
L3≥1..................................................................................(12)
S3≥1...................................................................................(13)
Here again the inequality (7) has been adjusted to accommodate the condition that size of the exclusive clubhouse has been reduced, which has changed the cost of the construction of exclusive clubhouse with parking.
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Option 2: The construction cost of the exclusive club house is reduced to $ 5,000,000.
The decision model is given as follows:
The golf course enjoyment of the golfers is the objective function which the company wants to maximize
Z= 2A5+ 1.5A4+ 1.5 B5+ 2B4+ 1.75L3 + 2.25S3+4
Subject to
A5+B5≤4....................................................................(1)
A4+B4≤14....................................................................(2)
L3+S3≤4.......................................................................(3)
A5+A4+B5+B4+ L3+S3 = 18..............................................(4)
70≤5A5+4A4+5B5+4B4+3L3+3S3≤ 72........................(5)
36≤3A5+ 2B4+3.5B5+ 2.5B4+L3+0.75S3≤42................(6)
100A5+75A4+150B5+90B4+60L3+65S3≤1500...................(7)
A5≥1...............................................................................(8)
A4≥2...............................................................................(9)
B5≥1................................................................................(10)
B4≥2.................................................................................(11)
L3≥1..................................................................................(12)
S3≥1...................................................................................(13)
As the construction cost of the exclusive clubhouse has been reduced it has affected the inequality (7).
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Option 3: The budget allocated for the project is increased to 30 million.
The decision model is given as follows:
The golf course enjoyment of the golfers is the objective function which the company wants to maximize
Z= 2A5+ 1.5A4+ 1.5 B5+ 2B4+ 1.75L3 + 2.25S3+4
Subject to
A5+B5≤4....................................................................(1)
A4+B4≤14....................................................................(2)
L3+S3≤4.......................................................................(3)
A5+A4+B5+B4+ L3+S3 = 18..............................................(4)
70≤5A5+4A4+5B5+4B4+3L3+3S3≤ 72........................(5)
36≤3A5+ 2B4+3.5B5+ 2.5B4+L3+0.75S3≤42............................(6)
100A5+75A4+150B5+90B4+60L3+65S3≤2400......................(7)
A5≥1...............................................................................(8)
A4≥2...............................................................................(9)
B5≥1................................................................................(10)
B4≥2.................................................................................(11)
L3≥1..................................................................................(12)
S3≥1...................................................................................(13)
The change in the budget has modified the inequality (7).
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Part 3: Business Report & Communication - Provide a description of the implementation of your five decision models (the management's standard clubhouse, the original shareholders' exclusive clubhouse and the three options for the exclusive clubhouse.
Provide an analysis of the four feasible models on their holes configuration, total enjoyment index, total land used and the total construction cost. Discuss the implication on four feasible models whether they meet shareholders' original exclusive clubhouse requirement.
Make a recommendation to Oscar your proposal model. In doing so you can rank your four feasible models based on international golfing requirement and whether meeting shareholders' requirement.
Answer - Business Report and Communication
To achieve the new goal of Cunningham Holdings Limited of constructing Cunningham Gudgal Golf Resort at Charters Towers, the company board needs to choose from two alternatives. First is building an 18-holes standard clubhouse model which has been proposed by the management and second is an 18-holes exclusive clubhouse model, which has been the request of the shareholders. The company wants to maintain the international golf course standard to maximize the golfer experience. Given its resources both physical and financial, the company builds decision models for each of the alternatives.
Standard Clubhouse Model
This is the model where the company attempts to maximize an objective function which is the golf course enjoyment of the golfers subject to several constraints. These constraints are developed based on the stipulations of international standard for golf course and the budget constraint.
Exclusive Clubhouse Model
The exclusive clubhouse model has the same objective, but the objective function differs slightly from that of the standard clubhouse model with the addition of the fact that its golfer enjoyment is more by 4 enjoyment indices. Also, the land requirement and the cost of construction of the exclusive clubhouse are more than that of the standard clubhouse, which alters some of the constraints. Solving this decision model, no feasible solution was obtained.
Three Options
That is why the board also needs to examine three more options in favor of an exclusive clubhouse, which are also presented as three distinct decision models where some changes in the independent variables like size of the clubhouse, construction cost and total budget have been incorporated to see if they offer any feasible solution.
The first option suggests reducing size of the exclusive clubhouse from 4 hectares to 3 hectares. The cost of construction accordingly changes. Based on these information and other details a decision model is formed.
The second option proposes lowering the construction cost of the exclusive clubhouse from $6,000,000 to $ 5,000,000. A new decision model is made based on the given information.
The third option recommends increasing the allocated budget from $20 million to $30 million.
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The Analysis
Standard Clubhouse model
Solving the standard clubhouse model, we get that the following hole configuration:
Straight par 5 holes: 1
Straight par 4 holes: 2
Dogleg par 5 hole: 1
Dogleg par 4 hole: 10
Long par 3 hole: 1
Short par 3 holes: 3
The maximum golfer enjoyment is 35.
Total land use = (1x3) + (2x2) + (1x3.5) + (10x2.5) + (1x1) + (1x0.75) +2 = 39.25 hectares. This land requirement is within the available land limit of the company of 42 hectares.
Total land cost = $[(1x1000000) + (2x750000) + (1x1500000) + (10x900000) + (1x600000) + (1x650000)] = $ 6150000
Construction of cost of standard clubhouse = $3500000
Total cost of construction = $ (6150000+3500000) = $ 9650000
Option 1: The size of exclusive clubhouse is reduced to 3 hectares
Solving the decision model, we get the following hole configuration:
Straight par 5 holes: 3
Straight par 4 holes: 5
Dogleg par 5 hole: 1
Dogleg par 4 hole: 5
Long par 3 hole: 1
Short par 3 holes: 3
The maximum golfer enjoyment is 37.
Total land use = (3x3) + (5x2) + (1 x3.5) + (5x2.5) + (1x1) + (3x0.75)+4 = 62.5 hectares. This land requirement is not within the available land limit of the company of 42 hectares
Total land cost = $[(3x1000000) + (5x750000) + (1x1500000) + (5x900000) + (1x600000) + (3x650000)] = $ 15200000
Construction of cost of exclusive clubhouse = $6000000
Total cost of construction = $ (15200000+3500000) = $ 15800000
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Option 2: The construction cost of the exclusive club house is reduced to $ 5,000,000.
Solving the decision model, we get the following hole configuration:
Straight par 5 holes: 1
Straight par 4 holes: 6
Dogleg par 5 hole: 1
Dogleg par 4 hole: 6
Long par 3 hole: 1
Short par 3 holes: 3
The maximum golfer enjoyment is 37.
Total land use = (1x3) + (6x2) + (1 x3.5) + (6x2.5) + (1x1) + (3x0.75)+4 = 49 hectares. This land requirement is not within the available land limit of the company of 42 hectares
Total land cost = $[(1x1000000) + (6x750000) + (1x1500000) + (6x900000) + (1x600000) + (3x650000)] = $ 14950000
Construction of cost of exclusive clubhouse = $6000000
Total cost of construction = $ (14950000+3500000) = $ 20950000
Option 3: The budget allocated for the project is increased to 30 million.
Solving the decision model, we get that the following hole configuration:
Straight par 5 holes: 1
Straight par 4 holes: 2
Dogleg par 5 hole: 1
Dogleg par 4 hole: 10
Long par 3 hole: 1
Short par 3 holes: 3
The maximum golfer enjoyment is 39.
Total land use = (1x3) + (2x2) + (1x3.5) + (10x2.5) + (1x1) + (1x 0.75)+ 4 = 41.25 hectares. This land requirement is within the available land limit of the company of 42 hectares.
Total land cost = $[(1x1000000) + (2x750000) + (1x1500000) + (10x900000) + (1x600000) + (1x650000)] = $ 6150000
Construction of cost of exclusive clubhouse = $6000000
Total cost of construction = $ (6150000+6000000) = $ 12150000
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Discussion
Analyzing these four feasible models, it can be seen that the standard clubhouse is a feasible option and well within the budget of the company. However, it does not fulfil the requirements of exclusive clubhouse. Option 1 has higher land requirement, but the total cost is within the budget. Option 2 has both land requirement and budget beyond the conditions of the exclusive clubhouse. Option 3 fulfils the requirements of the exclusive clubhouse and is well within the enhanced budget for construction.
Recommendation
The following table ranks the four feasible models:
|
Rank
|
Model
|
International Golfing Requirements
|
Total cost
|
Land requirement
|
Total golfer enjoyment
|
Whether meets shareholders' requirements
|
|
1
|
Standard Clubhouse
|
Yes
|
$ 9650000
|
39.25 hectares.
|
35
|
No
|
|
2
|
Option 3
|
Yes
|
$ 12150000
|
41.25 hectares
|
39
|
Yes
|
|
3
|
Option 1
|
Yes
|
$15800000
|
62.5 hectares.
|
37
|
No
|
|
4
|
Option 2
|
Yes
|
$ 20950000
|
49 hectares
|
37
|
No
|
The standard clubhouse is the most feasible and extremely cheap to construct options and should be given highest priority. This option meets all the standards of international golf course and results in a decently good golfer enjoyment. The option is will within the allocated budget of the company. Taking all these factors into account, the Standard Clubhouse model seems the best option.
However, if the board decides to adhere to the shareholders' requirements and go for an exclusive clubhouse, then the best course of action will be to increase the allocated budget. This is because an increase in the budget from $20 million to $30 million raised the golfer enjoyment the most to 39 whereas the other options raised it merely to 37. Also, this option fulfilled the exclusive clubhouse requirement that the enjoyment index of the exclusive clubhouse will be four more than the standard clubhouse enjoyment index. Moreover, the cost of option 1 and 2 are beyond the budget of $20 million.
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