A Case Study on Cunningham Gudgal Golf Resort 2022

International Standard Golf Course Modelling by Integer Programming –
A Case Study on Cunningham Gudgal Golf Resort
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Table of Contents
Part 1: Action Plan.....................................................................................................................2
Part 2: Spread Sheet Model Implementation.............................................................................3
Part 3: Business Report & Communication...............................................................................8
Executive Summary.................................................................................................................10
Overview of the Study.............................................................................................................11
Management Policy..............................................................................................................11
Mathematical Modelling......................................................................................................11
Analysis and Findings..............................................................................................................12
Model 1: Standard Clubhouse Model..................................................................................12
Model 2: Exclusive Clubhouse Model.................................................................................12
Model 3: Exclusive Clubhouse with Reduced Area............................................................13
Model 4: Exclusive Clubhouse with Reduced Cost.............................................................13
Model 5: Exclusive Clubhouse with Increased Overall Cost...............................................14
Discussion of Implications.......................................................................................................14
Recommendation......................................................................................................................15
References................................................................................................................................16
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Part 1: Action Plan
1. There were six decision variables in the optimization problem. Number of golfing holes
to be built were the desion variables of the study. The list provided below with
abbreviation and algebric name for each variable.
Table 1: Decision Variables with abbreviation and algebraic form
Kind of golfing hole Abbreviatio
n
Algebric Expression
“Straight par 5” Sp5 X1
“Dogleg par 5” Dp5 X2
“Straight par 4” Sp4 X3
“Dogleg par 4” Dp4 X4
“long par 3” lp3 X5
“short par 3” sp3 X6
2. The objective was to maximize enjoyment index of golfers. Hence, the objective function
was the enjoyment index from golf course and clubhouse.
3. The constraints were practical, mangement oriented or technological in nature. – There
were limitations as well as requirement criterion with some restrictions.
Table 2: Constraints with limitations, requirement and restrictions
Contraint
Type
Constraint Requirement Restrictio
n
Limitation
Technical Sp5 ≥ 1
Dp5 ≥ 1
Sp4 ≥ 2
Dp4 ≥ 2
lp3 ≥ 1
sp3 ≥ 1
Sp5 & Dp5 ≤ 4
Sp4 & Dp4 ≤ 14
lp3 & sp3 ≤ 4
Total Par ≥ 70 ≤ 72
Total Golf -Holes = 18
Total acreage ≥ 36 ≤ 42
Management Standard Clubhouse Acreage = 2
Standard Clubhouse Cost = $ 3.5 Million
Overall Budget = 20 Million
Exclusive Clubhouse Acreage ≤ 4
Exclusive Clubhouse Cost ≤ $ 6 Million
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Practical Sp5, Dp5, Sp4, Dp4, lp3, sp3 Integer
4. Mathematical modelling of the integer programming problem was stated as below.
Objective Function:
Max Z = 2X1 + 1.5 X2 + 1.5 X3 + 2X4 + 1.75 X5 + 2.25 X6 +X7
X7 = Enjoyment Index of Clubhouse (Standard = 0, Exclusive = 4)
Constraints:
Individual Pars => X1 ≥ 1, X2 ≥ 1, X3 ≥ 1, X4 ≥ 1, X5 ≥ 1, X6 ≥ 1
Sum of Pars => X1 + X2 ≥ 4, X3 + X4 ≥ 14, X5 + X6 ≥ 4
Total Par => 70 ≤ 5X1 + 5X2 + 4X3 + 4X4 + 3X5 + 3X6 ≤ 72
Total Holes => X1 + X2 + X3 + X4 + X5 + X6 = 18
Acreage: 36 ≤ 3X1 + 3.5X2 + 2X3 + 2.5 X4 + X5 + 0.75X6 + X8 ≤ 42
X8 : Clubhouse Areage (Standard = 2, Exclusive = 4)
Budget => 10,00,000 X1 + 15,00,000 X2 + 7,50,000 X3 + 9,00,000 X4 + 6,00,000 X5 +
6,50,000 X6 + X9 ≤ 2,00,00,000
X9 = Clubhouse Cost (Standard = $ 3.5 Million, Exclusive =$ 6 Million)
X1, X2, X3, X4, X5, X6 ≥ 0 (Integer), X7, X8, X9 ≥ 0 (Mason, 2012).
Part 2: Spread Sheet Model Implementation
Standard Clubhouse Model
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Standard Clubhouse Model Solution: Maximum Enjoyment Index = 35
Exclusive Clubhouse Model: No Integer Solution
Option 1: Exclusive Clubhouse Model: Acreage = 2: No Integer Solution
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Exclusive Clubhouse Model: Acreage = 2.5: No Integer Solution
Exclusive Clubhouse Model: Acreage = 3: No Integer Solution
Exclusive Clubhouse Model: Acreage = 3.5: No Integer Solution
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Option 2: Exclusive Clubhouse: Budget = $ 5.5 Million: Maximum Enjoyment Index =
35.5
Exclusive Clubhouse: Budget = $ 5 Million: Maximum Enjoyment Index = 37
Exclusive Clubhouse: Budget = $ 4 Million: Maximum Enjoyment Index = 38
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Exclusive Clubhouse: Budget = $ 3.5 Million: Maximum Enjoyment Index = 38
Option 3: Overall Budget = $ 21.5 Million: Maximum Enjoyment Index = 38
Overall Budget = $ 22 Million: Maximum Enjoyment Index = 38
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Overall Budget = $ 25 Million: Maximum Enjoyment Index = 38
Part 3: Business Report & Communication
The business report presents with the all five models with every possible variations
(McNally, Cerbone, & Maroun, 2017). Also, it helps in identify the best model from
management and practical point of view. The report discourses about the feasibility of
exclusive clubhouse model with recommendations about the probable change in clubhouse
budget and overall expenditure.
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Feasibility of International Standard Golf Course with Exclusive Clubhouse
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Executive Summary
The report elucidates the feasibility of construction an international standard golf-
course at Charters Towers. The proposed model by management for a golf course with a
standard clubhouse has been appraised. Parallel study on golf course with exclusive
clubhouse model has also been assessed in pursuit of best feasible model providing maximum
enjoyment to golfers. The optimization part of the mathematical problems has been estimated
using Integer Programming methodology. According to the guidelines, an international
standard golf course should have 18 golf holes with individual restrictions on each kind of
golfing holes as mentioned in the action plan. The purpose of using the Integer Programming
method was to satisfy all constraints and find integer solution for all kind of golfing holes. A
standard clubhouse model was first optimized to achieve a maximum enjoyment index (EI) of
35. The stakeholders were inclined towards higher EI with luxurious facilities in the
clubhouse. Hence, an exclusive clubhouse with international standard golf course model was
assessed, which lacked any feasible integer solution. Subsequently, the land area of exclusive
clubhouse was altered to achieve a realistic solution, only to learn that no such option existed.
The cost of the exclusive clubhouse was reduced gradually from $ 6 million to $ 3.5 million
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(standard model clubhouse cost), and optimum solution with integer number of holes was
evaluated to provide EI of 38 (at $ 4 million budget and below). Finally, overall budget was
hypothetically raised from $ 20 million to achieve EI of 38 at $ 21.5 million. Further increase
in budget did not confirm any further increase in EI.
Overview of the Study
Management Policy
The golf course project was a transcendent project of Cunningham Holdings Limited
(CHL) towards eco-friendly and sustainable project, planned for rural development (Addanki,
& Venkataraman, 2017). The business perspective of the company was to build world class
sustainable service driven by premium leadership skills that will heighten the brand value of
CHL. Accentuate of the golf course project was in boosting the neighbouring economy by
promoting tourism in a tropical area like Charters Towers. The objective of the management
was to build an international standard golf course with consisting of a standard clubhouse
within a budget of $ 20 million. An exclusive clubhouse model on 4 acreage land with an EI
of 4, and cost of $ 6 million for the clubhouse was later introduced due to demand from the
shareholders.
Mathematical Modelling
The standard clubhouse model with 18 holes golf course was outlined by linear
programming technique with integer constraints on decision variables (Vielma, 2015). The
decision variables of the study were the number of six types of golfing holes (Sp5, Dp5, Sp4,
Dp4, lp3, and sp3). Each type of golfing hole had enjoyment index associated with it, where
standard clubhouse had zero EI. The objective of the model was to maximize the total EI with
constraints of international guidelines for the golf course. Another mathematical model for
the exclusive clubhouse was constructed altering the acreage, cost, and EI of the clubhouse.
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The complexity of the golfing holes was learnt to increase EI of the players. Hence, special
note was taken about the combination of golfing holes in the optimal solution. Three
subsidiary exclusive clubhouse models were also constructed by varying the cost, EI, and
land area of the clubhouse. The Excel solver tool has been used to solve the integer
programming problems.
Analysis and Findings
Model 1: Standard Clubhouse Model
The standard clubhouse golf course model had a budget limitation of $ 20 million, in
which $ 3.5 million was allocated for the clubhouse. The land area of the standard clubhouse
was 2 hectares in 42 hectares of available land for the entire golf course project. There was no
enjoyment index associated with the standard clubhouse. The optimum integer solution for
the standard model has been provided in Table 3. The maximum enjoyment was evaluated to
be 35 with a budget of $ 19.05 million, where the construction has to be done on a land area
of 40.75 hectares.
Table 3: Solution for the golfing holes in Standard Model
Kind of golfing
hole
Solution
“Straight par 5” 1
“Dogleg par 5” 1
“Straight par 4” 2
“Dogleg par 4” 10
“long par 3” 1
“short par 3” 3
Model 2: Exclusive Clubhouse Model
The exclusive clubhouse cost was $ 6 million and required 4 hectares of land area
within the golf course premises. Importantly, the clubhouse had EI of 4 for ample delight of
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the shareholders. Guidelines for the international standard golf course persisted in this model.
No integer solution for Sp4 type of golf hole was found, and regrettably there existed no
possibility of implementing this model. This model was re-evaluated by changing the cost
and area requirement of the clubhouse. This model was also re-estimated with an increased
total budget where all other constraints and requirements were kept intact.
Model 3: Exclusive Clubhouse with Reduced Area
Acreage of the exclusive clubhouse was reduced from 4 hectares to 2 hectares in a
four step process, with a reduction of 0.5 hectares of area in each step. No integer solution
was found for Dp4 golfing hole for acreage of 3.5 and 3 hectares. Again, there was no integer
solution for Sp4 golfing hole for acreage of 2.5 and 2 hectares. The option of reduction of
area for the exclusive clubhouse to the limit of standard clubhouse yielded no practically
significant result. Therefore, this particular choice of alteration was not found to be feasible
for achieving any realistic solution for the exclusive model.
Model 4: Exclusive Clubhouse with Reduced Cost
Cost of the clubhouse was reduced to the level of standard model in a four step
approach, with a fixed requirement of land area of 4 hectares. First, cost of $ 5.5 million for
the clubhouse yielded a maximum EI of 35.5 with a requirement of 39.25 hectare of land for
the entire golf course for $ 20 million of overall expenditure. Reduction of cost to $ 5 million
for the clubhouse yielded EI of 37. Required total land area was 40.75 hectares and overall
cost was $ 19.95 million for the entire project. Further reduction of clubhouse cost to $ 4
million decreased the overall cost to $ 19.25 million with an EI of 38. Maximum acreage for
the project was 41.75 hectares. Further reduction of the clubhouse cost to $ 3.5 million failed
to increase EI above 38. The detailed optimal solutions can be noted in Table 4.
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Table 4: Optimal solution for reduced exclusive clubhouse cost
Clubhouse Cost ($
Million) Sp5 Dp5 Sp4 Dp4 lp3 sp3
5.5 1 1 9 3 1 3
5.0 1 1 6 6 1 3
4.0 1 1 4 8 1 3
3.5 1 1 4 8 1 3
Model 5: Exclusive Clubhouse with Increased Overall Cost
The initial overall cost of the model was $ 20 million. The overall budget was
hypothetically increased to verify the validity of the exclusive clubhouse model. A three step
increase was performed. First, the overall budget was increased to $ 21.5 million, where the
maximum EI was evaluated as 38. Total acreage required was 41.75 hectares and overall fund
required for the entire golf course project was $ 21.25 million. Cost, acreage, and EI of the
exclusive clubhouse were similar to model 2. Subsequent increase in overall budget to $ 22
million, and then to $ 25 million were noted to produce EI of 38 with parallel requirement
parameters to the $ 21.5 million model. Table 5 comprises of the detail solutions.
Table 5: Optimal solution for increase in overall cost
Overall Cost ($ Million) Sp
5 Dp5 Sp4 Dp4 lp3 sp3
21.5 1 1 4 8 1 3
22 1 1 4 8 1 3
25 1 1 4 8 1 3
Discussion of Implications
The prologue of the report stated the objective of CHL about construction of
international standard golf course in specified budget of $ 20 million. The standard clubhouse
model (Model 1) achieved an overall EI of 35 with an overall cost of $ 19.05 million to be
built on 40.75 hectare of land. No integer solution was found for the exclusive clubhouse
model (Model 2). The second feasible solution was the exclusive clubhouse golf course
model with $ 4 million cost for the clubhouse (Model 3). Optimum EI was 38 an overall cost
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of $ 19.25 million to be built on 41.75 hectare of land. Finally, hypothetical increase of
overall budget to $ 21.5 million yielded an optimum EI of 38 with an overall cost of $ 21.25
million to be built on 41.75 hectare of land (Model 4). Model 3 and model 4 were the two
realistic models which could meet shareholders’ expectation. Also, both the models were
feasible from company’s point of view.
Recommendation
Management of CHL should consider the exclusive model over the standard model if
it finds easier to entice golfers from all around the world and keep the shareholders pleased
(Dai, Puyang, & Han, 2016). Model 3 with $ 4 million cost of the exclusive clubhouse with a
budget of $ 19.25 million achieving optimum EI of 38 was found to be the best model,
although, reduction of budget could have a compromising impact on the quality of the
exclusive clubhouse. Secondly, the management could look forward to $ 3.5 million
exclusive clubhouse model with a budget of $ 18.75 million achieving optimum EI of 38
spread over land area of 41.75 hectares. But, due to at par budget with the standard clubhouse
the quality of the exclusive clubhouse has to be compromised, which can eventually
exasperate the shareholders. The third best model was noted to be the exclusive clubhouse
Model 4 with $ 21.5 million of overall budget. The required cost in this model was evaluated
as $ 21.25 million. CHL group can look forward to build an exclusive clubhouse model
without compromising with the quality of the clubhouse for an extra budget of mere $ 0.25
million. Finally, the standard model can also be implemented (Model 1) if the management
feels that EI of 35 should be at par with the international standard golf courses.
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References
Addanki, S. C., & Venkataraman, H. (2017). Greening the economy: A review of urban
sustainability measures for developing new cities. Sustainable Cities and Society, 32,
1-8.
Dai, Z., Puyang, X., & Han, L. (2016). Using assessment of net ecosystem services to
promote sustainability of golf course in China. Ecological indicators, 63, 165-171.
Mason, A. J. (2012). OpenSolver-an open source add-in to solve linear and integer
progammes in Excel. In Operations research proceedings 2011 (pp. 401-406).
Springer, Berlin, Heidelberg.
McNally, M. A., Cerbone, D., & Maroun, W. (2017). Exploring the challenges of preparing
an integrated report. Meditari Accountancy Research, 25(4), 481-504.
Vielma, J. P. (2015). Mixed integer linear programming formulation techniques. Siam
Review, 57(1), 3-57.
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