Cunningham Golf Course: Integer Programming for Development

This assignment presents a business report detailing the application of integer programming to optimize the development of an international standard golf course. The project focuses on Cunningham Holdings Limited's initiative to build a golf resort, exploring various decision variables such as the number and type of golf holes, objective functions like maximizing player enjoyment, and constraints including acreage, budget, and par requirements. The analysis includes a spreadsheet analysis using Excel's solver tool to determine optimal hole configurations for both standard and exclusive clubhouse models. The report presents findings on feasible models, including the optimum hole configuration for a standard clubhouse, which yielded a golfer's enjoyment index of 35 at a cost of $19.05 million. The study also explores the challenges of the exclusive clubhouse model and suggests alternative solutions by varying land area, construction costs, and overall project budgets. The conclusion emphasizes the feasibility of the standard model and recommends the best model based on cost, enjoyment index, and adherence to international standards. The report provides recommendations for future improvements and highlights the impact of different variables on the model's outcomes.

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An Integer Programming Approach for
International Standard Golf Course Development

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Table of Contents
Part 1: Action Plan...................................................................................................................3
Part 2: Spread Sheet Analysis.................................................................................................4
Part 3: Business Report...........................................................................................................4
Executive Summary...................................................................................................................6
Introduction................................................................................................................................7
Analysis and Findings................................................................................................................7
Conclusion..................................................................................................................................9
Recommendation........................................................................................................................9
References................................................................................................................................10
Appendices...............................................................................................................................11

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Part 1: Action Plan
1. The decision variables are: Number of holes of different types, which are
i. “Straight par 5” (X1)
ii. “Dogleg par 5” (X2)
iii. “Straight par 4 “ (X3)
iv. “Dogleg par 4 “ (X4)
v. “long par 3” (X5)
vi. “short par 3” (X6)
2. The objective function is:
Maximizing the player enjoyment due to complexity of holes and clubhouse (C.E.I)
3. Constraints are:
i. Total Acreage available = 42 hectares
ii. Total Budget available = $20 million
iii. Constraints on pars: AT LEAST
a. “Straight par 5” = 1
b. “Dogleg par 5” = 1
c. “Straight par 4 “ = 2
d. “Dogleg par 4 “ = 2
e. “long par 3” = 1
f. “short par 3” = 1
iv. Constraints on total pars: AT MOST
a. Total “Straight par 5” and “Dogleg par 5” = 4
b. Total “Straight par 4 “ and “Dogleg par 4 “ = 14
c. Total “long par 3” and “short par 3” = 4
d. Total par between 70 and 72
v. Total number of holes = 18
vi. Total acreage (course and clubhouse (C.A)) must be between 36 and 42 acres
4. Mathematical expression of objective function is:
Maximize Z = 2X1+1 .5 X2+1 .5 X3 +2 X4 +1. 75 X5+ 2. 25 X6+ C . E . I (=0)

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Mathematical expression of constraints:
Min Acreage: 3X1 + 3.5X2 + 2X3 + 2.5 X4 + X5 + 0.75X6 + C.A ≥ 36
Max Acreage: 3X1 + 3.5X2 + 2X3 + 2.5 X4 + X5 + 0.75X6 + C.A ≤ 42
Number of Pars:
X1 ≥ 1, X2 ≥ 1, X3 ≥ 1, X4 ≥ 1, X5 ≥ 1, X6 ≥ 1, X1 + X2 ≥ 4, X3 + X4 ≥ 14, X5 + X6 ≥ 4
Total Pars:
5X1 + 5X2 + 4X3 + 4X4 + 3X5 + 3X6 ≥ 70
5X1 + 5X2 + 4X3 + 4X4 + 3X5 + 3X6 ≤ 72
Holes:
X1 + X2 + X3 + X4 + X5 + X6 = 18
Budget:
10,00,000X1 + 15,00,000X2 + 7,50,000X3 + 9,00,000X4 + 6,00,000X5 +6,50,000X6 +
Clubhouse Cost ≤ 2,00,00,000
Non-negative constraints:
X1 ≥ 0, X2 ≥ 0, X3 ≥ 1, X4 ≥ 0, X5 ≥ 0, X6 ≥ 0
All of the decision variables have integer values (Prochaska, & Theodore, 2018).
Part 2: Spread Sheet Analysis
Spread sheet Analysis has been conducted for each issue using solver tool in MS Excel.
Part 3: Business Report

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Development of Cunningham Golf Course Model

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Executive Summary
The Cunningham management plans to build an international standard Golf course
with the standard Clubhouse in 2 hectare acreage, including parking within a construction
cost of $3.5 million. Shareholders called for the construction of an exclusive club with a
budget of $6 million in a four hectares property. Integer Programming was used to optimize
the linear model for standard as well as exclusive clubhouse models. Optimum hole
configuration for standard clubhouse model was of one “Straight par 5”, one “Dogleg par 5”,
two “Straight par 4 “, 10 “Dogleg par 4 “, a “long par 3”, and 3 “short par 3”. Golfers total
enjoyment index was 35, which cost $19.05 million. No feasible solution under exclusive
clubhouse constraints was possible. A set of integer solutions existed for land area of 2.5
hectares, but the solution failed to satisfy international standard of 18 golf holes constraint.
The best model was exclusive model with clubhouse build at $4.5 million and achieving
enjoyment index of 38 with optimum hole configuration as one “Straight par 5”, one “Dogleg
par 5”, 4 “Straight par 4 “, 8 “Dogleg par 4 “, a “long par 3”, and 3 “short par 3”.

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Introduction
In consultation with the golf course planners around the world, extensive research has
been carried out to support the development of proposals for Cunningham golf course by
identifying the key standards required to design a golf course and attract golfers. The study
featured Golf's fun and satisfaction with the golf course design, the complexity of the holes in
the golf course and facilities as key indicators for attracting national and international golfers.
Description of the decision models
Management plans to build an international standard Golf course with the standard
Clubhouse in 2 hectare acreage, including parking within a construction cost of $3.5 million.
According to international Golf Course standards, the new golf course should have an
international standard of 18 holes, at least one “Straight par 5”, one “Dogleg par 5”, two
“Straight par 4 “, 2 “Dogleg par 4 “, a “long par 3”, and “short par 3”. The golf course should
not exceed 4 pars 5’s, 14 pars 4’s, and 4 pars 3’s in total. Total pars would total between 70
and 72 within a total area of 36 and 42 hectares, where the total number of holes would be
exactly 18.
Shareholders called for the construction of an exclusive club with a budget of $6
million in a four hectares property, including parking space. With the current restrictions, it
was not possible to build exclusive golf club in the course. Three options have been adopted
to find a viable solution. First, the size of the entire exclusive club was reduced in the model.
Secondly, the cost of building an exclusive club was reduced, and the last assumption was
that the budget had been increased theoretically.
Analysis and Findings
Integer Programming was used to optimize the linear model for standard as well as
exclusive clubhouse models. Excel solver tool has been extensively used for solution of the
linear programming problems with integer constraint (Beyer, Dujardin, Watts, &
Possingham, 2016).

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Implication of feasible models
Standard model implied that total enjoyment of golfers was calculated as the sum of
product of pars and its corresponding enjoyment index and enjoyment index of clubhouse.
The total acreage was calculated as the sum of 2 hectares of standard clubhouse and total land
for 18 holes, which corresponds to the product of holes for every par multiplied with their
corresponding acreage. Total cost was evaluated as the sum of cost incurred to construct the
holes for every par and cost due to clubhouse construction.
Exclusive club house model has enjoyment index of 4 and required 4 hectares of land
including parking with a cost of $6 million along with international standard golf course.
Total land area was calculated similarly as that of the standard model, but the acreage of
exclusive clubhouse was considered. Cost of exclusive clubhouse was considered instead of
standard in total cost. Other constraints for the golf course were similar that of the standard
model. Exclusive model was the choice of shareholders’ for better comfort.
Feasible Models
Optimum hole configuration for standard clubhouse model was of one “Straight par
5”, one “Dogleg par 5”, two “Straight par 4 “, 10 “Dogleg par 4 “, a “long par 3”, and 3
“short par 3”. Golfers total enjoyment index was 35, which cost $19.05 million. This model
was feasible to use and satisfied international standard of 18 holes golf course.
The exclusive model was found to have no feasible solution under exclusive
clubhouse constraints. Therefore, three alternative options have been applied for checking the
feasibility of the exclusive clubhouse model.
First, the land required to build an exclusive clubhouse was varied between 2 hectares
and 4 hectares. Feasible solution of the golf course problem was tested for five different land
areas. No feasible integer solution existed for acreage of exclusive clubhouse as 2, 3, 3.5, and
4 hectares. A set of integer solutions existed for land area of 2.5 hectares, but the solution
failed to satisfy international standard of 18 golf holes constraint.
Secondly, the cost of the exclusive clubhouse was varied between $3.5 million and $6
million, with a break of $0.5 million. Optimum hole configuration was of one “Straight par
5”, one “Dogleg par 5”, 4 “Straight par 4 “, 8 “Dogleg par 4 “, a “long par 3”, and 3 “short
par 3”. Golfers total enjoyment index was 35.5, which cost $18.75 million. Here, the
construction cost for exclusive clubhouse was considered as $5.5 million. Further reduction

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of clubhouse building cost to $5 million was noted to obtain an optimal enjoyment index of
37. Optimum hole configuration was of one “Straight par 5”, one “Dogleg par 5”, 6 “Straight
par 4 “, 6 “Dogleg par 4 “, a “long par 3”, and 3 “short par 3”. Further reduction of clubhouse
build cost to $4.5 million obtained enjoyment index of 38 with optimum hole configuration
was of one “Straight par 5”, one “Dogleg par 5”, 4 “Straight par 4 “, 8 “Dogleg par 4 “, a
“long par 3”, and 3 “short par 3” with a budget of $19.75 million.
Lastly, budget of the overall project was hypothetically increased to $22 million for
the exclusive clubhouse model. It obtained enjoyment index of 38 with optimum hole
configuration was of one “Straight par 5”, one “Dogleg par 5”, 4 “Straight par 4 “, 8 “Dogleg
par 4 “, a “long par 3”, and 3 “short par 3”. Total cost incurred was $21.25 million. Further
increase in budget to $25 million and then to $30 million also yielded parallel results.
Conclusion
A preliminary study revealed that the area of 42 hectare land in the Charters Towers
could thrive and evolve in natural beauties without any harm to the environment. The
Cunningham Holdings Limited fully accepts this requirement as it is in line with the
company's vision. Construction of an international standard golf course with standard
clubhouse was a plan to realise that vision. Stakeholders’ were though inclined towards an
exclusive golf clubhouse along with the course. The viability of the both the models have
been validated in the present study. Standard clubhouse with international standard 18 holes
golf course with one “Straight par 5”, one “Dogleg par 5”, two “Straight par 4 “, 10 “Dogleg
par 4 “, a “long par 3”, and 3 “short par 3” was found to be feasible with golfers total
enjoyment index of 35 and a budget of $19.05 million. Exclusive model was supposed to be
much more striking, but the model was found to be infeasible under the set of constraints.
Viability of the model was tested with reduced clubhouse size, lower cost of clubhouse
construction, and hypothetical budget increment. Reduction in clubhouse size was not a
solution for a valid exclusive clubhouse model. Lowering construction cost to $4.5 million
was noted to increase enjoyment index and importantly yield a feasible integer solution.
Hypothetical increase in budget to $22 million was noted to obtain a maximum of 38
enjoyment index.

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Recommendation
A major drawback of the model was that the relation between enjoyment index and
land area as well as cost of clubhouse building was unknown for exclusive model. Therefore,
enjoyment index was kept fix in case of varying acreage and cost of clubhouse. This very fact
could impact the model from a practically significant angle.
Exhaustive analysis revealed that maximum enjoyment index that can be achieved
was 38. Hence, the golf course model with $3.5 million cost for exclusive clubhouse was the
best model with total cost of $18.75 million and acreage of 41.75 hectares. However, due to
the fact that cost of the standard clubhouse was also $3.5 million, this model appeared to
unrealistic. So, the best model was international standard golf course with $4.5 million
exclusive club house and one “Straight par 5”, one “Dogleg par 5”, 4 “Straight par 4 “, 8
“Dogleg par 4 “, a “long par 3”, and 3 “short par 3” within a budget of $19.75 million. There
is an increase in total cost of $0.7 million compare to the standard model, but the decision
was based on almost 8.5% increase in enjoyment index. Secondly, the standard model was
also could be the choice of the management if they are inclined towards lower cost over
enjoyment index. Model with hypothetical budget increase to $22 million could be third
choice considering the fact that enjoyment index in that model was also 38. However,
chances of increasing the budget seem an unrealistic decision when enjoyment score of 38
can be reached in other models.
References
Prochaska, C., & Theodore, L. (2018). Linear Programming Applications. Introduction to
Mathematical Methods for Environmental Engineers and Scientists, 465.
Beyer, H. L., Dujardin, Y., Watts, M. E., & Possingham, H. P. (2016). Solving conservation
planning problems with integer linear programming. Ecological Modelling, 328, 14-
22.

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Appendices
Table 1: Integer Solution for the Standard Clubhouse Problem
Table 2: No feasible solution output for the Exclusive Clubhouse Problem

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Table 3: Option 1: No feasible solution for Acreage of exclusive clubhouse = 2 hectares
Table 4: Option 1: No feasible solution for Acreage of exclusive clubhouse = 2.5 hectares

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Table 5: Option 1: No feasible solution for Acreage of exclusive clubhouse = 3 hectares
Table 6: Option 1: No feasible solution for Acreage of exclusive clubhouse = 3.5 hectares

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Table 7: Option 1: No feasible solution for Acreage of exclusive clubhouse = 4 hectares
Table 8: Option 2: Solution for Cost of exclusive clubhouse = $5.5 million

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Table 9: Option 2: Solution for Cost of exclusive clubhouse = $5.0 million
Table 10: Option 2: Solution for Cost of exclusive clubhouse = $4.5 million

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Table 11: Option 2: Solution for Cost of exclusive clubhouse = $4.0 million
Table 12: Option 2: Solution for Cost of exclusive clubhouse = $3.5 million

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Table 13: Option 3: Solution for budget for exclusive clubhouse = $22 million
Table 14: Option 3: Solution for budget for exclusive clubhouse = $25 million

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Table 15: Option 3: Solution for budget for exclusive clubhouse = $30 million