A developer is planning to construct a new five-star hotel...

A developer is planning to construct a new five-star hotel on a prime inner city site. Three alternative design and size options are under consideration, with net capital $$ \begin{array}{lccc} \hline \hline & \text { Design 1 } & \text { Design 2 } & \text { Design 3 } \\ \hline \text { Capital expenditure, EOY 0 (\$M) } & 2 & 5 & 3 \\ \text { Capital expenditure, EOY 1 (\$M) } & 12 & 15 & 11 \\ \text { Capital expenditure, EOY 2 (\$M) } & 4 & 6 & 8 \\ \hline \hline \end{array} $$ outlays in the first three years as shown in Table 12.8, after which the hotel should be self-funding. The developer has $$\$ 20 \mathrm{M}$$ in readily available funds, and can borrow further finance of up to $$\$ 5 \mathrm{M}$$ at an interest rate of $14 \%$. The three designs have estimated net present values over twenty years of $$\$ 10 \mathrm{M}$$, $$\$ 17 \mathrm{M}$$ and $$\$ 9 \mathrm{M}$$. Set up a linear programming model which can be used to assist in project choice.

A developer is planning to construct a new five-star hotel on a prime inner city site. Three alternative design and size options are under consideration, with net capital
$$
\begin{array}{lccc}
\hline \hline & \text { Design 1 } & \text { Design 2 } & \text { Design 3 } \\
\hline \text { Capital expenditure, EOY 0 (\$M) } & 2 & 5 & 3 \\
\text { Capital expenditure, EOY 1 (\$M) } & 12 & 15 & 11 \\
\text { Capital expenditure, EOY 2 (\$M) } & 4 & 6 & 8 \\
\hline \hline
\end{array}
$$
outlays in the first three years as shown in Table 12.8, after which the hotel should be self-funding.

The developer has $$\$ 20 \mathrm{M}$$ in readily available funds, and can borrow further finance of up to $$\$ 5 \mathrm{M}$$ at an interest rate of $14 \%$. The three designs have estimated net present values over twenty years of $$\$ 10 \mathrm{M}$$, $$\$ 17 \mathrm{M}$$ and $$\$ 9 \mathrm{M}$$. Set up a linear programming model which can be used to assist in project choice.

Key Concepts

Constraints

These are the linear equations or inequalities that restrict the decision variables. They capture practical limitations such as available funds, borrowing limits, and the timing of capital outlays. They ensure that the selected alternative and financing decisions do not exceed the budget and financing conditions at each time period.

Objective Function

A linear function that needs to be maximized or minimized, in this case, typically representing the net present value (NPV) of the project over a given planning horizon. The function aggregates the financial benefits of the selected alternative and guides the optimization.

Financial Modeling

Involves incorporating factors such as initial funds, future capital expenditures scheduling, borrowing limits, and borrowing costs (interest rate) into the model. This helps in representing the time-based cash flows and investment requirements, ensuring the project's financial feasibility while making the optimum selection.

Linear Programming Model

A framework for optimizing a linear objective function, subject to a set of linear equality or inequality constraints. In project selection problems, this involves making decisions such as selecting among alternatives while satisfying resource limitations and other requirements.

Decision Variables

Variables in the model represent the choices to make. These include binary variables to indicate which design alternative is selected and continuous or integer variables to represent the amounts of funds borrowed in specific periods.

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