# [R] R and LINGO?

Jan Olsen Røyland janoroyland at outlook.com
Fri Nov 10 17:04:10 CET 2017

```Hei
Im struggling with this problem:
b) Another company wants to compose the optimal project portfolio based on the following 5-
year project proposals. In the table, the cash flow for each project in each year is shown.
Project 1 Project 2 Project 3 Project 4 Project 5 Project 6
1st year of the project -58 -32 -18 -31 -33 -39
2nd year of the project 17 17 11 4 21 30
3rd year of the project 26 30 13 19 20 9
4th year of the project 18 7 4 7 22 13
5th year of the project 40 6 7 17 6 13
In this case, the company can also choose which year each project should commence. These six
candidate projects can begin either in 2018, in 2019 or in 2020, or not at all.
The current proposal is to undertake project 1, 2, 3 and 5, with project 3 and 5 starting in 2018,
project 2 in 2019 and project 1 in 2020. Available funds by the end of year 2017 will be 70 mill.
The resulting cash flow is given in the following table:
Project 1 Project 2 Project 3 Project 5
Total cash flow
from projects
Available
funds
2017 70
2018 -18 -33 -51 19
2019 -32 11 21 0 19
2020 -58 17 13 20 -8 11
2021 17 30 4 22 73 84
2022 26 7 7 6 46 130
2023 18 6 24 154
2024 40 40 194
Formulate an optimization model in LINGO to determine which projects to undertake, and in which
years. The goal is to maximize available funds by the end of year 2024, while making sure that
available funds are always non-negative throughout the planning horizon. How much can the
improve compared to the current proposal? (For simplicity, assume zero discount rate.)

Med Vennelig Hilsen
Jan Olsen Røyland

[[alternative HTML version deleted]]

```