Design the optimal tour for the spacecrafts (Mathmatical Model)

Boxes & Lights (B&L) is a private corporation, which recently joined the list of fortune 500. To
become largest and most valuable corporation in the coming years, B&L studied potential areas for
future investment. The research and development team identified many possible areas that will be
profitable in the future. Among these areas, B&L corp. selected to study possible avenues for handling
high human population in the future. One of the directions of study is to identify potential planets
that can provide basic needs for humans in the future. Human beings can be deployed in such foreign
planets with constant support until they establish sustainable ecosystem on the foreign planets. Once
such system is successfully established, then the foreign planets can become autonomous. In fact, the
indigenous resources of the foreign planet can enhance the current potential of the human beings.
The organization is looking for Industrial Engineers (IEs) to help in decision-making of this project,
called Wall-Z. The aim of Wall-Z project is to send spacecrafts with robots to explore space. The main
objectives in Wall-Z are described as follows:
1. Design the optimal tour for the spacecrafts.
2. Identify the hub planets and the location of satellites/relay stations.
Relevant data and details are provided in the following pages of this document. Since the organization
is unaware of the methodologies that you will be using to design the plan, you are allowed to make
reasonable assumptions for the missing data. You are expected to use the standards wherever
applicable. Your goal is to provide the organization with the best possible solution.
Project No: ISE0201321
Start Date: Nov 20, 2020
Due Date: Dec 20, 2020
Course No: ISE-321
Instructor: Syed Mujahid
Human population on earth is rising at alarming rates. Consequently, the resources available on earth
are at the verge of being drained. It is predicted that the available resources on earth soon will not be
able to meet the basic human needs. The Boxes & Lights (B&L) private corporation is planning to
invest on identifying possible other planets that are capable for human survival. All the activities under
this direction are termed as Wall-Z project. The goal of Wall-Z is to visit the planets, study the
ecosystem and environment, and estimate sustainability score for each project. The shortlisted planets
based on sustainability score and travel years will be considered for possible future settlements.
Wall-Z project might take hundreds of years. Thus, B&L plans to start this process soon, so that the
earth will be ready for expansion, when required, in the future. The researchers at B&L have
discovered around N planets that can be reached in reasonable time from earth. Also, there is a high
probability to establish continuous communication between earth and these planets. However, the
planets may not provide earth like atmosphere (air, land and water). In such cases, the easiness of
artificially generating earth like atmosphere will be the key part of sustainability score. On the other
hand, there could be indigenous species on the planet. In such cases, the co-existence will be the key
part of sustainability score.
The bottleneck of Wall-Z project is visiting the planets and returning to earth in shortest possible
time. Furthermore, the duration of space travel and the analysis to be done on planets may not be
viable with the involvement of human beings on the spacecraft. Thus, it is decided to send robots into
the space craft.
The primary challenge of Wall-Z is to visit the N planets with enough resources from earth. The
primary challenge can be divided into the following objectives:
Objective-1: Design the optimal tour for the spacecrafts
The aim of this objective is to find a closed tours for the spacecrafts (starting and ending on earth)
such that the maximum distance travelled by each spacecraft is minimized (the planets should be
visited only once by any ship). Thus, the first objective is to find the length of the tours for the above
criterion when 𝑛 ships are used, where 𝑛 = 1, … ,6. Based on the optimal length of the tours for
various values of 𝑛, the decision makers at B&L will decide on the number of ships and tours to be
used in the implementation phase of the project. The coordinates of all the planets are provided in
excel sheet titled Coordinates under the excel workbook DATA-xx.xlsx (where “xx” stands for
your group number).


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