Operation research using GAMS

Wormhole International Space Exploration (WISE) is an international organization, formed by all the countries of the earth. The main task of WISE organization is to identify potential planets where

humans can settle and extend the civilization. The organization was established after active

participation of all the countries. All the countries of the world realized that the current rate of

population growth may be unsustainable by the available space and resources on earth. Thus, WISE

was formed to identify potential planets that can provide basic needs for humans. Human beings can

be deployed in such planets with constant support until they establish sustainable system on the

planets. Once such system is successfully established, then the planets can become autonomous. In

fact, the indigenous resources of the 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 space

exploration project. Specifically, your team is formed by the WISE organization to design a successful

plan for the implementation of Phase-1 space exploration activities. The main objectives in Phase-1

are described as follows:

1. Design the optimal tour for the spaceships.

2. Optimize the amount of resources to be packed in the spaceships.

3. 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: ISE01610421

Start Date: Dec 11, 2016

Due Date: Jan 17, 2017

Course No: ISE-421-03

Instructor: Syed Mujahid Contact: [email protected]

Phase-1

By the year 3000 AD, human population level on earth became unsustainable due to the limited

amount of resources available on planet earth. Thus, all the world governments agreed to form

Wormhole International Space Exploration (WISE) organization. The goal of WISE organization is

to identify possible planets where humans can live with basic support from the planet’s environment.

The scientists and researchers of WISE have discovered around 400 planets that can support human

race. The planets provide earth like atmosphere (air, land and water). However, there are no living

creatures and no vegetation on the planet. Due to humongous population growth, and limited space

and resources on earth, all the world governments agreed to smoothly distribute human beings across

the planets.

With enormous efforts from international governmental collaborations and hypersonic spaceships,

humans have been safely distributed across the planets. However, now the main issues is their

sustenance. Apparently, it will take at least another 50 years for the humans (deployed on the other

planets) to setup a livable sustainable system on the planet. The system includes: agriculture, medicine,

industrial, academic, and defense sectors. In addition to that, mining and exploring the planet for its

indigenous resources will be considered after Phase-1 of 50 years. Thus, the success of the space

mission relies heavily on the success of Phase-1.

The primary challenge of Phase-1 is to continuously supply the 400 planets with enough resources

from earth. It is estimated that at least for the next 20 years, the resources must be shipped and

replenished to the planets on a regular basis. The primary challenge can be divided into the following

objectives:

Objective-1: Design the optimal tour for the spaceships

Due to the resource limitations on earth, currently there are only 6 hypersonic spaceships on earth

that can be used in parallel for delivering the resources. The aim is to find a closed tours for the

spaceships (starting and ending on earth) such that the maximum distance travelled by each spaceship

is minimized (the planets should be visited only once by any ship). In addition to that, using all the 6

ships simultaneously may not be wise, i.e., few ships can be kept for the backup. Thus, the first

objective is to find the optimal length of the tour 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 WISE will decide on the number of ships and tours to be used for delivering the resources. The

coordinates of all the planets are provided in excel sheet titled Coordinates under the excel workbook

DATA01610421.xls.

Objective-2: Optimize the amount of resources to be packed in the spaceships

Once a ship is selected for dispatching the necessary resources to a group of planets, it should be

packed efficiently with the resources. Each resource has a level of significance per unit (on a scale of

1-100) for the survival of human race. The aim is to maximize the total significance level of resources

that are packed on the ship. Each planet has a minimum requirement per trip of the ship for each

resource that must be met for the survival of the people. The capacity of the ship (C), the total number

of resources (R), minimum value per planet per trip (Lr), the volume (Vr) per unit, and the level of

significance (Sr) for each resource are provided in the excel sheet titled Dispatch, under the excel

workbook DATA01610421.xls.

Objective-3: Identify the hub planets and the location of satellites/relay stations

This objective can be divided into the following sub-objectives:

(3a) In order to establish continuous communication with the planets, WISE would like to install

satellites and relay stations. The aim is to build communication among all the planets including earth.

Thus, a relay station on each planet must be built. In addition to that, some planets will be selected to

maintain a satellite. That is, a satellite will be associated with a planet (say hub planet). This satellite

can receive (or send) signals from (or to) relay station of the other planets, if the distance between the

relay station and the hub planet is less than 50 × 1013 𝐾𝑚. The objective is to find the set of hub planets such that the total maintenance cost is minimized. The cost of maintenance of the satellite at

each planet (CMp) is given in the excel sheet titled Satellites-1, under the workbook

DATA01610421.xls.

(3b) In addition to that, finding the locations of the satellite and relay stations is very crucial. In this

sub-objective, the focus in on identifying the location of the satellites. The idea is to keep the satellite

near the hub planet, but also to minimize the total distance from the other planets. Following figure

illustrates the scenario. The objective is to find the optimal location of the satellite for the following

configuration of 1 hub planet and 10 neighbor planets. The data related for the following configuration

is given in the excel sheet titled Satellites-2, under the workbook DATA01610421.xls.

(3c) Finally, the location of the relay stations on the planet can be obtained from the location of the

associated satellite. The focus of this sub-objective is to identify the location of the relay station based

on the location of the satellite. For example, based on the location of the satellite the nearest point on

the planet can be taken as the spot for building the relay stations. For the following configuration of

1 hub planet and 10 neighbor planets, identify the location of the relay station on all the planets in the

configuration. Ignore the rotations of the planets for this sub-objective.

Hub

Planet

Satellite can be located

anywhere inside the

green region.

4 × 105𝐾𝑚

satellite

Planet-1

Planet-2

Planet-10