Discrete Structures (ITS66204)Matlab

Java Python Discrete Structures (ITS66204)

Group Assignment (Weightage: 30%)

Case Study Title:

Due Date: Sunday, 01 December 2024 (Week 11), 11:59 PM

Group Assignment (30%)

MLO2: Demonstrate findings and insights derived from applications of discrete structure concepts in real-world and computational science scenarios.

CASE STUDY 1: OPTIMIZING A SMART CITY TRANSPORTATION AND LOGISTICS SYSTEM

Scenario:

You are part of a team hired by a smart city initiative to optimize the city's transportation and logistics system. The goal is to improve traffic flow, reduce congestion, optimize delivery routes, and ensure efficient allocation of resources such as public transport, delivery trucks, and road space. The project will also consider the impact of uncertainty (e.g., traffic delays, accidents) in the system and develop a model to minimize disruptions.

You are required to use concepts from Set Theory, Counting Principles, Graph Theory, and Probability to develop solutions that will enhance the efficiency and reliability of the city's transportation and logistics network.

Data Sources:

For this case study, students will access real-world data from the following platforms:

Kaggle: For datasets related to traffic incidents, transportation schedules, and other logistical data. OpenStreetMap: For road network data, including distances, locations, and travel times between different parts of the city.

Government Data Portals: For publicly available datasets on traffic volumes, vehicle types, public transport schedules, and traffic conditions.

CASE STUDY 1 TASKS

Task 1: Traffic Management Using Set Theory

The smart city initiative collects traffic data from multiple sensors across the city. These data points are organized based on vehicle types, time of day, road sections, and traffic conditions.

Data Source:

Traffic data from Kaggle or government data portals, representing vehicle types and congestion levels for various roads at different times of the day.

Questions:

1. Set Operations:

a)   Represent the data as sets, where each set contains data points related to different vehicle types (e.g., cars, trucks, buses), time slots, and traffic conditions (e.g., peak hours, nonpeak hours).

b)   Perform. set operations such as union and intersection to analyze traffic patterns.

2. Cartesian Product and Relations:

a)   Define a Cartesian product of road sections and time slots. Use this to establish a relation between different road sections and the severity of traffic congestion.

Task 2: Optimizing Public Transport Scheduling (Counting Principles)

The city operates a public transport network with multiple bus routes, and the challenge is to develop an optimal schedule that minimizes wait times while ensuring buses are evenly distributed.

Data Source:

Public transport schedules from Kaggle or government data portals for bus and train services.

Questions:

1. Permutations and Combinations:

a)   Calculate the number of different ways buses can be assigned to&nb