Context: You are a courier tasked with delivering a set of Kidentical parcels to K different customers, with each customer expecting only one parcel. Your goal is to find the most efficient route that minimizes travelled distance while ensuring every customer receives their parcel.

Problem Statement:

Generate Random Customer Locations: Firstly, generate a set of K random geographical locations representing the customers' addresses. These locations can be simulated as points on a grid or using real-world coordinates in Doha.

Formulate the Problem: Model this problem as LP, considering each customers location as a node in a graph, and the distance between any two customers as the edge connecting those nodes. The challenge is to find the shortest possible route that visits each node exactly once and returns to the starting point.

Constraints:

Each customer receives exactly one parcel.

The route must start and end at the courier's depot (node zero)

Tasks for Students:

1. Data Generation: Generate K+1 random locations. This could be done using random number generators for grid points or geographical coordinates, K nodes will represent the customers and one node represents the courier depot.

2. Problem Formulation: Express the problem using mathematical models. Define variables, objective functions (minimizing distance or time), and constraints.

3. Results Generation: Solve the problem for K=6,12, and 20customers. Record the routes, total travel distance, and computational time for each scenario.

4. Analysis: Compare the results for different values of K. Discuss the scalability of the chosen algorithm and the trade-offs between accuracy and computational efficiency.

Expected Outcome: Students should be able to formulate the problem, and analyze the results. They should gain insights into how problem complexity increases with more customers and the effectiveness of different algorithms in finding efficient routes.