## Challenge Overview

**Prize**

1st place - $20002nd place - $1000

3rd place - $500

**Challenge Overview**

In this challenge, we are looking for reports discussing when using “relay warehouse” will lead to a better solution in the vehicle routing problem (VRP) to minimize the total operating cost of trucks for 10 days. You are asked to conduct an analysis based on a small dataset and derive your rules and conclusions.
**Background**

This challenge is variation derived from the previous challenge we ran. The VRP problem in the previous challenge is similar to what you are going to explore in this challenge. You might want to have a look at the previous challenge to understand what the VRP is.

Please note that the goal of this challenge is no longer about analyzing public Solvers. It is your choice to develop your own solver or tailor public Solver for your report.**Task Details**

We have 5 datasets. Each dataset expresses a number of warehouses and the distance between them. The goal of this task is to create accurate, intuitive mathematical formulae to determine when and how to choose relay warehouse(s), in order to minimize the total operation cost minimum in these 5 datasets. You are asked to submit a report about how you have analyzed data and derived the rules and conclusions.

Please note that there could be cases that we do not need any relay warehouse. Also, in your analysis and conclusion, it is NOT necessary to think of a case beyond the given 5 datasets -- you can “overfit” your conclusions just for these 5 datasets.

The data can be found in these spreadsheets (#1, #2, #3, #4, #5). There are

- The depot has an infinite amount of the product;
- The “demand” column describes the daily consumption at each warehouse;
- Each warehouse has a capacity of 1,000 units of the product. Warehouses cannot store more than its capacity;
- Each warehouse has a specific size of trucks (small or medium) that it can use. “Use” means that the truck can initially depart from here and finally return here to load and unload;
- The distance matrix describes the number of days that are required for the truck to travel between each warehouse/depot. Truck needs to spend 6 hours while loading/unloading product at depot/warehouse.

**Relay Warehouse**is a special type of warehouse where it can serve as temporary depots for other warehouses. You are allowed to use zero or more relay warehouses.

In VRP, we should schedule trucks to deliver the product to warehouses and make sure every warehouse has enough product to consume every day. There are no product at all warehouses initially. The amount of product at warehouse increases only after the truck unloaded some product there. Of course, in the first a few days, there might be some warehouses lack of the product, but the schedule should meet a long-term needs.

There are 2 small-size trucks and 1 medium-size truck. Total of 3 trucks for all cases.

- A small-size truck can carry up to 160 units of products
- A medium-size truck can carry up to 320 units of products

**Operating Cost**consists the following 3 parts:

- For small truck
- Cost = 5.4876 * <truck operation days> + (<number of truck stops at depot or warehouse> * 2)

- For medium truck
- Cost = 6.6452 * <truck operation days> + (<number of truck stops at depot or warehouse> * 2)