## Challenge Overview

**checkpoint deadline is 2019/02/20 19:00 (EST)**, and keep in mind we do NOT need a working code!

- [Mathematical Formulae] Create accurate and intuitive mathematical formulae to determine when and how to choose relay warehouse(s), in order to minimize the total cost for given 5 datasets (#1, #2, #3, #4, #5). You are asked to submit a report about how you have analyzed data and derived the rules and conclusions. As mentioned in the scoring criteria, the small number of mathematical formulae, the better your solution will be scored.
- [Truck Route Pattern] Provide a truck route pattern for the given 7300 days implementing the above 1. Mathematical Formulae model. The route pattern format is explained below.

1. Depot/Warehouse Name

A depot is a place where all the products are created.

2. Demand

Consumption of products per day at each warehouse

Note that the products are consumed gradually over time and not at the end of each day, meaning for example in 12hours the products will decrease half the amount of its daily demand

3. Possible Truck Size

A maximum size of truck that each warehouse can use to load/unload products

4. Maximum Warehouse Capacity

Maximum warehouse capacity of products each warehouse can hold

5. Travel Time between the depot and/or each warehouses [days]

The minimum travel distance between warehouses in days

Please note that a truck can take more than the days defined to travel between warehouses (ex. It can take rest at warehouses) but not less.

Relay warehouse(s) should be chosen from the existing list of warehouses and not newly created. Thus, the demand and the maximum capacity stays the same.

- This means that the following formula needs to be accomplished at any time.
- warehouse stock > 0
- warehouse stock ≤ maximum warehouse capacity

- Total Cost = <Equipment Cost> + <Normalized Operating Cost>
- Equipment Cost = <Truck Purchase Cost> + <Warehouse Building Cost>
- Truck Purchase Cost = 8350.6 * ln(C) - 14542.5
- C: Maximum load capacity of truck (20 ~ 320, 20 increments)

- Warehouse building cost = 29.725 * T
- T: Maximum warehouse capacity

- Truck Purchase Cost = 8350.6 * ln(C) - 14542.5
- Normalized Operating Cost = <Truck Operating Cost> * <Total Demand consumed in 7300 days> / (<Total Demand consumed in 7300 days > + <total stock of products at the end> - <total stock of products at the beginning>)
- Total stock of products: All products aggregated from every trucks and warehouses.

- Truck Operating Cost = (1.67012 * ln(C) - 2.9885) * <truck operation days> + <number of truck stops at depot or warehouse> * 2
- C: Maximum load capacity of a truck (20 ~ 320, 20 increments)
- “truck operation days” is the actual days took that truck was moving. Loading/Unloading and parking time are not included.
- note that trucks can spend more than the days between warehouses mentioned in the datasets. Meaning trucks can be parked at the warehouses or depots.
- If there are warehouse#1 and warehouse#2 that needs 3 days of travel time, the truck could park at #1 for 2 days or travel slowly to make travel time as 5 days. In both cases, the “total operation days” should be calculated as 3 days.

- “a number of truck stops at depot or warehouse” will count all the “arrival” action -- stops the trucks -- made to depot or warehouse. Ex. if truck moved from 1.depot (departure) then to 2.warehouse#1 (arrival), 3. warehouse#3 (arrival), 4.warehouse#6 (arrival), finally to 5.depot (arrival) then, it will be 4.

Your truck route pattern might be made up of the same repeating cycles to become 7300 days.

When we say “repeating cycle”, this means that truck will start at "departure" action at some

depot/warehouse and then returns to the same depot/warehouse and performs "departure"

action again.

During which the route actions in between is the same.

2. Warehouse stock

Warehouse stock cannot be less than zero at no time.

Note that trucks need 6 hours to load and unload.

3. Multiple trucks at one location

Multiple trucks can be at the same warehouse at the same time.