Combinatorial Problem Solving - Optimize Routes

Goal of the project Solve the following highly constrained routing problem within 1 week, for $500 (hiring multiple freelancers to gauge output: - You have a delivery center ( hereinafter referred to “depot” ) and 22 warehouses ( hereinafter referred to “w1”,”w2” etc. ). - Products must be delivered to satisfy supply and demand of each warehouse. - You must determine a delivery plan using the provided types of trucks that minimizes the total cost. - About the data, only around 20% cells of all the tables are filled in the attached powerpoint file. We’ll disclose all information after finishing NDA contract. Deliverables - Route files which are written in a JSON format. We provide a checker (windows/ubuntu 64bit) to validate the routes in regard to the constraints of the problem. (See [login to view URL] and [login to view URL]) * these routes must fulfill all the constraints of the problem to be considered acceptable. - Documents describing the method and/or concept to reproduce the process of obtaining the Route files. - In order to derive the delivery plan with the minimum cost, programs may or may not be used. If used, the source code must also be submitted. Objective function Minimizing total cost of all trips Constraints - The products are delivered by truck only from the “depot” to each warehouse or from each warehouse to the “depot”. They are never delivered between warehouses. - All trip must start from the “depot”, goes around only warehouses and return to the “depot”. - In single trip, the truck can visit the same warehouse up to twice. - It is possible to go to the same warehouse with multiple trips. - In each trip, it is possible to perform loading and unloading of the products at once in the warehouses that go only once. - In each trip, they can only unload for the first time and only load for the second time in the warehouses that go twice. - There are only two kinds of products to be delivered : “Product A” and “Product B”. - The trucks are five types “a”, “b”, “c”, “d” and “e” with different load capacity. The number of trucks is unlimited - The Table 1 shows the maximum loading capacity of “Product B” against number of “Product A” to be loaded for each track type. - Trucks of type “d” and “e” can go around only warehouse “w1”, “w7”, “w14” and “w16” - The Table 2 shows the number of products to be delivered from the “depot” to each warehouse and from each warehouse to the “depot”. - The Table 3 shows the traveling time between warehouses, and between “depot” and each warehouse. - Regardless of the number of loading and unloading in the warehouse, each work takes “1” as time. - All trucks must leave the “depot” after time “0”, and must be returned to the “depot” by time “58”. * Truck leaving at time "0" is allowed. - Unloading in each warehouse must be completed by the time indicated as t1 (“final unloading time”) in the Table 4. - All tracks can go to warehouses for loading after the time indicated as t2 (“start-time for loading”) in the Table 4. - In each warehouse, the final truck visiting said warehouse must leave at t3 (“last trip load wait time”) in the Table 4. - The Table 5 shows the cost corresponding to the operation time for each truck type. * The price is constant for each operation time window(for example: a truck running 1 unit of time has the same cost as a truck running 24 unit of times. * Operation time + x means the preparation time is already included in the time window and it thus the cost for the time spent outside of depot. - The total cost of the delivery plan is the sum of the cost for each trip.