Development of an Optimal Solution for a Location-Routing-Problem Based on 3rd Party Providers

The transportation is the movement of people, animals and goods from one place to another. Nowadays it includes several modes: air, rail, road, water and other modes. In mathematically, the transportation theory is to optimize transportation and allocation of results. In reality, the problem is more complicated: firstly, the distance between 2 places is not always the straight-line distance, that means the transport route will be divided into several parts; secondly the cost of each parts will not be always the same. For example, the high-way transportation cost is not equal to the city or state road cost, if a road transport plan includes both of high-way and normal road, then cost of each parts will be completely different. This means the total cost need to be calculate by adding the cost of all the parts, and the cost of each parts should be figured out first, it will be very tedious if the route is divided into a lot of parts. This paper will give a solution to solve this problem; it includes software using computer navigation technology, and shows how to get the optimize transportation mode by this software. Brief Introduction of Technology Background GPS Technology The main concept of GPS is to use the transmitted data by the satellite to figure out the location of the GPS receiver, the GPS receiver can measure the distance from a satellite to itself, and with this distance, the position of the receiver can be determined. In 2-dimention space, we need at least 3 satellites to determine the position of receiver. Figure 1 shows this situation[2]. Figure 1. Working principle of GPS With 3 equation[4], the location of receiver can be figured out: