Capacitated Vehicle Routing Problem Case Study

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1.1.1 The constituent elements of capacitated vehicle routing problem
All kinds of the vehicle routing problem contain a series of essential elements, which primarily are depot, customers, goods, vehicles, routes and the constraints and objective functions proposed to resolve the problem.
1. Depot. Depot is usually the beginning point and terminal of every delivery route. In a specific vehicle routing problem, the number of depot can be one or more than one. The location of the depot can be fixed or flexible. But in capacitated vehicle routing problem, there is only one depot and the location is always fixed.
2. Customer. The customer is the core element in vehicle routing problem. Customer is a common name, in real world, it can also be distribution
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In some vehicle routing problems, the maximum distance of each vehicle cannot exceed a specific number.
(4) Customer priority constraint. The order of delivery should be accomplished according to the customers’ priority.
7. Objective function. According to different vehicle routing problem, the optimizing goal can be more than one. The typical objective functions include shortest delivery distance, minimum delivery cost, minimum number of vehicle involved, etc. In capacitated vehicle routing problem, the optimizing cost is usually minimum delivery cost.
1.2 The formulas of capacitated vehicle routing problem
A central depot, which has k vehicles each with a loading capacity of D. The goods are delivered from the depot to different customers by the k vehicles. The routes are from the depot, then to customers, ultimately to the depot. The goods demand of customer i is assumed as d, which is less than D. The distance between customer i and j is known. The objective is to find the minimum delivery cost.
3.2.1 Symbol definition
In the capacitated vehicle routing problem, the symbols can be defined as follow:
: The delivery cost between customer i to customer j. A cost matrix can be constructed using all the delivery cost between different customer

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