This research discusses determination of the best route for the goods distribution from one depot to customers in various locations using the Capacitated Vehicle Routing Problem with Time of Windows (CVRPTW) model with a goal programming approach. The goal function of this model are minimize costs, minimize distribution time, maximize vehicle capacity and maximize the number of customers served. We use case study in CV. Oke Jaya companies which has 25 customers and one freight vehicle with 2000 kg capacities to serve the customers in the Serang, Pandeglang, Rangkasbitung and Cikande. For simulation we use software LINGO. Based on this CVRPTW model with a goal programming approach, there are four routes to distribute goods on the CV. Oke Jaya, which considers the customer’s operating hours, with total cost is Rp 233.000,00, the total distribution time is 17 hours 57 minutes and the total capacity of goods distributed is 6150 kg.

Let  be a simple, connected, and undirected graph. The graph  can be represented as a matrix such as antiadjacency matrix. An antiadjacency matrix for an undirected graph with order  is a matrix that has an order  and symmetric so that the antiadjacency matrix has a determinant and characteristic polynomial. In this paper, we discuss the properties of antiadjacency matrix of a graph join, such as its determinant and characteristic polynomial. A graph join  is obtained of a graph join operation obtained from joining two disjoint graphs  and .