A new linear programming-based algorithm has been demonstrated to find the best way for arc routing. In most arc routing problems, the main goal is to minimize the total cost on the lane. To find the minimum cost giving lane, the existing algorithms find the smallest possible sum of weights by ticking the shortest paths [7-12]. The proposed computer-based algorithm is based on focusing the minimized total cost with some constraint criteria of fixed values. The routes are marked with a series of variables that may differ according to the lane choice and more accurately estimates the exact total cost considering the remaining weight. Finally, a stochastic model for a private company vehicle transport has been discussed with some possible solution expectations.