This paper presents an optimal path planning aiming at minimization of energy consumption and decrement of operation time of an automated guided vehicle (AGV) under dynamic operation conditions in a graph containing random slopes and distances. To convey one load to a desired- destination by AGVs is considered common practice in a logistic center. Loads of varying mass are transferred to desired-destinations in a graph composed of vertices and edges. In the graph, slopes and distances required for calculation of weight of edges are randomly given between a pair of vertices. Considering tractive forces of the AGV, a tractive force model is developed and this model is applied to path planning method. Mass variation of the AGV that occurs when it places the loads to each vertex is used for calculation of the energy consumption. According to the mass variation of an AGV and road conditions, the weights between vertices are determined. Based on the graph with the weights, the Dijkstra algorithm is applied to get an optimal path for the AGV. Proposed approach demonstrates minimization of AGV’s energy consumption and improvement of operation time with the optimal path.