In today’s modern society, optimizing logistic processes plays a pivotal role in the economy and sustainability. One of the challenges in logistics is the capacitated vehicle routing problem, where trucks are used to deliver cargo to various locations. This problem requires the optimal allocation of trucks to customers to minimize the traveled distance of vehicles. The paper begins by defining the capacited vehicle routing problem and provides a mathematical model for the problem. It then introduces the simulated annealing (SA) algorithm and the empirical-type simulated annealing (ETSA) algorithm as methods for solving this problem. SA employs an exponential distribution for accepting worse solutions, while ETSA utilizes a gamma distribution. Subsequently, the paper extensively describes the implementation of these algorithms and their application to the capacited vehicle routing problem. Different components of the implementation are presented, including the generation of initial solutions and candidates, as well as the SA algorithm itself. In the third part of the paper, the results obtained by applying these algorithms to various datasets (A, B, P) are analyzed. Optimal solutions are compared with solutions obtained using SA and ETSA. The results demonstrate that both algorithms are capable of providing satisfactory solutions, with several instances achieving optimal solutions. The analysis of absolute and relative errors reveals a high level of precision in the algorithms. The most significant conclusion arises from the analysis of the objective functions, showing that the objective function of ETSA converges more quickly to the optimal solution compared to that of SA. ETSA has also proven to be more efficient in finding better solutions more rapidly and has provided better solutions on average. This paper contributes to the understanding of the effectiveness of SA and ETSA algorithms in optimizing the vehicle routing problem with capacity constraints.