Evaluation Of Algorithm Performance For Simulated Square And Non-Square Logistic Assignment Problems

The optimal allocation of transportation tasks to a fleet of vehicles, especially for large-scale systems of more than 20 Autonomous Mobile Robots (AMRs), remains a major challenge in logistics. Optimal in this context refers to two criteria: how close a result is to the best achievable objective value and the shortest possible computational time. Operations research has provided different methods that can be applied to solve this assignment problem. Our literature review has revealed six commonly applied methods to solve this problem. In this paper, we compared three optimal methods (Integer Linear Programming, Hungarian Method and the Jonker Volgenant Castanon algorithm) to three three heuristic methods (Greedy Search algorithm, Vogel’s Approximation Method and Vogel’s Approximation Method for non-quadratic Matrices). The latter group generally yield results faster, but were not developed to provide optimal results in terms of the optimal objective value. Every method was applied to 20.000 randomised samples of matrices, which differed in scale and configuration, in simulation experiments in order to determine the results’ proximity to the optimal solution as well as their computational time. The simulation results demonstrate that all methods vary in their time needed to solve the assignment problem scenarios as well as in the respective quality of the solution. Based on these results yielded by computing quadratic and non-quadratic matrices of different scales, we have concluded that the Jonker Volgenant Castanon algorithm is deemed to be the best method for solving quadratic and non-quadratic assignment problems with optimal precision. However, if performance in terms of computational time is prioritised for large non-quadratic matrices (50×300 and larger), the Vogel’s Approximation Method for non-quadratic Matrices generates faster approximated solutions.