Exploiting Symmetries in Logistics Distribution Planning

Logistics distribution and movements planning involves developing an efficient plan to move all of the required supplies, equipment and personnel to desired locations in a timely manner. It is an inherently difficult problem to solve and given the complexity of the problem, scenarios of a realistic size can take a significant amount of time to compute. A greedy distribution algorithm has been created for the task of developing transport schedules to satisfy the movement requirements. At each phase of the simulation the algorithm assigns the most capable transport to deliver the highest priority resources. Although it is observed that the distribution algorithm performs faster than exact algorithms based on integer programming or brute force, even greedy based approaches can have performance issues as the scenario size increases. In this paper, a technique is examined which exploits redundancies garnered due to symmetries in the distribution model to improve performance of the distribution algorithm. A key redundancy in the model occurs when there are multiple similar transports at the same location. By performing one calculation for all transports of a similar type at the same location, it is suspected that computational savings could be made. Given that many of the distribution scenarios are complex, many of the transports are not always at the exact location as each other. One way to increase the effectiveness of the symmetry exploitation is to perform only one calculation for all transports of a similar type within a certain range. However, there is a side effect to increasing the range value, and that is it introduces an error in the planning calculation. Part of the analysis to be explored through simulation is what an effective range is, given that the larger the range the greater the computational savings but also the greater the error is introduced into the distribution plan. Simulations were run testing the performance of the distribution algorithm with and without utilising the symmetries with varying range values to minimize the distribution model. It is shown empirically that by exploiting the symmetries in the distribution model, for the scenarios tested computation time could be reduced on average by approximately 24-45%, while the efficiency of the distribution plan is only reduced by approximately 0.3-18% due to introduced error.