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In this paper, we present a tactical model to assist in the task faced by the railroad industry on a day-to-day basis of centrally managing the distribution and repositioning of empty railcars for shipping automobiles. The problem involves a group of eight principal automobile manufacturers (shippers) who have pooled their autorack resources (railcars for shipping automobiles) to improve utilization and reduce the number of empty miles logged. However, this consolidation gives rise to various equity and priority issues related to timeliness in service, particularly in the case of shortages. Accordingly, our model takes into account such practical issues, including uncertainties in transit times, priorities with respect to time and demand locations, multiple objectives related to minimizing different degrees of latenesses in delivery, and blocking considerations. We investigate the performance of two principal models that have been developed for this purpose. The first model, TDSS1 incorporates all the identified features of the problem except for blocking (a consolidation of shipments from any origin to only a limited number of destinations), and results in a network formulation of the problem. The second model, TDSS2 extends TDSS1 by further including blocking considerations, and results in a network flow problem with side constraints and discrete side variables. We then show how the resulting mixed-integer-programming formulation can be enhanced via some partial convex hull constructions. To accommodate the strict run-time limit requirements imposed in practice, 21 principal heuristics are developed and tested to solve this problem. By examining the performance of these procedures with respect to speed of operation and the quality of solutions produced on a test bed of real-world problem instances, we prescribe a solution strategy for implementation in making production runs.