{'fraction_non_alphanumeric': 0.018077239112571898, 'fraction_numerical': 0.0, 'mean_word_length': 5.619565217391305, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Impacts of Efficient Transportation Capacity Utilization via Multi-Product Consolidation on Transportation Network Usage and Congestion

Multi-item inventory problems that explicitly account for realistic transportation cost structures and constraints, including a per-truck capacity and per-truck cost are studied. The authors analyze shipment consolidation and coordination policies under these conditions. A set partitioning problem is formulated to determine the best consolidation policy. The authors first use a branch-and-price method to solve the resulting set partitioning problem. Since the pricing problem for the general case is NP-hard, two heuristic methods are proposed to generate new columns. The authors also show that the pricing problem can be solved in polynomial time for a practical special case. Furthermore, they develop two heuristic methods as alternatives to the branch-and-price method. Numerical studies are conducted to demonstrate the efficiency of the heuristic column generators, heuristic methods to the set partitioning problem, and how the modeling approach helps mitigate truck density on transportation networks while resulting in higher truck utilization and lower total costs.