Flow Merging and Hub Route Optimization in Collaborative Transportation

Table 1

Problem parameters of AP data package and computational result of Branch & Cut algorithm.

Problem parameters				Branch & Cut algorithm
Problem	𝑎	𝑛	Number of transportation tasks	Optimal solution	Time (s)
AP10-6	0.6	10	90	251524	2.55
AP15-6	0.6	15	210	337655	62.59
AP20-6	0.6	20	380	1214739	255.85
AP25-6	0.6	25	600	—	—
AP30-6	0.6	30	870	—	—
AP10-7	0.7	10	90	281348	2.43
AP15-7	0.7	15	210	379664	24.82
AP20-7	0.7	20	380	1384638	86.78
AP25-7	0.7	25	600	—	—
AP30-7	0.7	30	870	—	—
AP10-8	0.8	10	90	311134	1.05
AP15-8	0.8	15	210	421537	5.27
AP20-8	0.8	20	380	1553251	21.62
AP25-8	0.8	25	600	—	—
AP30-8	0.8	30	870	—	—