Dantzig–Wolfe decomposition approach to the vehicle assignment problem with demand uncertainty in a hybrid hub-and-spoke network

In this article, we investigate the vehicle assignment problem with demand uncertainty in a hybrid hub-and-spoke network with a single hub. The problem is deciding both the transportation routes and the number and types of vehicles to be deployed to minimize the sum of costs to transport all quantities in a hybrid hub-and-spoke network which allows direct transportation between spokes. Daily changes in quantities are reflected with a finite number of scenarios. Regularly scheduled vehicles and temporarily scheduled vehicles are considered to meet the demand variation. We propose a Dantzig–Wolfe decomposition approach which yields a strong LP relaxation bound by introducing a set of feasible direct route patterns. We develop an algorithm which incorporates a column generation procedure at the root node and repeats iteratively a variable fixing and column generation procedure at the non-root nodes until an integral solution is found. Finally, we present computational results using the well-known CAB data sets and real-life data from the Korea Post. The results show that our algorithm can find near optimal solutions very efficiently.