Vehicle Routing Problems in Hospital Transportation. I Models and Solution Approaches

4.5. Summary p In this chapter we have developed several approaches to solve VRP-PDTWs in hospital transportation. These include exact optimization algorithms (MILP and column enumeration) and heuristic methods. The exact methods are designed to solve online problems of small or modest size. While the MILP approach (Section 4.3.1) often requires a long time to prove optimality, the column enumeration approach (CEA, Section 4.3.3) allows to compute optimal solutions very fast. This approach is based on decomposing the problem into a master problem (a set partitioning problem controlling the assignment of orders to vehicles) and a set of subproblems (intra-tour problem, routing and scheduling). To solve the routing and scheduling problem exactly we have developed a branch-and-bound method which prunes nodes if they are value-dominated by previous found solutions or if they are infeasible w.r.t. the capacity or temporal constraints. This approach works fast for up to 10 orders per vehicle. This branch-and-bound method is suitable to solve any kind of sequencing-scheduling problem involving cumulative objective functions and constraints, which can be evaluated sequentially.

To solve intra-tour problems containing more than 10 orders we have developed various construction and improvement heuristics (Section 4.4). Especially, to treat larger offline problems with several hundred orders we developed a heuristics to reassign orders to other vehicles, and improve existing tours by simulated annealing (Section 4.4.3).