A generalized assignment heuristic for vehicle routing

Abstract

mtts 02163We consider a common variant of the vehicle routing problem in which a vehicle fleet delivers products stored at a central depot to satisfy customer orders. Each vehicle has a fixed capacity, and each order uses a fixed portion of vehicle capacity. The routing decision involves determining which of the demands will be satisfied by each vehicle and what route each vehicle will follow in servicing its assigned demand in order to minimize total delivery cost. We present a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost. This heuristic has many attractive features. It has outperformed the best existing heuristics on a sample of standard test problems. It will always find a feasible solution if one exists, something no other existing heuristic can guarantee. It can be easily adapted to accommodate many additional problem complexities. By parametrically varying the number of vehicles in the fleet, our method can be used t o optimally solve the problem of finding the minimum size fleet that can feasibly service the specified demand.

Projection results for vehicle routing

“…This formulation, which we call the three-index vehicle flow formulation, is based on those of Fisher and Jaikumar [15] and Fischetti et al [14]. Therefore, any valid inequality for the multiple knapsack polytope [13] yields valid inequalities for the three-index formulation that only involve the y-variables.…”

“…We call such inequalities multiple knapsack inequalities. The inequalities (15) and (16) (2)- (4), subtour elimination inequalities (8), and the trivial bounds 0 ≤ x ij ≤ 1.…”

Industrial aspects and literature survey: Fleet composition and routing

“…First, the heuristic uses a lower bound procedure in branch-and-bound (BB) to create the optimal fleet mix, and then a VRP is solved using that vehicle mix as the available fleet. The assignment of customers to vehicles is determined by solving the generalized assignment problem (GAP) due to the method proposed by Fisher and Jaikumar [62]. Gheysens et al [70] show that this heuristic usually performs better than the savings and giant tour heuristics, but there is no guarantee to find a feasible solution and the running times are much larger for the lower bound heuristic.…”

On the impact of real-time information on field service scheduling

“…After the clustering phase, the routing phase constructs routes by solving the TSP in each cluster [10]. Our heuristic follows a new approach: It uses the well-known linear version of the assignment problem 2 to directly construct routes instead of the two-phase approach, which is not applicable to the FSSP without extensive modifications (due to multiple depots, priorities, and skills).…”