Variable-Depth Search for the Single-Vehicle Pickup and Delivery Problem with Time Windows

Abstract

We consider a single depot and a set of customers with known demands, each of which must be picked up and delivered at specified locations and within given time windows. We seek a route and a schedule for a single vehicle with known capacity, which minimizes the route duration, i.e., the difference between the arrival time and the departure time at the depot. We develop a local search method for this problem based on a variable-depth search, similar to the Lin-Kernighan algorithm for the traveling salesman problem. The method consists of two phases. In the first phase, a feasible route is constructed; in the second phase, it is iteratively improved. In both phases, we use a variable-depth search built up out of seven basic types of arc-exchange procedures. When tested on real-life problems, the method is shown to produce near-optimal solutions in a reasonable amount of computation time. In spite of this, there is the theoretical possibility that the method may end up with a poor or even infeasible solution. As a safeguard against such an emergency, we have developed an alternative algorithm based on simulated annealing. As a rule, it finds high quality solutions in a relatively large computation time.

Static pickup and delivery problems: a classification scheme and survey

“…For an experimental comparison of classical construction heuristics and local search methods for the capacitated SVRPPD, see Kubo and Kasugai (1990). Van der Bruggen et al (1993) have constructed a heuristic procedure for the capacitated SVRPPD with time windows. Their local search method, which is similar to the Lin and Kernighan (1973) algorithm for the TSP, consists of two phases.…”

A new regret insertion heuristic for solving large-scale dial-a-ride problems with time windows

“…Sol (1995, 1998) study a general version of the Pickup and Delivery Problem in which each request can have more than one delivery point. Local search procedures are reported in Van Der Bruggen et al (1993) and Healy and Moll (1995). A tabu search technique has been applied by Nanry and Barnes (2000), whereas Teodorovich and Radivojevic (2000) use a fuzzy logic approach.…”

An Analysis of Special Needs Student Busing

“…In a student transporta tion application, the Vehicle Routing Problem with Pickups and Deliveries and Time Windows (VRPPDTW) examines the case in which students from different schools with different starting times are on the same school bus. There are some heuristic approaches developed to tackle VRPPDTW such as variable-depth algo rithm, which has two steps of finding an initial solution and improving the solution (Bruggen et al 1993). Ioachim et al (1995) developed a clustering approach for the VRPPDTW problem.…”