Efficient Insertion Heuristics for Vehicle Routing and Scheduling Problems

Abstract

Insertion heuristics have proven to be popular methods for solving a variety of vehicle routing and scheduling problems. In this paper, we focus on the impact of incorporating complicating constraints on the efficiency of insertion heuristics. The basic insertion heuristic for the standard vehicle routing problem has a time complexity of O(n3). However, straightforward implementations of handling complicating constraints lead to an undesirable time complexity of O(n4). We demonstrate that with careful implementation it is possible, in most cases, to maintain the O(n3) complexity or, in a few cases, increase the time complexity to O(n3 log n). The complicating constraints we consider in this paper are time windows, shift time limits, variable delivery quantities, fixed and variable delivery times, and multiple routes per vehicle. Little attention has been given to some of these complexities (with time windows being the notable exception), which are common in practice and have a significant impact on the feasibility of a schedule as well as the efficiency of insertion heuristics.

A General Vehicle Routing Problem

“…Efficient methods for handling complex side constraints in insertion methods are presented in Campbell and Savelsbergh (2004). Comprehensive surveys on construction methods, neighbourhood search methods, and metaheuristics for the VRPTW are given by Bräysy and Gendreau (2005a), and Bräysy and Gendreau (2005b).…”

Service capacity design problems for mobility allowance shuttle transit systems

“…Furthermore, as outlined in Campbell and Savelsbergh (2004), this type of a simple greedy heuristic is commonly used in practice due their ability to perform well in a dynamic setting whereas the preplanned globally optimal solutions tend to perform poorly, and the greedy heuristics are computationally efficient which is especially important in a dynamic environment.…”

“…Although the meta-heuristics generate routes that are on average less costly than the insertion type heuristics, the most common algorithms used in practice are the insertion type heuristics due to their computational efficiency and ease of understanding (Hunsaker and Savelsbergh, 2002;Campbell and Savelsbergh 2004). Furthermore these types of heuristics tend to perform well in a dynamic environment.…”

A Decomposition Approach for the Inventory-Routing Problem

“…Insertion heuristics have proven their value in many routing and scheduling contexts; insertion heuristics are fast, produce decent solutions, are easy to implement, and can be extended easily to handle various practical complexities. For an elaborate treatment of insertion heuristics for routing and scheduling problems, including a discussion on how to handle variable demands, see Campbell and Savelsbergh (2004b). To keep the complexity of the algorithm a low-order polynomial, it is important to maintain values for the earliest and latest start times for each inserted delivery, as well as the minimum and maximum delivery quantities.…”