The multiple vehicle routing problem with time windows (VRPTW) is a hard and extensively studied combinatorial optimization problem. This paper considers a dynamic VRPTW with stochastic customers, where the goal is to maximize the number of serviced customers. It presents a multiple scenario approach (MSA) that continuously generates routing plans for scenarios including known and future requests. Decisions during execution use a distinguished plan chosen, at each decision, by a consensus function. The approach was evaluated on vehicle routing problems adapted from the Solomon benchmarks with a degree of dynamism varying between 30% and 80%. They indicate that MSA exhibits dramatic improvements over approaches not exploiting stochastic information, that the use of consensus function improves the quality of the solutions significantly, and that the benefits of MSA increase with the (effective) degree of dynamism.

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Scenario-Based Planning for Partially Dynamic Vehicle Routing with Stochastic Customers

Many companies with consumer direct service models, especially grocery delivery services, have found that home delivery poses an enormous logistical challenge due to the unpredictability of demand coupled with strict delivery windows and low profit margin products. These systems have proven difficult to manage effectively and could benefit from new technology, particularly to manage the interaction between order capture and order delivery. In this article, we define routing and scheduling problems that incorporate important features of this emerging business model and propose algorithms, based on insertion heuristics, for their solution. In the proposed home delivery problem, the company decides which deliveries to accept or reject as well as the time slot for the accepted deliveries so as to maximize expected profits. Computational experiments reveal the importance of an approach that integrates order capture with order delivery and demonstrates the quality and value of the proposed algorithms.

/pdf/decision-support-for-consumer-direct-grocery-initiatives-w5kfzsww7m.pdf

Decision Support for Consumer Direct Grocery Initiatives

Many difficult combinatorial optimization problems have been modeled as static problems. However, in practice, many problems are dynamic and changing, while some decisions have to be made before all the design data are known. For example, in the Dynamic Vehicle Routing Problem (DVRP), new customer orders appear over time, and new routes must be reconfigured while executing the current solution. Montemanni et al. [1] considered a DVRP as an extension to the standard vehicle routing problem (VRP) by decomposing a DVRP as a sequence of static VRPs, and then solving them with an ant colony system (ACS) algorithm.

This paper presents a genetic algorithm (GA) methodology for providing solutions for the DVRP model employed in [1]. The effectiveness of the proposed GA is evaluated using a set of benchmarks found in the literature. Compared with a tabu search approach implemented herein and the aforementioned ACS, the proposed GA methodology performs better in minimizing travel costs.

Dynamic vehicle routing using genetic algorithms

In this paper we propose and evaluate an evolutionary-based hyper-heuristic approach, called EH-DVRP, for solving hard instances of the dynamic vehicle routing problem. A hyper-heuristic is a high-level algorithm, which generates or chooses a set of low-level heuristics in a common framework, to solve the problem at hand. In our collaborative framework, we have included three different types of low-level heuristics: constructive, perturbative, and noise heuristics. Basically, the hyper-heuristic manages and evolves a sophisticated sequence of combinations of these low-level heuristics, which are sequentially applied in order to construct and improve partial solutions, i.e., partial routes. In presenting some design considerations, we have taken into account the allowance of a proper cooperation and communication among low-level heuristics, and as a result, find the most promising sequence to tackle partial states of the (dynamic) problem. Our approach has been evaluated using the Kilby's benchmarks, which comprise a large number of instances with different topologies and degrees of dynamism, and we have compared it with some well-known methods proposed in the literature. The experimental results have shown that, due to the dynamic nature of the hyper-heuristic, our proposed approach is able to adapt to dynamic scenarios more naturally than low-level heuristics. Furthermore, the hyper-heuristic can obtain high-quality solutions when compared with other (meta) heuristic-based methods. Therefore, the findings of this contribution justify the employment of hyper-heuristic techniques in such changing environments, and we believe that further contributions could be successfully proposed in related dynamic problems.

DVRP: a hard dynamic combinatorial optimisation problem tackled by an evolutionary hyper-heuristic

In this paper, we present a solution for a dynamic rescheduling problem involving new orders arriving randomly while static orders have been given in advance in warehouse environments. We propose two variations of an incremental static scheduling scheme: one based on the steepest descent insertion, called OR1, and the other, on multistage rescheduling, called OR2. Both techniques are enhanced by a local search procedure specifically designed for the problem at hand. We also implemented several existing online algorithms to our problem for evaluative purposes. Extensive statistical experiments based on real picking data indicate that the proposed methodologies are competitive with existing online schedulers and show that load-balancing algorithms, such as OR1, yield the best results on the average and that OR2 is effective in reducing the picking time when dynamism is low to moderate.

Online rescheduling of multiple picking agents for warehouse management

The real time dynamic vehicle routing problem (RT-DVRP) is an extension of VRPTW, in which the problem parameters change in real time. We present a solution to RTDVRP: a concurrent, agent-based reactive vehicle routing system (RVRS) and the implementation of the RVRS, which combines a generic, concurrent infrastructure and a powerful incremental local optimization heuristic.

Kar-Loon Ong

Papers

A reactive method for real time dynamic vehicle routing problem