van T Tom Woensel

Multimodal freight transportation planning: A literature review

Multimodal transportation offers an advanced platform for more efficient, reliable, flexible, and sustainable freight transportation. Planning such a complicated system provides interesting areas in Operations Research. This paper presents a structured overview of the multimodal transportation literature from 2005 onward. We focus on the traditional strategic, tactical, and operational levels of planning, where we present the relevant models and their developed solution techniques. We conclude our review paper with an outlook to future research directions.

Vehicle routing with dynamic travel times: A queueing approach

Transportation is an important component of supply chain competitiveness since it plays a major role in the inbound, inter-facility, and outbound logistics. In this context, assigning and scheduling vehicle routes is a crucial management problem. In this paper, a vehicle routing problem with dynamic travel times due to potential traffic congestion is considered. The approach developed introduces mainly the traffic congestion component based on queueing theory. This is an innovative modeling scheme to capture travel times. The queueing approach is compared with other approaches and its potential benefits are described and quantified. Moreover, the optimization of the starting times of a route at the distribution center is evaluated. Finally, the trade-off between solution quality and calculation time is discussed. Numerous test instances are used, both to illustrate the appropriateness of the approach as well as to show that time-independent solutions are often unrealistic within a congested traffic environment, which is usually the case on European road networks.

Vehicle routing with soft time windows and stochastic travel times: A column generation and branch-and-price solution approach

We study a vehicle routing problem with soft time windows and stochastic travel times. In this problem, we consider stochastic travel times to obtain routes which are both efficient and reliable. In our problem setting, soft time windows allow early and late servicing at customers by incurring some penalty costs. The objective is to minimize the sum of transportation costs and service costs. Transportation costs result from three elements which are the total distance traveled, the number of vehicles used and the total expected overtime of the drivers. Service costs are incurred for early and late arrivals; these correspond to time-window violations at the customers. We apply a column generation procedure to solve this problem. The master problem can be modeled as a classical set partitioning problem. The pricing subproblem, for each vehicle, corresponds to an elementary shortest path problem with resource constraints. To generate an integer solution, we embed our column generation procedure within a branch-and-price method. Computational results obtained by experimenting with well-known problem instances are reported.

Vehicle routing with stochastic time-dependent travel times

Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the traffic congestion is captured in an analytical way using queueing theory. The congestion is then applied to the VRP problem. In this paper, we introduce the variability in traffic flows into the model. This allows for an evaluation of the routes based on the uncertainty involved. Different experiments show that the risk taking behavior of the planner can be taken into account during optimization. As more weight is given to the variability component, the resulting optimal route will take a slightly longer travel time, but will be more reliable. We propose a powerful objective function that is easily implemented and that captures the trade-off between the average travel time and its variance. The evaluation of the solution is done in terms of the 95th-percentile of the travel time distribution (assumed to be lognormal), which reflects well the quality of the solution in this stochastic time-dependent environment.

Buffer allocation in general single-server queueing networks

The optimal buffer allocation in queueing network systems is a difficult stochastic, non-linear, integer mathematical programming problem. Moreover, the objective function, the constraints or both are usually not available in closed form, making the problem even harder. A good approximation for the performance measures is thus essential for a successful buffer allocation algorithm. A recently published two-moment approximation formula to obtain the optimal buffer allocation in general service time single queues is examined in detail, based on which a new algorithm is proposed for the buffer allocation in single-server general service time queueing networks. Computational results and simulation results are shown to evaluate the efficacy of the approach in generating optimal buffer allocation patterns.

A stochastic approach to traffic congestion costs

The real world is a complex dynamic and stochastic environment. This is especially true for the traffic moving daily on our roads. As such, accurate modeling that correctly considers the real-world dynamics and the inherent stochasticity is very important, especially if government will base its road tax decisions on the outcomes of these models. The contemporary traffic prices, if any, however, do not reflect the external congestion costs. In order to induce road users to make the correct decision, marginal external costs should be internalized. To assess these costs, the public sector managers need accurate operational models. We show in this article that using a better representation and characterization of the road traffic, via stochastic queueing models, leads to a more adequate reflection of the congestion costs involved. Using extensive numerical experiments, we show the superiority of the stochastic traffic flow models.

Topological network design of general, finite, multi-server queueing networks

The topological network design of general service, finite waiting room, multi-server queueing networks is a complex optimization problem. Series, merge, and split topologies are examined using an approximation method to estimate the performance of these queueing networks and an iterative search methodology to find the optimal buffer allocation within the network. The coefficient of variation is shown to be a significant factor in the buffer allocation for multiple servers in uniform and bottleneck server networks. Extensive computational results are included to illustrate the symmetries and asymmetries in the buffer patterns which emerge from the series, merge, and splitting topologies.

On the system optimum of traffic assignment in M/G/c/c state-dependent queueing networks

The classical Wardrop System Optimum assignment model assumes that the users will cooperate with each other in order to minimize the overall travel costs. The importance of the system optimum model lies on its well-recognized ability of producing solutions that correspond to the most efficient way of using the scarce resources represented by the street and road capacities. In this paper, we present a version of the system optimum model in which the travel costs incurred on each path come from M/G/c/c state-dependent queueing networks, a stochastic travel time estimation formula which takes into account congestion effects. A Differential Evolution algorithm is proposed to solve the model. We motivate this version of the problem in several ways and computational results show that the proposed approach is efficient.

Modelling handling operations in grocery retail stores: an empirical analysis

Shelf stacking represents the daily process of manually refilling the shelves with products from new deliveries. For most retailers, handling operations are labour-intensive and often very costly. This paper presents an empirical study of the shelf-stacking process in grocery retail stores. We examine the complete process at the level of individual sub-activities and study the main factors that affect the execution time of this common operation. Based on the insights from different sub-activities, a prediction model is developed that allows estimating the total stacking time per order line, solely on the basis of the number of case packs and consumer units. The model is tested and validated using real-life data from two European grocery retailers and serves as a useful tool for evaluating the workload required for the usual shelf-stacking operations. Furthermore, we illustrate the benefits of the model by analytically quantifying the potential time savings in the stacking process, and present a lot-sizing analysis to demonstrate the opportunities for extending inventory control rules with a handling component.

Performance optimization of open zero-buffer multi-server queueing networks

Open zero-buffer multi-server general queueing networks occur throughout a number of physical systems in the semi-process and process industries. In this paper, we evaluate the performance of these systems in terms of throughput using the generalized expansion method (GEM) and compare our results with simulation. Secondly, we embed the performance evaluation in a multi-objective optimization setting. This multi-objective optimization approach results in the Pareto efficient curves showing the trade-off between the total number of servers used and the throughput. Experiments for a large number of settings and different network topologies are presented in detail.