A branch-and-price method for the Vehicle Routing Problem with Cross-Docking and Time Windows

One important factor in supply chain management is to efficiently control the supply chain flows. Due to its importance, many companies are trying to develop efficient methods to increase customer satisfaction and reduce costs. Cross-docking is considered a good method to reduce inventory and improve responsiveness. The Vehicle Routing Problem with Cross-Docking and Time Windows (VRP-CD-TW) consists on designing the minimum-cost set of routes to serve a given set of transportation requests while respecting constraints on vehicles capacity, customer time windows and using transfers on a cross-docking base. Each customer must be visited just once and mixed tours comprising pick-up and delivery stops are not allowed. For a given vehicle, the designed pick-up tour must precede its delivery tour. In this work, we model the VRP-CD-TW assuming that all feasible orders are known in advance. We present a new mixed integer program to model the VRP-CD-TW and reformulate it via Dantzig–Wolfe decomposition to later develop a column generation procedure. The proposed branch-and-price algorithm shows encouraging results on solving some Solomon-based instances.Sociedad Argentina de Informática e Investigación Operativ

A Branch-and-price Method for the Vehicle Routing problem with Cross-docking and Time Windows

One important factor in supply chain management is to efficiently control the supply chain flows. Due to its importance, many companies are trying to develop efficient methods to increase customer satisfaction and reduce costs. Cross-docking is considered a good method to reduce inventory and improve responsiveness. The Vehicle Routing Problem with Cross-Docking and Time Windows (VRP-CD-TW) consists on designing the minimum-cost set of routes to serve a given set of transportation requests while respecting constraints on vehicles capacity, customer time windows and using transfers on a cross-docking base. Each customer must be visited just once and mixed tours comprising pick-up and delivery stops are not allowed. For a given vehicle, the designed pick-up tour must precede its delivery tour. In this work, we model the VRP-CD-TW assuming that all feasible orders are known in advance. We present a new mixed integer program to model the VRP-CD-TW and reformulate it via Dantzig-Wolfe decomposition to later develop a column generation procedure. The proposed branch-and-price algorithm shows encouraging results on solving some Solomon-based instances.Fil: Dondo, Rodolfo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química (i); Argentin

Cross-docking: A systematic literature review

This paper identifies the major research concepts, techniques, and models covered in the cross-docking literature. A systematic literature review is conducted using the BibExcel bibliometric analysis and Gephi network analysis tools. A research focus parallelship network (RFPN) analysis and keyword co-occurrence network (KCON) analysis are used to identify the primary research themes. The RFPN results suggest that vehicle routing, inventory control, scheduling, warehousing, and distribution are most studied. Of the optimization and simulation techniques applied in cross-docking, linear and integer programming has received much attention. The paper informs researchers interested in investigating cross-docking through an integrated perspective of the research gaps in this domain. This paper systematically reviews the literature on cross-docking, identifies the major research areas, and provides a survey of the techniques and models adopted by researchers in the areas related to cross-docking

Vehicle routing problem with cross-docking as part of industry 4.0 logistics

The work presented in this paper has been supported by West Bohemia University in Pilsen (project No.SGS SGS-2021-022 - Financial (stock) markets, modeling and prediction of behavior).The trends associated with the onset of Industry 4.0 are obvious and require a prompt response from the company. An indisputable advantage is the use of the cross-docking strategy, which makes it possible to coordinate all logistics processes and achieve optimization of transport costs while maintaining minimal handling and storage. The goods are directly redistributed within the distribution system to specific customers according to their requirements without the need for storage. This logistic method is very often associated with various types of vehicle routing problem. It enables the introduction and use of Industry 4.0 principles. The aim of this contribution is to find out the possibilities of using Cross-docking within the vehicle routing problem. The output is a classification of five vehicle routing problems and their further breakdown, which are successfully connected with the idea of Cross-docking technology. This is a Capacitated vehicle routing problem with cross-docking, Open vehicle routing problem with cross-docking, Vehicle routing problem with cross-docking for multi-products, Multi-echelon distribution networks and Rich vehicle routing problem with cross-docking. Literature analysis shows that it is not an isolated technology but a tool offering a comprehensive logistics service connecting several processes. Offer various combinations of technologies in conjunction with vehicle routing problems to provide economic benefit and reduce the environmental impact of logistics chains

Comparing an Approximate Queuing Approach with Simulation for the Solution of a Cross-Docking Problem

Cross-docking is a logistics management concept in which products are temporarily unloaded at intermediate facilities and loaded onto output trucks to be sent to their final destination. In this paper, we propose an approximate nonstationary queuing model to size the number of docks to receive the trucks, so that their unloading will be as short as possible at the receiving dock, thus making the cross-docking process more efficient. It is observed that the stochastic queuing process may not reach the steady equilibrium state. A type of modeling that does not depend on the stationary characteristics of the process developed is applied. In order to measure the efficiency, performance, and possible adjustments of the parameters of the algorithm, an alternative simulation model is proposed using the Arena® software. The simulation uses analytic tools to make the problem more detailed, which is not allowed in the theoretical model. The computational analysis compares the results of the simulated model with the ones obtained with the theoretical algorithm, considering the queue length and the average waiting time of the trucks. Based on the results obtained, the simulation represented very well the proposed problem and possible changes can be easily detected with small adjustments in the simulated model

The multi-vehicle dial-a-ride problem with interchange and perceived passenger travel times

The Dial-a-Ride Problem (DARP) introduced in the early 1980s is the NP-Hard optimization problem of developing the most cost-efficient vehicle schedules for a number of available vehicles that have to start from a depot, pick up and deliver a set of passengers, and return back to the same depot. DARP has been used in many modern applications, including the scheduling of demand-responsive transit and car pooling. This study departs from the original definition of DARP and it extends it by considering an interchange point where vehicles can exchange their picked-up passengers with other vehicles in order to shorten their delivery routes and reduce their running times. In addition to that, this study introduces the concept of generalized passenger travel times in the DARP formulation which translates the increased in-vehicle crowdedness to increased perceived passenger travel times. This addresses a key issue because the perceived in-vehicle travel times of passengers might increase when the vehicle becomes more crowded (i.e., passengers might feel that their travel time is higher when they are not able to find a seat or they are too close to each other increasing the risk of virus transmission or accidents). Given these considerations, this study introduces the Dial-a-Ride Problem with interchange and perceived travel times (DARPi) and models it as a nonlinear programming problem. DARPi is then reformulated to a MILP with the use of linearizations and its search space is tightened with the addition of valid inequalities that are employed when solving the problem to global optimality with Branch-and-Cut. For large problem instances, this study introduces a tabu search-based metaheuristic and performs experiments in benchmark instances used in past literature demonstrating the computation times and solution stability of our approach. The effect of the perceived passenger travel times to the vehicle running costs is also explored in extensive numerical experiments.</p

Application of exact and multi-heuristic approaches to a sustainable closed loop supply chain network design

Closed-loop supply chains (CLSC) are gaining popularity due to their efficiency in addressing economic, environmental, and social concerns. An important point to ponder in the distribution of CLSC is that imperfect refrigeration and bad road conditions may result in product non-conformance during the transit and thus such products are to be returned to the supply node. This may hinder the level of customer satisfaction. This paper presents a sustainable closed-loop supply chain framework coupled with cross-docking subject to product non-conformance. A cost model is proposed to investigate the economic and environmental aspects of such systems. The transportation cost is analyzed in terms of total carbon emissions. A set of metaheuristics are administered to solve the model and a novel lower bound is proposed to relax the complexity of the proposed model. The results of different size problems are compared with the branch and bound approach and the proposed lower bound. The results indicate that the proposed research framework, mathe-matical model, and heuristic schemes can aid the decision-makers in a closed-loop supply chain context

Robust Cross-dock Location Model Accounting for Demand Uncertainty

The objective of this thesis was to develop optimization models to locate cross-docks in supply chain networks. Cross-docks are a type of intermediate facility which aid in the consolidation of shipments, in which the goods spend little or no time in storage. Instead, the goods are quickly and efficiently moved from the inbound trucks to the outbound docks. Two deterministic facility location models were developed. One followed the p-median facility problem type, where only p facilities were opened in order to minimize total network costs. In the second model, as many cross-docks as necessary were opened and facility location costs were considered while minimizing total network costs. In order to account for uncertainty in demands, a robust optimization model was created based on the initial deterministic one. Robust counterparts were developed for each equation that contained the demand term. The robust model allowed for the creation of a network with the ability to handle variations in demand due to factors such as inclement weather, seasonal variations, and fuel prices. Numerical analysis was performed extensively on both the deterministic and robust models, following the p-median facility problem type, using three networks and parameters coherent with industry standards. The results showed that accounting for uncertainty in demands had a real effect on the facilities which were opened and total network costs. While the deterministic network was less expensive, it was unable to handle increases in demand due to uncertainty, whereas the robust network had no capacity shortages in any scenario. Simple demand inflation, along with the use of a robust model for baseline comparison, also proved to be a legitimate strategy to account for uncertainties in demand among small freight carriers