Multi-echelon Distribution Systems Research Articles

Two-echelon multi-commodity multimodal vehicle routing problem considering user heterogeneity in city logistics

The considerable increase in parcel deliveries has negatively impacted the accessibility and livability of cities. One solution strategy is to decouple short-distance from long-distance shipping so that last-mile transport can be performed with low-footprint vehicles. Such solutions are referred to in the literature as multi-echelon distribution systems. This study introduced a new variant of the two-echelon vehicle routing problem that considers multiple alternative transport modes as well as multiple commodities over a multi-period time horizon, where customers can obtain their commodities from any store. We referred to this problem as the two-echelon multi-commodity multimodal vehicle routing problem (MCM-2E-VRP). The objective of service providers is to minimize total generalized costs while satisfying customer requirements. We formulated this as a mathematical model based on a space–time network and introduced a random utility discrete choice model to capture variations in performance and preferences. We developed an adaptive large-neighborhood search (ALNS) algorithm to provide solutions for newly generated MCM-2E-VRP instances based on the Beijing Yizhuang transportation network. Extensive numerical experiments were conducted to verify the effectiveness of the proposed model and algorithm. A sensitivity analysis revealed some policy-relevant findings regarding the effects of store distribution and vehicle capacity.

Surrogate-assisted evolutionary optimization for perishable inventory management in multi-echelon distribution systems

Simulation is widely used for analyzing supply chains with complex structures and stochastic nature. However, optimizing supply chain simulation models is usually computationally expensive. This study proposes a surrogate-assisted evolutionary optimization approach to optimize the inventory policies in multi-echelon distribution systems for perishable items under a limited number of evaluations. The random forest algorithm is used to build the surrogate model for a faster estimation of the performance of the inventory policies. A co-evolutionary differential evolution algorithm is proposed to simultaneously evolve the population through multiple searching strategies. The generated solutions are estimated by the low-cost surrogate model to select the promising solutions, which will be evaluated by the inventory model. Moreover, this study also integrates the surrogate model into two classic metaheuristic algorithms, particle swarm optimization and differential evolution. Also, a new performance indicator is proposed to examine the efficiency of the surrogate model in evolutionary computation. Two case studies are used to investigate the performance of the proposed algorithms. The experimental results show that both particle swarm optimization and differential evolution exhibit performance improvements exceeding 55% by using surrogate models under the limited number of function evaluations. Furthermore, the surrogate model reduces computational time for both algorithms by over 34% to achieve equivalent objective values. Finally, the proposed co-evolutionary differential evolution algorithm is compared with 12 algorithms, and the results show that the proposed algorithm consistently outperforms them. These findings confirm the usefulness of the surrogate model in evolutionary algorithms and the effectiveness of the proposed co-evolutionary strategy for solving perishable inventory problems.

Integrated strategic and tactical design of multi-echelon city distribution systems with vehicles synchronization: A case of the Greater Montréal area

The sharp increase in e-commerce volume drives the explosive demand growth for urban parcel delivery. Consequently, more and more logistics service providers (LSP) are moving toward establishing more distribution centres in customers' vicinity within metropolitan areas to ensure fast deliveries to online shoppers and reduce costs. Such LSP seeks to optimize the design of their multi-echelon distribution systems by finding the best satellite locations and vehicle routing solutions. However, since satellites have limited parking and no storage spaces, synchronizing the vehicles' arrival times at these facilities and minimizing their waiting times to be loaded/unloaded are essential in designing multi-echelon distribution systems. This study proposes a new Two Echelons Location Routing problem (2E-LRP) model that incorporates vehicles' temporal synchronization at satellites through minimization and setting of a maximum duration to the second echelon vehicle's waiting times, which had not until now been dealt with in 2E-LRP literature. The 2E-LRP new extension is called Two-Echelon Capacitated Location Routing Problem with Vehicles Synchronization (2E-CLRPVS), and the Binary Variable Fixing (BVF) method is proposed to solve it. To assess the validity and applicability of the 2E-CLRPVS model and the efficiency and robustness of the proposed solving method, we conducted computational experiments for a network with up to 99 customers and 5 five satellites based on data from the Great Montreal area in Canada. We also conducted an extensive sensitivity analysis of some critical parameters of the problem to provide some interesting managerial insights regarding multi-echelon urban distribution network design decision-making.

Two-Echelon Multi-Trip Multi-Traffic Pickup and Delivery Problem with Time Windows and Synchronization

In City Logistics context, multi-echelon distribution system normally supports multi-traffic: inbound, outbound, and intra-city traffic. Tackling multi-echelon model with multi-traffic simultaneously will take benefit from saving time and money. Therefore, we study a new problem class, the Two-Echelon Multi-Trip Multi-Traffic Pickup and Delivery Problem with Time Windows and Synchronization. We consider the synchronization process of transshipment at satellites between vehicles with the temporary storage mechanism. As the proposed problem consists of two echelons with two separate fleets of vehicles, we thus propose the bottom-up approach to solve the problem. The experiment is to study the proposed model and analyze the satellite synchronization.

Simulation of a stochastic multi-echelon distribution supply chain under a continuous inventory control policy

Multi Echelon Distribution System (MEDS) is a multifaceted system focusing on integration of all factors involved in the entire distribution process of finished goods to customers. This paper proposes a simulation framework at the operational level of MEDS. The proposed model includes three echelons, based on discrete-event simulation approach, where the performed operations within our system are depending on several key variables that often seem to have strong interrelationships. It is necessary to simulate such complicated system, in order to understand the whole mechanism, to analyze the interactions between various components and eventually to provide information without decomposing the system. The simulation framework is used to evaluate the performance of the considered system at initial conditions and to compare it with different scenarios generated by simulation running. The study concludes with an analysis of system performance and the finding results according to each scenario.  Â

The two echelon open location routing problem: Mathematical model and hybrid heuristic

Multi echelon distribution systems have become more common in recent years. This paper addresses the two echelon open location routing problem (2E-OLRP) which is a variant of the two echelon location routing problem (2E-LRP). This problem seeks to find a minimum-cost set of vehicle routes that do not return to the depot in the first echelon and do not return to satellites in the second echelon due to the presence of individual contractors and third party logistics (3PL) providers. In spite of the large amount of research on LRPs, the 2E-OLRP has received very little attention. Three flow-based mixed-integer linear programs and a hybrid heuristic algorithm are proposed to deal with this problem. Extensive experiments evaluate the effectiveness of these methods.

Effective bullwhip metrics for multi-echelon distribution systems under order batching policies with cyclic demand

A large number of problems in a distribution supply chain require that decisions are made in the presence of the bullwhip effect phenomenon. The impact of the order batching policies on the bullwhip effect is analysed in this paper, when cycle demand on a multi-echelon supply chain operating is considered. While investigating which bullwhip effect metrics are more adequate to measure the bullwhip effect in these type of systems, the optimal reordering plan that minimises the operation costs of the overall system is calculated. A Mixed Integer Linear Programming (MILP) model is developed that takes into account an inventory and distribution system formed by multiple warehouses and retailers with lateral transshipments. The bullwhip effect is measured through four metrics: the echelon average inventory; the echelon inventory variance ratio; the echelon average order; and the echelon order rate variance ratio. As conclusion the inventory metrics suggest that (i) using batching policy reduces instability; (ii) batching may reduce in general order variance if using larger batches and (iii) cycle demand length has no major impact in the bullwhip effect. A motivational example and a real word case study are used and tested.

On Integral Policies in Deterministic and Stochastic Distribution Systems

The “integrality” question for dynamic optimization models of inventory control asks if there exists an integral optimal policy, given integral initial inventory levels, capacities, and demand realizations. One practical implication of this question lies in whether or not full-truckload (FTL) shipping is optimal if customer demand is in integral number of truckloads. In this paper, we investigate the integrality question in single-product, multiechelon distribution systems and show that integrality holds under deterministic demand but fails to hold under stochastic demand. In distribution systems with stochastic demand, less-than-truckload (LTL) shipping can be significantly cheaper than the cost of the optimal FTL shipping policy, even in the presence of economies of scale. For instance, this occurs in settings where shipping costs are expected to increase in the future and/or inventories are more expensive to hold upstream than downstream. In such situations, our results highlight the importance of strategically positioning inventory: LTL shipments can offer a more balanced allocation of inventory across the distribution network, leading to benefits that can exceed the savings from FTL shipments due to economies of scale. However, when the cost parameters are fairly constant across time and inventory holding costs are not significantly higher upstream than downstream, then the difference between the costs of optimal FTL and optimal LTL shipping is provably marginal. The online appendix is available at https://doi.org/10.1287/opre.2016.1586 .

Performance Evaluation of Complex Decentralized and Centralized Multi-Echelon Distribution Supply Chain

In this paper, we consider a multi-echelon multi-products distribution system, made up of a single supplier, and multiple distributors, wholesalers and retailers. Each participant places its orders to the upstream (previous) node according to a continuous review policy. To be in the real complexity of this system, we have presented demand, lead time and capacity as stochastic variables. In a multi-echelon distribution system, several decision centers interact to keep up the performance of this system. In this context, there are two control system architectures whereas each one differs from another to afford to the supply chain a better ability to meet the customers’ demand, namely, the centralized and the decentralized architecture. We first develop a generic discrete event simulator, which can be used as a support for simulation of both centralized and decentralized control system. Subsequently, the results of our model provide a performance analysis based on comparing local and global decision making.

A survey on two-echelon routing problems

The delivery of freight from its origin to its destination is often managed through one or more intermediate facilities where storing, merging and consolidation activities are performed. This type of distribution systems is commonly called multi-echelon, where each echelon refers to one level of the distribution network. Multi-echelon distribution systems are often considered by public administrations when implementing their transportation and traffic planning strategies as well as by private companies in their distribution networks. City logistics and multi-modal transportation systems are the most cited examples of multi-echelon distribution systems. Two-echelon distribution systems are a special case of multi-echelon systems where the distribution network comprises two levels. This latter type of distribution systems has inspired an ever growing body of literature in the last few years. This paper provides an overview of two-echelon distribution systems where routes are present at both levels. We consider three classes of problems: the two-echelon location routing problem, the two-echelon vehicle routing problem, and the truck and trailer routing problem. For each class we provide an introduction and survey the foremost related papers that have appeared in the operations research literature.

Simulating Demand Uncertainty and Inventory Control Variability of Multi-Echelon Distribution Supply Chain

Development of simulation models allows performance analysis of multi-echelon inventory networks, and this part of supply chain is not well-established research area. Moreover, by encapsulating all major characteristics of multi-echelon system, the simulation modeling does not allow only its study, but also it provides the means to achieve the desired system performance. This paper deals with a multi-echelon distribution inventory system made of suppliers, distributors and retailers. The retailer faces stochastic demands placed by customers and replenishing from its distributor, which in turn procures from its supplier at the upstream of the chain. The main purpose of this simulation model is to analyze the multi-echelon distribution system behavior according some key performance metrics such as cost and backorder, as well as customer service level at each echelon.

A novel integrated approach to the modelling and solving of the Two-Echelon Capacitated Vehicle Routing Problem

The paper presents a concept and implementation of a novel approach to the modelling and solving of the Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP). Multi-echelon distribution systems are quite common in supply-chain and logistic systems. Two environments, mathematical programming (MP) and constraint logic programming, in which constraints are treated in different ways and different methods are implemented, were combined to use the strengths of both. The proposed approach is particularly important for the decision models with an objective function and many discrete decision variables added up in multiple constraints. The 2E-CVRP is an extension of the classical Capacitated Vehicle Routing Problem (CVRP) where the delivery depot-customers pass through intermediate depots (called satellites). The 2E-CVRP was selected as a known and documented example for verification and evaluation of the effectiveness of the proposed approach. The presented approach will be compared with classical MP on the same data-sets in computational tests. The proposed approach will be used also for extensions of the modelled problem beyond the standard.

Demand selection decisions for a multi-echelon inventory distribution system

In this paper, we study an integrated demand selection and multi-echelon inventory control problem that generalizes the classical deterministic single distribution centre (DC) multi-retailer model by incorporating demand selection decisions. In addition to the ordering and holding cost components, a concave operating cost of the DC and a capacity on the total market demand served are also considered. For given revenue and cost parameters, the problem is to determine which sets of demand to fulfill and which multi-echelon inventory control policy to implement so as to maximize the net profit. We show that the problem can be formulated as a nonlinear discrete optimization model. We analyse the structural properties of the model and, based on these, outline an approach to solve the model efficiently. We also present some interesting managerial insights obtained from the numerical experiments.

Vehicle Routing in Multi-Echelon Distribution Systems with Cross-Docking: A Systematic Lexical-Metanarrative Analysis

Multi-echelon distribution systems and more precisely, optimization of LTL routes related to them is one of the most popular subjects in the last 5 years of vehicle routing research. Although a plethora of models, methods and visions is found, it is still difficult to compare them because they use different terminologies and some authors insist on the fact there are a multitude of close but different problems. This paper presents the main concepts of multi-echelon distribution with cross-docks and the notation standards for cost optimization in this field on an attempt of unification, in order to provide a guide to researchers and practitioners. A literature review is first presented, in order to list the main problems and methods that are found in the literature. Then, by a hybrid systematic analysis method combining a lexical and a meta-narrative analysis, the main concepts and standards of multi-echelon based vehicle routing optimization problems are presented. A theoretical model as well as a classification of solving methods, both exact and heuristic, is presented. Finally, research paths are proposed to support both scientists and outbound logistics practitioners.

The Two-Echelon Capacitated Vehicle Routing Problem: Models and Math-Based Heuristics

Multiechelon distribution systems are quite common in supply-chain and logistics. They are used by public administrations in their transportation and traffic planning strategies, as well as by companies, to model own distribution systems. In the literature, most of the studies address issues relating to the movement of flows throughout the system from their origins to their final destinations. Another recent trend is to focus on the management of the vehicle fleets required to provide transportation among different echelons. The aim of this paper is twofold. First, it introduces the family of two-echelon vehicle routing problems (VRPs), a term that broadly covers such settings, where the delivery from one or more depots to customers is managed by routing and consolidating freight through intermediate depots. Second, it considers in detail the basic version of two-echelon VRPs, the two-echelon capacitated VRP, which is an extension of the classical VRP in which the delivery is compulsorily delivered through intermediate depots, named satellites. A mathematical model for two-echelon capacitated VRP, some valid inequalities, and two math-heuristics based on the model are presented. Computational results of up to 50 customers and four satellites show the effectiveness of the methods developed.

New Families of Valid Inequalities for the Two-Echelon Vehicle Routing Problem

Abstract Multi-echelon distribution systems are quite common in supply-chain and logistic management. They are used by public administrations in their transportation and traffic planning strategies as well as by companies to model their distribution systems. In the literature, most studies address issues related to the movement of flows throughout the system from the origins to their final destinations. In this paper we consider the Two-Echelon Vehicle Routing Problem (2E-CVRP), the two-echelon variant of the well known Capacitated Vehicle Routing Problem, where the delivery from one depot to the customers is managed by routing and consolidating freight through intermediate depots, called satellites. Valid inequalities based on the TSP and CVRP, the network flow formulation, and the connectivity of the transportation system graph are presented. Extensive computational results on instances with up to 50 customers show an improvement of the best known results between 4% and 15%.

Incorporating a delay mechanism in ordering policies into multi-echelon distribution systems

In this paper, we devise a framework for obtaining the optimal ordering policy in a single location, continuous-review inventory system with arbitrary inter-demand times. We show that it is optimal to order at demand arrival epochs only if the inter-demand time has a constant or decreasing failure rate. When the inter-demand time has an increasing failure rate, we show that the optimal policy is to delay the order. We then extend this policy to multi-echelon distribution systems consisting of one supplier and many retailers. Both decentralized and centralized systems are considered. We derive expressions and procedures for the evaluation of the total cost and the computation of optimal delay in all the considered settings. More importantly, we study the impact of our delay policy in all the settings. The numerical results indicate that for the single-location model, the optimal delay can significantly reduce the total cost. Results from the single-location model can be applied to the decentralized multi-echelon system, where the upstream supplier acts as a single-location system. The supplier order delay can also have a significant impact (either positive or negative) on the retailers' total cost as well as the system's total costs. Finally, the impact of supplier order delay is minimal in the centralized multi-echelon setting. We offer an intuitive explanation for this observation.

Inventory Control at Spiegel Grove

Quantitative models for inventory decision making in a multi-echelon distribution system are very challenging for most undergraduate business or engineering students. To expose students to the challenges of managing multi-echelon inventory levels in an uncertain environment, we have created the Inventory Control at Spiegel Grove classroom exercise, which simulates the inventory management process for a single product in a serial supply chain. Shipments are subject to both transportation quality variability and product quality variability, and students are challenged with adjusting their levels of safety inventory appropriately without carrying an inordinate amount of stock.

Comparison of supply chain replenishment strategies in a non-capacitated distribution system

This research considers inventory replenishment in a stochastic, non-capacitated, multi-echelon distribution system. Simulation is used to model Distribution Requirements Planning (DRP), reorder point and Kanban replenishment strategies. Additional experimental factors include demand seasonality, lot sizes, demand uncertainty and transit time uncertainty. Trade-off curves between inventory and delivery performance are generated. Statistical techniques, including ANOVA and regression, are then used to determine the relative dominance of the replenishment strategies by comparing the areas under the trade-off curves. Results show the methodology developed for analysis of the results works well in identifying both main and interaction effects. DRP performance is found to be the most robust, followed by that of reorder point and Kanban systems, respectively.

Controlling general multi-echelon distribution supply chains with improved reorder decision policy utilizing real-time shared stock information

The objective of this paper is to introduce an improved reorder decision policy for controlling general multiechelon distribution systems utilizing shared stock information. Since traditional reorder policies sometimes show poor performances when applied to distribution systems, the order risk policy, which utilizes shared stock information more accurately, was developed for the two-echelon distribution system in the previous research. In this paper, the order risk policy is extended to general multi-echelon systems. Since the calculation of the exact order risk for general multi-echelon systems is complex, a practical approximation method is developed. Through computational experiments, the superior performance of the order risk policy, compared to the existing reorder policies, is shown and the value of shared stock information varying with the characteristics of the supply chain is analyzed.