Two-echelon Distribution System Research Articles

A decomposition and coordination method for optimising (Q, S ) policies in a two-echelon distribution system with joint replenishment

A continuous-review, two-echelon distribution system with one central distribution centre (CDC) and multiple regional distribution centres (RDCs) is studied. The CDC jointly replenishes its inventories of multiple items from an external supplier, while each RDC replenishes its inventories of the items from the CDC. Each RDC faces a Poisson demand for each item, and the inventories of each stock in the system are controlled by a (Q, S ) policy. Under this policy, an order is placed by a stock whenever its aggregate demand since the last order reaches a given quantity, and the inventory position of each item is raised up to its order-up-to level after the order placement. The objective is to optimise these (Q, S ) policies so that the expected total cost of this system is minimised. We propose a decomposition and coordination method for this optimisation after deriving analytically the cost function of the system. Our extensive numerical experiments demonstrate the effectiveness of the proposed method. Furthermore, a parameter sensitivity analysis is conducted to analyse the impacts of some key system parameters on the performance of the method, and managerial insights are provided for optimising distribution systems with joint replenishment and real applications of the method.

Two-echelon vehicle routing problem with direct deliveries and access time windows

Nowadays, heavy-duty trucks are usually restricted from entering urban areas due to emission and congestion problems in most cities. So, a two-echelon distribution system becomes vastly applicable, in which satellites transfer cargo and avoid heavy-duty trucks entering urban areas. However, with the development of new energy vehicles and access policies and regulations, some environmentally friendly trucks are accessible to urban areas within specific time windows of daytime directly. In light of this, we introduce a two-echelon vehicle routing problem with direct deliveries and access time windows (2E-VRPDDATW) arising in city logistics. In this problem, customers are served by the two-echelon distribution systems within their required time windows and are allowed to be directly delivered by the first echelon vehicles within access time windows, which provides more flexible routing schemes. A novel mixed integer linear programming (MILP) model for the above problem is presented, and the corresponding adaptive large neighborhood algorithm is developed. The computational experiments are provided to verify the validity of the proposed model and the effectiveness of the algorithm. Finally, the sensitivity analysis shows some interesting findings about the number of two-echelon vehicles and the assignment of customers. Moreover, we conclude that direct deliveries are advantageous in transportation costs when the proportion of the end time of access time window to the last end time of customers is greater than 0.25.

E-Commerce Parcel Distribution in Urban Areas with Sustainable Performance Indicators

E-commerce transactions have increased during the pandemic as people living in urban areas turn to buy goods online rather than offline. A two-echelon distribution system using parcel mobile hubs (PMHs) with small vehicles can increase operational cost efficiency and reduce greenhouse gas emissions. The originality of this study is in building and testing a conceptual framework for selecting PMH locations with three variables (parcel distribution, internet quota for e-commerce, and center of e-buyer) and two constraints (space availability and traffic flow). Spatial analysis is used as a method to test the conceptual framework with a parcel distribution database from Bandung. As a city whose profile represents urban areas in developing countries well, Bandung is chosen as a case study. The proportion of distance to variables and the outermost point of each cluster is less than 10%, which proves that the three variables are correlated. This study proves that the selection of PMH locations based on this conceptual framework results in better sustainable performance compared to existing conditions. Using PMHs combined with city freighters can reduce operational costs by 19.7% and prevent 3.4 tons of CO2 emissions per year with conventional motorcycles and 7.2 tons of CO2 emissions per year with electric motorcycles or scooters.

An alternating direction method of multipliers for optimizing (s, S) policies in a distribution system with joint replenishment volume constraints

In this paper, we study a two-echelon distribution system in which multiple products are jointly replenished at each stocking location and the inventory of each product at each location is controlled by an (s, S) policy. The transportation capacity in volume of products for each joint replenishment is limited, and linear rationing policies are used for both on-hand inventory and transportation capacity allocation in the system in case of shortage. We propose a novel scenario-based model for the optimization of the (s, S) policies in the system that considers the rationing policies. Because of its high complexity when the number of scenarios is large, an Alternating Direction Method of Multipliers is proposed to solve the model. Based on real data, forty instances were generated and tested to evaluate the model and the solution method. Our numerical experiments show that for these instances this method could find a better solution in a much shorter computation time compared with CPLEX 12.9, whereas the latter often runs out of memory for large-size instances on a personal computer. Moreover, the inventory policies found by this scenario-based optimization approach can reduce costs by 5.1% and improve fill rates by 9.7% on average compared with those currently used in Alibaba.

A Chance-Constrained Two-Echelon Vehicle Routing Problem with Stochastic Demands

Two-echelon distribution systems are often considered in city logistics to maintain economies of scale and satisfy the emission zone requirements in the cities. In this work, we formulate the two-echelon vehicle routing problem with stochastic demands as a chance-constrained stochastic optimization problem, where the total demand of the customers in each second-echelon route should fit within the second-echelon vehicle capacity with a high probability. We propose two efficient solution procedures based on column generation. Key to the efficiency of these procedures is the underlying labeling algorithm to generate new columns. We propose a novel labeling algorithm based on simultaneous construction of second-echelon routes and a labeling algorithm that builds second-echelon routes sequentially. To further enhance the performance of the solution procedure, we use statistical inference tests to ensure that the chance constraints are met. We reduce the number of customer combinations for which the chance constraint needs to be verified by imposing feasibility bounds on the stochastic customer demands. With these bounds, the runtimes of the labeling algorithms are reduced significantly. The novel labeling algorithm, statistical inference, and feasibility bounds can also be applied to dependent, correlated, and data-driven (scenario-based) demand distributions. Finally, we show the value of the stochastic formulation in terms of improved solution cost and guaranteed feasibility of second-echelon routes. Funding: This work was funded by the Dutch Research Council (NWO) DAREFUL project [Grant 629.002.211] and was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1162 .

The two-echelon stochastic multi-period capacitated location-routing problem

Given the emergence of two-echelon distribution systems in several practical contexts, this paper tackles, at the strategic level, a distribution network design problem under uncertainty. This problem is defined as the two-echelon stochastic multi-period capacitated location-routing problem (2E-SM-CLRP). It considers a network partitioned into two capacitated distribution echelons: each echelon involves a specific location-assignment-transportation schema that must cope with the future demand. It aims to decide the number and location of warehousing/storage platforms (WPs) and distribution/fulfillment platforms (DPs), and on the capacity allocated from first echelon to second echelon platforms. In the second echelon, the goal is to construct vehicle routes that visit ship-to locations (SLs) from operating distribution platforms under a stochastic and time-varying demand and varying costs. This problem is modeled as a two-stage stochastic program with integer recourse, where the first-stage includes location and capacity decisions to be fixed at each period over the planning horizon, while routing decisions of the second echelon are determined in the recourse problem. We propose a logic-based Benders decomposition approach to solve this model. In the proposed approach, the location and capacity decisions are taken by solving the Benders master problem. After these first-stage decisions are fixed, the resulting sub-problem is a capacitated vehicle-routing problem with capacitated multiple depots (CVRP-CMD) that is solved by a branch-cut-and-price algorithm. Computational experiments show that instances of realistic size can be solved optimally within a reasonable time and provide relevant managerial insights on the impact of the stochastic and multi-period settings on the 2E-CLRP.

A heuristic for two-echelon urban distribution systems

The negative impacts of urban freight transport have fostered the design of new distribution systems for inner city deliveries. One of the proposed city logistics solutions is the establishment of two-echelon distribution systems, where freight originating from the periphery of the city is transferred at intermediate locations (satellites) from larger vehicles (urban freighters) to smaller more environmentally friendly vehicles (city freighters), deemed more suited to operate in the city centre. In this paper, we address a variant of the two-echelon (capacitated) vehicle routing problem (2E-CVRP) arising in the context of city logistics encompassing characteristics such as a heterogeneous fleet of city freighters, time windows, vehicles synchronisation at satellites, direct deliveries, the possibility of freight transfers at customers, and multiple trips by city freighters. We propose a heuristic solution method for this problem based on a Variable Neighbourhood Search (VNS) heuristic, as well as a set of auxiliary evaluation metrics designed to support the decision making process. Preliminary results show the flexibility of the proposed heuristic to account for different problem characteristics, as well as the impacts of considering different best insertion criteria for the initial solution construction. Additionally, the proposed evaluation metrics have allowed for an improved assessment of the trade-offs between different city logistic solutions, and may be considered when developing decision support systems.

Optimising inventory placement in a two-echelon distribution system with fulfillment-time-dependent demand

We study a two-echelon, single-product fulfillment system where a regional fulfillment center (FC) replenishes multiple independent local distribution center (LDC) orders within an internal committed resupply leadtime, and LDCs serve end customers within a committed demand fulfillment time, or committed delivery time. Expected system-wide demand depends on the product's price, the committed delivery time, and the number of LDCs in the system. Our proposed model determines the values of product price, committed resupply time, and committed delivery time that maximise expected system-wide profit per period, while accounting for product holding costs and fixed facility costs. We characterise key properties of optimal solutions that permit an efficient solution for a fixed number of LDCs, and consider the impacts of several proposed demand growth models as the number of LDCs increases. The results of a computational study provide interesting managerial insights on how operational constraints and the scale of the distribution system influence strategic stock placement and distribution system structure.

Location of Urban Logistics Spaces (ULS) for Two-Echelon Distribution Systems

The main concern in city logistics is the need to optimize the movement of goods in urban contexts, and to minimize the multiple costs inherent in logistics operations. Inspired by an application in a medium-sized city in Latin America, this paper develops a bi-objective mixed linear integer programming (MILP) model to locate different types of urban logistics spaces (ULS) for the configuration of a two-echelon urban distribution system. The objective functions seek to minimize the costs associated with distance traveled and relocation, in addition to the costs of violation of time windows. This model considers heterogeneous transport, speed assignment, and time windows. For experimental evaluation, two operational scenarios are considered, and Pareto frontiers are obtained to identify the efficient non-dominated solutions to select the most feasible ones from such a set. A case study of a distribution company of goods for supermarkets in the city of Barranquilla, Colombia, is also used to validate the proposed model. These solutions allow decision-makers to define the configuration of ULS networks for urban product delivery.

Solving the Two Echelon Vehicle Routing Problem Using Simulated Annealing Algorithm Considering Drop Box Facilities and Emission Cost: A Case Study of Reverse Logistics Application in Indonesia

A two echelon distribution system is often used to solve logistics problems. This study considers a two-echelon distribution system in reverse logistics context with the use of drop box facility as an intermediary facility. An optimization model of integer linear programming is proposed, representing a two-echelon vehicle routing problem with a drop box facility (2EVRP-DF). The aim is to find the minimum total costs consisting of vehicle transportation costs and the costs to compensate customers who have to travel to access these intermediary facilities. The results are then compared to those of common practice in reverse logistics. In common practice, customers are assumed to go directly to the depot to drop their goods. In addition, this study analyzes the environmental impact by adding a component of carbon emissions emitted by the vehicles. A set of comprehensive computational experiments is conducted. The results indicate that the 2EVRP-DF model can provide optimal costs and lower carbon emissions than the common practice.

Intraroute Resource Replenishment with Mobile Depots

In numerous practical vehicle-routing applications, larger vehicles are employed as mobile depots to support a fleet of smaller vehicles that perform certain tasks. The mobile depots offer the possibility of keeping the task vehicles operational by supplying them en route with certain resources. For example, in two-echelon distribution systems, small task vehicles are used to navigate narrow streets and to deliver/collect goods or to collect waste, and larger vehicles serve as mobile depots to replenish the goods to be delivered or to receive collected goods or waste at the outskirts of the urban area. Accessibility constraints may also be imposed by regulations on emissions, which make some areas only accessible for environmentally friendly vehicles such as, for example, battery-powered electric vehicles. Especially if the respective refueling infrastructure is sparse, mobile refueling stations seem to be an interesting alternative. In this paper, we introduce the vehicle-routing problem with time windows and mobile depots (VRPTWMD) to capture the routing decisions of the described applications in a generalized fashion. The VRPTWMD is characterized by fleets of task vehicles (TVs) and support vehicles (SVs). The SVs may serve as mobile depots to restore either the load or the fuel capacity of the TVs that are used to fulfill the customer requests. We present a mixed-integer program for the VRPTWMD with which small instances can be solved using a commercial solver. Moreover, we develop a high-quality hybrid heuristic composed of an adaptive large neighborhood search and a path relinking approach to provide solutions on larger problem instances. We use a newly generated set of large VRPTWMD instances to analyze the effect of different problem characteristics on the structure of the identified solutions. In addition, our approach shows very convincing performance on benchmark instances for the related two-echelon multiple-trip VRP with satellite synchronization, which can be viewed as a special case of the VRPTWMD. Our heuristic is able to significantly improve a large part of the previous best-known solutions while spending notably less computation time than the comparison algorithm from the literature.

A generic mathematical formulation for two-echelon distribution systems based on mobile depots

The negative impacts of urban logistics have fostered the search for new distribution systems in inner city deliveries. In this context, interesting solutions can be developed around two-echelon distribution systems based on mobile depots (2E-MD), where loads arriving from the periphery of the city are directly transferred, at intermediate locations, from larger to smaller vehicles more suited to operate in the city centre. Four types of 2E-MD can be identified, according to the degree of mobility of larger vehicles and their accessibility to customers.In this paper, we propose a generic three-index arc-based mixed integer programming model, for a two-echelon vehicle routing problem, with synchronisation at the satellites and multi-trips at the second echelon. This generic base model is formulated for the most restrictive type of problems, where larger vehicles visit a a single transfer location and do not perform direct deliveries to customers, but it can be easily extended to address the other types of 2E-MD. The paper presents how these extensions account for the characteristics of the different types of 2E-MD.The generic model, its extensions and the impact of a set of valid inequalities are tested using problem instances adapted from the VRP literature. Results show that the proposed extensions do adequately address the specific features of the different types of 2E-MD, including multiple visits to satellites, and direct deliveries to customers. Nevertheless, the resulting models can only tackle rather small instances, even if the formulations can be strengthened by adding the valid inequalities proposed in the paper.

Stock allocation in a two-echelon distribution system controlled by (s, S) policies

Stock allocation is an important decision in distribution systems, which determines how the on-hand inventory of an upstream stock is allocated to its immediate downstream stocks if their replenishment orders cannot be fulfilled completely. In the literature, almost all studies assume each stock in a distribution system is controlled by a base stock policy, although a real system may be controlled by (s, S) policies because of the existence of fixed ordering costs. In this paper, we study stock allocation in a real distribution system of Alibaba and propose two easy-to-implement Allocation-to-S methods that are more effective than three well-known rationing rules and a rationing rule currently used in Alibaba. For the 300 instances tested, one of the methods can reduce the expected cost per period by more than 1.5% and improve the service level by more than 1.3% on average with respect to the best of the four rules. In addition, a general procedure is provided to solve the imbalance problem of linear rationing rules which include the rules.

Inventory replenishment planning of a distribution system with storage capacity constraints and multi-channel order fulfilment

In this paper, an inventory replenishment planning problem in a two-echelon distribution system of Alibaba with a central distribution centre (CDC) and multiple front distribution centers (FDCs) is studied. In the system, the CDC replenishes its inventories of multiple products from external suppliers, while each FDC replenishes its inventories of the products from the CDC. These products are jointly replenished at each stock. This problem arises when Alibaba prepares its annual “double 11” promotion. Facing stochastic demands of the products in the promotion period, the objective of the problem is to optimally determine the inventory replenishment quantities of the products for each stock before the promotion so that the expected total profit of the system is maximized, subject to the storage capacity constraint of each stock. During the promotion, customer orders may be fulfilled through multiple channels, that is, a customer order may be fulfilled by its local FDC, other FDCs, or the CDC. This stochastic optimization problem is formulated as a convex nonlinear programming model and solved optimally by a piecewise linear approximation approach. The effectiveness of the model and the approach is demonstrated by numerical experiments on instances generated based on data of Alibaba. The results show that our model can lead to a significantly higher expected total profit compared with a deterministic planning model.

Optimised solutions to the last-mile delivery problem in London using a combination of walking and driving

Inspired by actual parcel delivery operations in London, this paper describes a two-echelon distribution system that combines the use of driving and walking as part of last-mile deliveries in urban areas for a single driver. The paper presents an optimisation model that explicitly treats and integrates the driving and walking elements, and describes a branch-and-cut algorithm that uses new valid inequalities specifically tailored for the problem at hand. Computational results based on real instances obtained from a courier operating in London are presented to show the performance of the algorithm.

A Simulated Annealing Algorithm for Solving Two-Echelon Vehicle Routing Problem with Locker Facilities

We consider the problem of utilizing the parcel locker network for the logistics solution in the metropolitan area. Two-echelon distribution systems are attractive from an economic standpoint, whereas the product from the depot can be distributed from or to intermediate facilities. In this case, the intermediate facilities are considered as locker facilities present in an accessible location in the vicinity of the final customers. In addition, the utilization of locker facilities can reduce the cost caused by the unattended deliveries. The problem is addressed as an optimization model that formulated into an integer linear programming model denoted as the two-echelon vehicle routing problem with locker facilities (2EVRP-LF). The objective is to minimize the cost of transportation with regards to the vehicle travelling cost, the intermediate facilities renting cost, and the additional cost to compensate the customer that needs to travel to access the intermediate facilities. Because of its complexity, a simulated annealing algorithm is proposed to solve the problem. On the other hand, the modelling approach can be conducted by generating two-phase optimization model approaches, which are the p-median problem and the capacitated vehicle routing problem. The results from both methods are compared in numerical experiments. The results show the effectiveness of 2EVRP-LF compared to the two-phase optimization. Furthermore, the simulated annealing algorithm showed an effective performance in solving 2EVRP-LF.

Operational level planning of a multi-item two-echelon spare parts inventory system with reactive and proactive interventions

In this paper, we investigate operational spare parts planning in a multi-item two-echelon distribution system, taking into account real-time supply information in the system. We consider a broad range of operational interventions, either reactive (to solve a shortage) or proactive (to avoid a shortage). These interventions particularly include lateral transshipments between warehouses (local warehouses), emergency shipments from the depot (central warehouse), and doing nothing and waiting for pipeline inventory. We propose an integrated approach to determine the optimal timing and size of each intervention type to minimize the total downtime and shipment costs associated with interventions. Data from a leading original equipment manufacturer of high-tech systems is used to test the performance of our approach. We find that our integrated approach reduces total downtime considerably with a very limited increase in total shipment costs. Proactive emergency shipments contribute most to downtime reduction. The benefit of our approach is higher for high demand parts. Allowing complete pooling between warehouses increases downtime savings and usage of proactive emergency shipments even further. Our approach is efficient enough to solve practical size problems. We also propose a heuristic based on a greedy algorithm, which is well known in the literature. We find that the gap between the heuristic and the optimal solution is relatively large.

A two-echelon location-routing problem with synchronisation

Motivated by an actual problem of a national postal service company, we introduce and define a new two-echelon location-routing problem (2E-LRP). The 2E-LRP is defined in a two-echelon distribution system where products are transported from origins to destinations through intermediate facilities. A major question that arises in a two-echelon distribution system is how to synchronise the flows of the two echelons at intermediate facilities. The synchronisation is important due to limited storage space or waiting times for transshipments at the intermediate facilities. In our new 2E-LRP, the activities in the two echelons are organised into two waves; a delivery wave, where products are sent from the primary facility to the customers through the intermediate facilities, and a following pickup wave, where the flow of products is reversed. The model only considers temporal constraints, assuming that capacities are never binding; the vehicles are always large enough given the constraints on time. As a solution approach, we propose a decomposition-based heuristic. Besides the solution approach, we propose data-driven schemes for use in combination with the model and we provide the computational results for different sets of instances.

Sustainable Open Vehicle Routing with Release-Time and Time-Window: A Two-Echelon Distribution System

In an increasingly competitive economic environment, outsourcing for logistics has emerged as a cost-efficient strategy during freight transportation. The open vehicle routing problem is a type of classical vehicle routing problem, in which businesses outsource logistics to a third-party company and the vehicles do not return to the depot at the end of their journey. This paper develops a mixed integer linear programming model for two-echelon open vehicle routing problem that integrates city distribution constraints such as time-window and release-time. The release-time refers to the time at which products become ready at satellites for downstream distribution, and it is influenced by limited available resources and work load of each satellite. The proposed model determines the optimal configuration of the routes while minimizing the handling costs, penalty costs, and transportation costs. We use a comprehensive emission model that accounts for load, distance, speed and vehicle characteristics to estimate fuel consumption. Finally, we utilize a numerical example to illustrate the proposed model and explore the effects of release-time on total cost.

Research on Order-Inventory Transshipment Mechanism in Dual-Channel Distribution Supply Chain

The development of e-commerce has prompted traditional enterprises to open up online channels and form a dual-channel sales model. The increase in the number of channels has led to an increase in the number of orders, so how to properly and effectively match the order with the inventory will test the operational capabilities of the enterprise. Based on this practical problem, this thesis considers a two-echelon distribution system with online and offline dual-channel sales, which consists of one group node (G) and multiple distribution nodes (D). When online orders are not fully satisfied, we propose an operation mechanism of transporting inventory to online orders through offline inventory. An optimal decision model is constructed by using the Analysis Target Cascading (ATC). Finally, the model is simulated and analyzed with a specific case. The results show that the ATC method and the transshipment mechanism are effective.