Two-echelon Distribution Network Research Articles

Dynamic Inventory Allocation for Seasonal Merchandise at Dillard’s

We consider how to allocate inventory of seasonal goods in a two-echelon distribution network for Dillard’s Inc., a large department store chain in the United States. Our objective is to allocate products with limited inventory from a distribution center to multiple retail stores over the selling season to maximize total sales revenue. Under the assumption that the true demand distributions are available to the retailer, we develop an effective dynamic inventory allocation heuristic. We further consider a more realistic and challenging setting for seasonal goods, where demand distributions are unknown to the retailer, and propose two “learning-while-doing” extensions of our inventory allocation heuristic; these policies update demand distribution estimates in a rolling horizon using censored point-of-sales data. We evaluate the performance of the policies using simulation on Dillard’s historical sales data. Dillard’s Inc. has incorporated the proposed policy into their current replenishment methodology and has been using the policy to set order levels for its seasonal merchandise.

Production, Replenishment and Inventory Policies for Perishable Products in a Two-Echelon Distribution Network

The research on production, delivery and inventory strategies for perishable products in a two-echelon distribution network integrates the production routing problem (PRP) and two-echelon vehicle routing problem (2E-VRP), which mainly considers the inventory and delivery sustainability of perishable products. The problem investigated in this study is an extension of the basic problems, and it simultaneously optimizes production, replenishment, inventory, and routing decisions for perishable products that will deteriorate over the planning horizon. Additionally, the lead time has been considered in the replenishment echelon, and the unit inventory cost varying with the inventory time is considered in the inventory management. Based on a newly designed model, different inventory strategies are discussed in this study: old first (OF) and fresh first (FF) strategies both for the first echelon and second echelon, for which four propositions to model them are proposed. Then, four valid inequalities, including logical inequalities, a ( ℓ , S , W W ) inequality, and a replenishment-related inequality, are proposed to construct a branch-and-cut algorithm. The computational experiments are conducted to test the efficiency of valid inequalities, branch-and-cut, and policies. Experimental results show that the valid inequalities can effectively increase the relaxed lower bound by 4.80% on average and the branch-and-cut algorithm can significantly reduce the computational time by 58.18% on average when compared to CPLEX in small and medium-sized cases. For the selection of strategy combinations, OF–FF is suggested to be used in priority.

Two-Echelon Vehicle-Routing Problem: Optimization of Autonomous Delivery Vehicle-Assisted E-Grocery Distribution

The last mile problem of E-grocery Distribution comprises one of the most costly and highest polluting components of the supply chain in which companies deliver goods to end customers. To reduce transport cost and fuel emissions, a new element of ground-based delivery services, autonomous delivery vehicles (ADVs), is included in the E-grocery distribution system for improving delivery efficiency. Thus, the objective of this study is to optimize a two-echelon distribution network for efficient E-grocery delivery, where conventional vans serve the delivery in the first echelon and ADVs serve delivery in the second echelon. The problem is formulated as a two-echelon vehicle routing problem with mixed vehicles (2E-VRP-MV) with a nonlinear objective function, in which the total transport and emission costs are optimized. This optimization is based on the flow assignment at each echelon and to realize routing choice for both the van and ADV. A two-step clustering-based hybrid Genetic Algorithm and Particle Swarm Optimization (C-GA-PSO) algorithm is proposed to solve the problem. First, the end customers are clustered to the intermediate depots, named satellites, based on the minimized distance and maximized demand. To enhance the efficiency of resolving the 2E-VRP-MV-model, a hybrid GA-PSO algorithm is adopted to solve the vehicle routing problem. Computational results of up to 21, 32, 50, and 100 customers show the effectiveness of the methods developed here. At last, the impacts of the layout of the depot-customer and customer density on the total cost are analyzed. This study sheds light on the tactical planning of the multi-echelon sustainable E-grocery delivery network.

Designing a two-echelon distribution network under demand uncertainty

This paper proposes a comprehensive methodology for the stochastic multi-period two-echelon distribution network design problem (2E-DDP) where product flows to ship-to-points are directed from an upper layer of primary warehouses to distribution platforms (DPs) before being transported to the ship-to-points. A temporal hierarchy characterizes the design level dealing with DP location and capacity decisions, as well as the operational level involving transportation decisions as origin-destination flows. These design decisions must be calibrated to minimize the expected distribution cost associated with the two-echelon transportation schema on this network under stochastic demand. We consider a multi-period planning horizon where demand varies dynamically from one planning period to the next. Thus, the design of the two-echelon distribution network under uncertain customer demand gives rise to a complex multi-stage decisional problem. Given the strategic structure of the problem, we introduce alternative modeling approaches based on two-stage stochastic programming with recourse. We solve the resulting models using a Benders decomposition approach. The size of the scenario set is tuned using the sample average approximation (SAA) approach. Then, a scenario-based evaluation procedure is introduced to post-evaluate the design solutions obtained. We conduct extensive computational experiments based on several types of instances to validate the proposed models and assess the efficiency of the solution approaches. The evaluation of the quality of the stochastic solution underlines the impact of uncertainty in the two-echelon distribution network design problem (2E-DDP).

Lagrangian heuristic for supply perishable products in two-echelon distribution network

This article presents a planning problem in a distribution network incorporating two levels inventory management of perishable products, lot-sizing, multi-sourcing and transport capacity with a homogeneous fleet of vehicles. This study is carried out in collaboration with a designer of an advanced planning system (APS) software. This type of network has been encountered in recent years by several customers, such as in the distribution of dairy products or beverages and with instances that can reach large sizes. A mixed integer linear programming (MILP) is developed to solve this real planning problem. There are some instances for which the solver cannot give a good lower bound within the maximum calculation time and for other instances it takes a lot of time to solve MILP. A Lagrangian relaxation is implemented to evaluate these instances. A repair heuristic is applied to the corresponding solutions, for which the cost tends to fall during iterations.

Lagrangian heuristic for supply perishable products in two-echelon distribution network

Lagrangian heuristic for supply perishable products in two-echelon distribution network

Cost-based evaluation of different processing rules for backlog and load-building queues in multi-echelon supply chains

Backlog and load-building queues introduce delay to supply chains which increase the expected lead time of orders. This study aims to investigate the effects of implementing priority rules on backlog and load-building queues, and the effects of applying different load-building methods on the performance of multi-echelon supply chains based on cost and time measures. Further, the study discovers the impact of improving the lead time of orders on the total cost of multi-echelon supply chains. The study was applied on a two-echelon distribution network that includes one central warehouse, six retailers, and four item types. Customer satisfaction costs were incorporated in the cost structure of the studied network through applying penalties on untimely order deliveries based on delivery windows. A discrete-event simulation model was used to run multiple scenarios of implementing queue priority rules and load-building methods. Results indicated that applying priority rule on backlog queues and altering load building methods are effective in decreasing the average lead time of orders, while they had minimal impact on the total cost of retailers.

Cost-based evaluation of different processing rules for backlog and load-building queues in multi-echelon supply chains

Backlog and load-building queues introduce delay to supply chains which increase the expected lead time of orders. This study aims to investigate the effects of implementing priority rules on backlog and load-building queues, and the effects of applying different load-building methods on the performance of multi-echelon supply chains based on cost and time measures. Further, the study discovers the impact of improving the lead time of orders on the total cost of multi-echelon supply chains. The study was applied on a two-echelon distribution network that includes one central warehouse, six retailers, and four item types. Customer satisfaction costs were incorporated in the cost structure of the studied network through applying penalties on untimely order deliveries based on delivery windows. A discrete-event simulation model was used to run multiple scenarios of implementing queue priority rules and load-building methods. Results indicated that applying priority rule on backlog queues and altering load building methods are effective in decreasing the average lead time of orders, while they had minimal impact on the total cost of retailers.

A New Bi-Objective Location-Routing-Inventory Problem with Fuzzy Demands

This paper presents a new bi-objective location-routing-inventory (LRI) problem that considers a multi-period and multi-product problem with heterogeneous fleets in a two-echelon distribution network. The uncertainty in the demand of customers is defined by a fuzzy approach. Two conflicting fuzzy objective functions are included, first of which is to minimize the costs of the used vehicles, fuel consumption, inventory holding, transporting and locating open distribution centers. The second objective is to minimize the shortage of products for each customer. Numerical results demonstrate the validity of the presented model and show the ability of the model to confront real cases.

An Effective Inventory Allocation Policy in Two-Echelon Distribution Network

In this research, we look at the distribution in a two-echelon divergent system that considers periodic review in determining the optimal order-up-to level and rationing parameters to maintain customer service level target. We consider three policies that can provide assistance to inventory managers/planners for quick and effective in determining a rationing parameter that is flexible and effective with the dynamic nature of the demand during the rationing process. Performance comparisons between these policies are given for various problems including the application in real operational/planning setting, and least deviation from the intended objective amongst them suggests otherwise a better policy to adopt.

Near-optimal heuristics to set base stock levels in a two-echelon distribution network

We consider a continuous review two-echelon distribution network with one central warehouse and multiple local stock points, each facing independent Poisson demand for one item. Demands are fulfilled from stock if possible and backordered otherwise. We assume base stock control with one-for-one replenishments and the goal is to minimize the inventory holding and backordering costs. Although this problem is widely studied, only enumerative procedures are known for the exact optimization. A number of heuristics exist, but they find solutions that are far from optimal in some cases (over 20% error on realistic problem instances). We propose a heuristic that is computationally efficient and finds solutions that are close to optimal: 0.2% error on average and less than 5.0% error at maximum on realistic problem instances in our computational experiment

Design of Six Sigma Supply Chains

Variability reduction and business-process synchronization are acknowledged as keys to achieving sharp and timely deliveries in supply-chain networks. In this paper, we introduce a new notion, which we call six sigma supply chains to describe and quantify supply chains with sharp and timely deliveries, and develop an innovative approach for designing such networks. The approach developed in this paper is founded on an intriguing connection between mechanical design tolerancing and supply-chain lead-time compression. We show that the design of six sigma supply chains can be formulated as a mathematical programming problem, opening up a rich new framework for studying supply-chain design optimization problems. To show the efficacy of the notion and the design methodology, we focus on a design optimization problem, which we call the inventory optimization (IOPT) problem. Given a multistage supply-chain network, the IOPT problem seeks to find optimal allocation of lead time variabilities and inventories to individual stages, so as to achieve required levels of delivery performance in a cost-effective way. We formulate and solve the IOPT problem for a four-stage make-to-order liquid petroleum gas supply chain. The solution of the problem offers rich insights into inventory-service level tradeoffs in supply-chain networks and proves the potential of the new approach presented in this paper. Note to Practitioners-This paper builds a bridge between mechanical design tolerancing and supply-chain management. In particular, the paper explores the use of statistical tolerancing techniques in achieving outstanding delivery performance through variability reduction. Informally, a six sigma supply chain is that which delivers products within a customer specified delivery window, with at most 3.4 missed deliveries per million. The innovations in this paper are the following: 1) to define two performance metrics delivery probability and delivery sharpness to describe the precision and accuracy of deliveries, in terms of process capability indexes C/sub p/,C/sub pk/, and C/sub pm/; 2) to formulate the supply-chain design optimization problem using the process capability indices; 3) to suggest an efficient solution procedure for the design optimization problem. The paper presents the case study of a two-echelon distribution network and using the framework developed in the paper shows the role of inventory in controlling lead time variability and achieving six sigma levels of delivery performance.

Outsourcing inventory management decisions in healthcare: Models and application

Traditionally healthcare systems have paid little attention to the management of inventories. However, with the implementation of diagnostic related groups by the United States government (which resulted in a pre-fixed level of compensation for specific medical services), these systems have turned their attention to cost containment as a means of increased profitability. This research addresses the issue of managing inventory costs in a healthcare setting. The specific problem addressed in this paper is a comparison of inventory costs and service levels of an in-house three-echelon distribution network vs. an outsourced two-echelon distribution network. In comparing inventory policies in both networks, we focus on non-critical inventory items. Based on our analysis, we find that the recent trend of outsourcing to distribute non-critical medical supplies directly to the hospital departments using them (i.e., the two-echelon network) results not only in inventory cost savings but also does not compromise the quality of care as reflected in service levels.

Time-partitioning heuristics: Application to one warehouse, multiitem, multiretailer lot-sizing problems

We describe effective time partitioning heuristics for dynamic lot-sizing problems in multiitem and multilocation production/distribution systems. In a time-partitioning heuristic, the complete horizon of (say) N periods, is partitioned into smaller intervals. An instance of the problem is solved, to optimality, on each of these intervals, and the resulting solution coalesced into a solution for the complete horizon. The intervals are selected to be of a size which permits the use of exact and effective solution methods (e.g., branch-and-bound methods). Each interval's problem is specified to include options for starting conditions which adequately complement the solutions obtained for prior intervals. The heuristics can usually be designed to be of low polynomial complexity as well as to guarantee ϵ-optimality for any desired precision ϵ > 0, and asymptotic optimality as N goes to infinity. We first give a general description of the design of time-partitioning heuristics for dynamic lot-sizing problems. We subsequently develop such a heuristic in detail, for the one warehouse multiretailer model representing a two-echelon distribution network with m retailers, selling J distinct items. A comprehensive numerical study exhibits that the partitioning heuristics are very efficient and close-to-optimal. Even problems with a planning horizon of up to 150 periods can be solved within 1.5% of optimality, employing intervals of 5–10 periods only and in a matter of CPU seconds, or up to a few minutes, using longer intervals and when the number of items and retailers is large. These CPU times refer to a SUN 4M (SPARC) workstation. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 463–486, 1999