Two-Echelon Inventory Research Articles

Considering Continuous Review Policy in a Two-Echelon Inventory System using a Reinforcement Learning Approach

Considering Continuous Review Policy in a Two-Echelon Inventory System using a Reinforcement Learning Approach

Two-echelon Inventory Management for Sustainable Pharmaceutical Supply Chain through Waste Reduction

Improving sustainability in Pharmaceutical Supply Chain (PSC) becomes the primary concern for its involved members. It lends major challenges to its management as it has economic, social, and environmental responsibilities more weighed than other supply chains. Providing the day-to-day need for medicines must be satisfied while taking into account the use of the economic resource, customer satisfaction, and the impact of pharmaceutical waste on the environment. Medicines waste affects healthcare expenses and harms the environment. Therefore, avoiding unused medication leftover through the pharmaceutical chain presents an efficient approach to attaining a sustainable supply of medicines. This article aims to deal with the sustainability of a PSC by minimizing the deterioration rate of medicines at both distributor and hospitals sites. We propose an inventory management model based on a mixed-integer non-linear program (MINLP) that seeks the optimal replenishment order quantity of multiple types of products and the shipment time in a two-echelon PSC consisting of a pharmaceutical company (PC), a central pharmacy (CP), and multiple hospitals over a planning horizon, while considering shipment costs, perishability, and shortage constraints.

An integrated optimization approach using a collaborative strategy for sustainable cities freight transportation: A Case study

• Logistics collaboration is studied in the planning of sustainable city freight transportation. • An integrated and collaborative approach is proposed for sustainable freight logistics networks. • Three sustainability dimensions are considered. • A case study is conducted to show the applicability of proposed approach and the effects of collaboration on the sustainable development of the society and the environment. In recent years, the increasing freight transportation activities has caused extensive economic, environmental and social impacts on society. Therefore, it becomes necessary for logistics companies to find high-performance strategies to enhance their sustainability. Collaboration between companies appears as one of the promising solution that improves the freight transport efficiency of modern cities. Existing studies on collaborative transport did not sufficiently account for sustainability aspects and they mainly discuss the independent planning of decision-making problems with economic objectives. However, collaboration an integrated decision-making process can significantly ameliorate the effectiveness of urban transportation systems. This study addresses the issue of sustainable freight transportation planning by formulating and solving a collaborative and integrated two-echelon inventory, location and routing problem (2E-CILRP). The 2E-CILRP is formulated as a multi-objective integer programming model that minimizes logistics costs, C O 2 emissions and accident rate. A hybrid heuristic based on machine learning is also introduced to solve the studied problem. The proposed approach combines k -means clustering and genetic algorithms. Comparison of the obtained results with those provided with exact method reveals that the developed approach is more efficient and more practical for designing integrated and collaborative networks with large-sized data. A case study of four agri-food SMEs in France is investigated in order to demonstrate the sustainable benefits of the developed optimization approach. The obtained results suggest that the developed approach can significantly reduce the level of C O 2 emissions, logistics costs and accident rate caused by transportation in cities.

Technical Note—A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems

Analyzing Capacitated Two-Echelon Systems with Permutation-Dependent Separability Capacitated multiechelon systems are common in practice due to the escalating costs of labor and advanced manufacturing technology. However, identifying the optimal replenishment policies for such systems is a largely open area of research due to the intrinsic complexity, especially when there is an upstream bottleneck. In “A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems”, Shen, Yu, and Huh propose a new approach, that is, permutation-dependent separability, to tackle a capacitated two-echelon system in which the capacity of upstream stage can be the bottleneck. They show that the value function for the capacitated two-echelon system in each period is permutation-dependent separable, and that for each echelon, a permutation-dependent echelon base stock policy is optimal. The authors also develop efficient solution procedures on how to obtain the optimal policy.

Two-Echelon Inventory Model With Service Consideration and Lateral Transshipment

This paper considers a two-echelon inventory system with service consideration and lateral transshipment. So far, researchers have not extensively considered the use of lateral transshipment for such systems. Demand arrivals at both echelons follow the Poisson process. We introduce a continuous review base stock policy for the system in steady state, which determined the expected level for on-hand inventory, expected lateral transshipment level and expected backorder level. We showed that the model satisfied convexity with respect to base stock level. Computational experiments showed that the model with lateral transshipment performed better that the model without lateral transshipment.

A Two-Echelon Inventory System with a Minimum Order Quantity Requirement

In this paper, we study a two-echelon inventory system with one warehouse and multiple retailers, under the setting of periodic review and infinite horizon. In each period, retailers replenish their stocks from the warehouse, and the warehouse in turn replenishes from an external supplier. Particularly, as stipulated by the supplier, there is a minimum order quantity (MOQ) requirement for the warehouse. That is, the warehouse must order either none or at least as much as the MOQ. To investigate this system analytically, we assume retailers adopt the base-stock policy, and we design for the warehouse a new heuristic ordering policy, called refined base-stock policy, which conforms to the MOQ requirement. Moreover, in the case of shortages, we assume the warehouse adopts a virtual allocation policy, and therefore the orders for individual units are filled in the same order as the original demands at the retailers. To evaluate the long-run average system cost exactly, we present a position-based cost-accounting scheme, in which the cost associated with each unit is assigned to its first position at the warehouse. We also derive lower and upper bounds of the inventory parameters, facilitating the search for the optimal policy that minimizes the long-run average system cost.

A Two-Echelon Inventory Model for Ameliorating/Deteriorating Items with Single Vendor and Multi-buyers

This research work introduces an inventory model for ameliorating items as livestock (say fishes, chickens, ducklings), where the demand rate and deterioration rate are assumed as constant. Delivery times for buyers are introduced in the proposed model. The accumulated inventory contains amelioration rate of livestock with deterioration rate due to death of ameliorating items. The proposed model reduces the integrated total cost of inventory. In addition, the demand and deterioration rates are constant, and the amelioration rate is assumed to adhere to the Weibull distribution. The inventory model is discussed for single manufacturer, who produces the ameliorating items and sells the finished goods to the multiple buyers. The connections between framework parameters and solution procedure illustrate the optimal solutions. Numerical examples are provided to illustrate the theoretical results. Finally, the sensitivity analysis of the framework parameters is discussed.

A Three-level Location-inventory Problem With Perishable Product

This article studies a three-level multi-product location-inventory problem in which location, allocation and inventory decisions are taken in a three-level supply chain including plants, distribution centers and retailers. The direct shipment from plant to retailer is allowed and two-echelon inventory and demand correlation among retailers are considered in this supply chain network. A mixed integer nonlinear programming formulation is presented to describe the problem and trade off the costs of setup, transportation, inventory and deterioration. Then it is transformed to a conic quadratic mixed integer programming formulation and solved with a standard optimization software packages-CPLEX. In addition, we demonstrate that the distribution network allowing for direct shipment from plant to retailer is more optimal than the distribution network ignoring it in the three-level supply chain network with perishable product.

Risk supply chain culture and creative product inventory policy

Due to the globalization, the changes of international transportation are evolving from processing and marketing system. Especially for culture and creative industries (CCI), which are popular industries nowadays. Culture and creative product is more vulnerable than normal goods. Hence, the packing and transportation are more important and difficult. The culture and creative enterprises are forced to speed up their supply because of the requirements of customers. Thus, many culture and creative enterprises want to manage their supply chain more effectively. However, for the international transport, it would cause the transportation risk frequently. This study tries to find a feasible way of applying integrated inventory model with the consideration of incorporating production programs and maintenance to an imperfect process. In addition, this article also thinks about the transportation risk among suppliers, retailers and manufactures. Consequently, the two-echelon inventory and transportation risk model is special for culture and creative industries, and then have real verification.

Continuous Review Two-Echelon (s,S) Inventory System with Partial Backlogging

Inventories exist throughout the supply chain in various forms for various reasons. This paper presents a continuous review two echelon inventory system. The operating policy at the lower echelon is (s, S) that is whenever the inventory level traps to s on order for Q = (S-s) items is placed, the ordered items are received after a random time which is distributed as exponential. We assume that the demands accruing during the stock-out period are partially backlogged. The retailer replenishes their stock from the regular supplier which adopts (0,M) policy, M = n1Q. When the regular supplier stock is empty the replacement of retailer stock made by the outside supplier who adopts (0,N) policy N = n2Q. The joint probability disruption of the inventory levels of retailer, regular supplier and the outside supplier are obtained in the steady state case. Various system performance measures are derived and the long run total expected inventory cost rate is calculated. Several instances of numerical examples, which provide insight into the behavior of the system are presented.

Coordinated Two-Echelon Inventory Model for Optimal Inventory and Shipment Decisions under Exponential Price Dependent Demand

In this paper, a two echelon inventory system with a single-warehouse and single-retailer is considered. Mathematical model is developed for the retailer, warehouse and for the entire chain by incorporating the ordering/setup costs, carrying costs and transportation costs. Replenishment quantity at the retailer and the number of shipments from the warehouse to the retailer are considered as the decision variables. The objective of the proposed work is to demonstrate the optimality of centralised inventory & shipment decisions and total relevant costs at the respective entities and the chain. Numerical example is considered and the model is solved using the computer program written in MATLAB. From the research findings, it is concluded that the percentage variation in optimality of total transportation cost of the supply chain is in decreasing order with respect to the increased ordering cost of the retailer and set-up cost of the manufacturer. Finally, few managerial implications are derived based on the sensitivity analysis.

Analysis of Two-Echelon Inventory System with Two Demand Classes with Partial Backlogging

This paper deals with a continuous review two-echelon inventory system with two demand classes. Two echelon inventory systems consist of one retailer (lower echelon) and one distributor (upper echelon) handling a single finished product. The demand at retailer is of two types. The First type of demand is usual single unit and the second type is of bulk or packet demand. The arrival distribution for single and packet demands are assumed to be independent Poisson with rates λ1(>0) and λd (>0) respectively. The operating policy at the lower echelon for the (s, S) that is whenever the inventory level drops to ‘s’ on order for Q = (S-s) items is placed, the ordered items are received after a random time which is distributed as exponential with rate µ>0. We assume that the demands occurring during the stock-out period are lost. The retailer replenishes the stock from the distributor which adopts (0, M) policy. The objective is to minimize the anticipated total cost rate by simultaneously optimizing the inventory level. The joint probability disruption of the inventory levels at retailer and the distributor are obtained in the steady state case. Various system performance measures are derived and the long run total expected inventory cost rate is calculated. Several instances of numerical examples, which provide insight into the behavior of the system, are presented.

Joint Optimization of Distribution Network Design and Two-Echelon Inventory Control with Stochastic Demand and CO2 Emission Tax Charges.

This study develops an optimization model to integrate facility location and inventory control for a three-level distribution network consisting of a supplier, multiple distribution centers (DCs), and multiple retailers. The integrated model addressed in this study simultaneously determines three types of decisions: (1) facility location (optimal number, location, and size of DCs); (2) allocation (assignment of suppliers to located DCs and retailers to located DCs, and corresponding optimal transport mode choices); and (3) inventory control decisions on order quantities, reorder points, and amount of safety stock at each retailer and opened DC. A mixed-integer programming model is presented, which considers the carbon emission taxes, multiple transport modes, stochastic demand, and replenishment lead time. The goal is to minimize the total cost, which covers the fixed costs of logistics facilities, inventory, transportation, and CO2 emission tax charges. The aforementioned optimal model was solved using commercial software LINGO 11. A numerical example is provided to illustrate the applications of the proposed model. The findings show that carbon emission taxes can significantly affect the supply chain structure, inventory level, and carbon emission reduction levels. The delay rate directly affects the replenishment decision of a retailer.

Impact of lead time reduction and fuel consumption on a two-echelon supply chain inventory with a subsidised price and pick-up policy

Impact of lead time reduction and fuel consumption on a two-echelon supply chain inventory with a subsidised price and pick-up policy

Impact of lead time reduction and fuel consumption on a two-echelon supply chain inventory with a subsidised price and pick-up policy

In this paper, the issue of vendor-buyer coordination in a supply chain involving a logistics provider has been investigated. The purpose is to analyse the impact of lead time reduction, fuel prices and fuel consumption of the fleet on the total cost incurred by the single vendor-buyer supply chain. We consider stochastic demand and the fact that fuel prices are subsidised and regulated by the government. The objective is to minimise the total cost incurred by a single vendor-buyer supply chain. Logistics costs are a function of weight, distance, fuel price and consumption with two load conditions: truckload (TL) and less-than-truckload (LTL) shipments. This paper develops two models based on the prevailing operating conditions: in the first model, the vendor delivers their product to the logistics provider; and in the second model, the logistics provider offers a pick-up policy. Numerical examples and sensitivity analyses are given to illustrate the results.

Two-Echelon Inventory Optimization for Imperfect Production System under Quality Competition Environment

This paper develops two integrated optimization models of two-echelon inventory for imperfect production system under quality competition environment, in which the vendor’s production process is assumed to be imperfect, and JIT delivery policy is implemented to ship product from the vendor to the buyer. In the first model, product defect rate is fixed, and, in the second model, quality improvement investment is function of defect rate. The optimal policies of ordering quantity of buyer and shipment from vendor to buyer are obtained to minimize the expected annual total cost of vendor and buyer. Numerical examples are used to demonstrate the effectiveness and feasibility of the models. Sensitivity analysis is taken to analyze the impact of demand, production rate, and defect rate on the solution. Implications are highlighted in that both the vendor and the buyer can benefit from the vendor’s investing in quality improvement.

Exact Analysis of Capacitated Two-Echelon Inventory Systems with Priorities

We consider a two-echelon inventory system with a capacitated centralized production facility and several distribution centers (DCs). Both production and transportation times are stochastic with general distributions. Demand arrives at each DC according to an independent Poisson process and is backlogged if the DC is out of stock. We allow different holding and backlog costs at the different DCs. We assume that inventory at DCs is managed using the one-for-one replenishment policy. The main objective of this paper is to investigate the control of the multiechelon M/G/1 setting with general transportation times. To achieve this objective, we analyze several decentralized allocation policies including the first-come, first-served (FCFS), strict priority (SP), and multilevel rationing (MR) policies. For our analytic results, we assume no order crossing. We derive the cost function for a capacitated two-echelon inventory system with general transportation times under these policies. Our numerical examples show that the FCFS policy may outperform the MR policy, even though the latter has been shown to be better in the centralized setting. This suggests that in decentralized settings there is a need to focus on policies that prioritize customers when there is backlog. This focus is in contrast to the centralized settings, where inventory rationing policies that focus on prioritization when there is available inventory are effective. We therefore introduce and analyze the generalized multilevel rationing (GMR) priority policy. We compare the GMR policy with other policies and show that the GMR policy outperforms the three policies used in the centralized setting. We also compare the GMR policy with the myopic (T), longest queue first (LQF), and the optimal (when order crossing is allowed during the transportation time) policies. Our results show that when the uncertainty of the transportation times is low, the GMR policy outperforms the myopic (T) and LQF policies and that the gap between the optimal policy and the GMR policy is not high.

Two-Echelon Inventory Stochastic Model of Supply Chain Based on Service Level Constraints

The study on multi-echelon inventory of supply chain is becoming more and more important in E-business era. This paper proposes a two-echelon inventory model with one supplier and several retailers, in which a certain service level has to be satisfied and the goal is to minimize the total inventory cost. In addtion it puts forward an effective algorithm for this model to obtain the optimal replenishment period and inventory level of each supply chain node.

Optimality of Inventory Decisions and Shipment Policies in a Two-Echelon Inventory System under Quadratic Price Dependent Demand

This document is proposing an inventory system that is two-echelon for a supply chain that is coordinated and non-coordinated with one retailer and manufacturer. The retailer experiences the demand that is dependent on quadratic price and assumed to be price driven. Profit is completely dependent on the effectiveness of supply chain. Profit is the difference between the gross revenue and the total cost, whereas total cost includes carrying cost, transportation cost along with the cost of annual ordering. For a coordinated and non-coordinated supply chain, a mathematical model is being introduced. The primary objective of the mathematical model is to show the effective ordering quantity of the retailer, effective lot size of the producer, and the optimal quantity of the transportation from manufacturer to the retailer. The impact of the model parameters on objective function and variables is demonstrated with the help of a sensitivity analysis.

Reducing the Shelf Life of Perishable Items with Stochastic Replenishment in a Two-Echelon Inventory System

Reducing the Shelf Life of Perishable Items with Stochastic Replenishment in a Two-Echelon Inventory System