Multi-echelon Inventory Models Research Articles

Modeling Payment Timing in Multiechelon Inventory Systems with Applications to Supply Chain Coordination

Problem definition: How can one adapt multiechelon inventory models to capture the cash flows generated by various payment-timing contracts? What competitive inventory policy behavior arises under these various payment-timing arrangements? Academic/practical relevance: Technology advancements are increasing the variety of payment triggers between supply chain stages. However, traditional multiechelon inventory models, which were originally developed for vertically integrated systems, do not explicitly account for payments flowing up the supply chain nor issues of payment timing between stages. Methodology: We introduce an analytical modeling methodology to incorporate financial inventory costs generated by payment-timing arrangements between stages in multiechelon inventory models. We also combine these methods with established inventory theory to study competitive inventory policies in a two-echelon system. Results: Under a class of payment-timing contracts, we show how to express payment flows at each stage in terms of standard physical inventory metrics and the demand-arrival process. We also show how to calculate the average inventory costs for each stage under given inventory policies and payment-timing contracts. In the two-echelon base-stock model, we first show that the cost of decentralization under standard wholesale price contracts is significantly driven by too much inventory at the supplier; it is not exclusively driven by too little inventory at the retailer as in the selling-to-the-newsvendor literature. We show that wholesale price contracts with a type of popular consignment payment timing still leads to too little inventory at the retailer. However, we prove there exists a wholesale price contract with partial consignment timing that can achieve the centralized inventory levels at both the supplier and the retailer. Managerial implications: Researchers can leverage our methodology to incorporate the price transfers and timing aspects of contracts in multiechelon inventory models. Our insights also help managers better understand the impact of prices and payment timing on decentralized chain behavior and performance.

A typology and literature review on stochastic multi-echelon inventory models

We develop a typology for multi-echelon inventory management. The typology is used to classify and review the extensive research of multi-echelon inventory management under uncertain demand. We identify clusters of model assumptions, research goals and applied methodologies. Based on this review, existing research gaps and avenues for further research are proposed.

Optimizing multi-echelon inventory with three types of demand in supply chain

This paper proposes multi-echelon inventory models with three types of demand. The stakeholders consist of a retailer, a plant and a number of middlemen. Because the modes of demand for stakeholders are different, the stakeholders have different inventory modes. Based on these different inventory modes, three models and the procedures to solve these models are developed. In computational experiments, the applicability of the proposed models and procedures is verified. Management insights are summarized through analyzing the composition of average total inventory cost. Finally, the relationship between the parameters and the optimal solutions is investigated by two sensitivity analyses.

Provably Near-Optimal Balancing Policies for Multi-Echelon Stochastic Inventory Control Models

We develop the first algorithmic approach to compute provably good ordering policies for a multi-echelon, stochastic inventory system facing correlated, nonstationary and evolving demands over a finite horizon. Specifically, we study the serial system. Our approach is computationally efficient and provides worst-case guarantees. That is, the expected cost of the algorithms is guaranteed to be within a constant factor of the optimal expected cost; depending on the assumption the constant varies between two and three. Our algorithmic approach is based on an innovative scheme to account for costs in a multi-echelon, multi-period environment, as well as repeatedly balancing between opposing cost. The cost-accounting scheme, called a cause-effect cost-accounting scheme, is significantly different from traditional cost-accounting schemes in that it reallocates costs with the goal of assigning every unit of cost to the decision that caused the cost to be incurred. We believe it will have additional applications in other multi-echelon inventory models.

Payment Timing in Multiechelon Supply Chains: Cost Assessment, Incentives, and Coordination

Advanced information technologies are increasing the variety of payment triggers between supply chain stages. The cost assumptions made by standard multiechelon inventory models, however, do not have the flexibility to account for these rapid changes. We take one step towards closing this gap by focusing on common payment triggers used with wholesale prices. We introduce a notation system to explicitly connect physical and financial flows so that payment streams can be expressed as functions of standard physical inventory metrics. We then derive a new cost formulation that captures the financial inventory cost implications of such payment streams. These tools are powerful because they dramatically increase the usability and adaptability of existing multiechelon inventory models, under both traditional and more general payment terms. To illustrate, we apply these methods to derive insights on three supply chain topics in a two-echelon base stock model. First, we examine how wholesale prices affect competitive inventory policies and supply chain efficiency under standard payment terms – showing that the cost of decentralization is not only due to too little inventory at the retailer, but also to too much inventory at the supplier. Second, we explore consignment as a possible coordination mechanism – showing that full consignment causes the supplier to overly restrict the inventory at the retailer, but partial consignment can achieve coordination. Third, we study the impact of unequal costs of capital between supply chain members - providing insight into when extending lower capital cost rates to supply chain partners is beneficial.

The effect analysis of multi-echelon inventory models considering demand rate uncertainty and limited maintenance capacity

Multi-echelon technique for recoverable item control (METRIC) has been a basic model in spare part stocking problem for high value with relatively low demand items. As METRIC is improved to vari-METRIC, the accuracy of the model is significantly increased. However, METRIC-based analytical models require strict assumptions for calculating spare stock levels. Many researchers have dedicated to relax those assumptions. Most of those efforts become either computing heuristics or relatively complex models. In this study, we propose a relatively simple METRIC-based model for the optimal allocation of spare stocking problems considering uncertain demand rate and limited repair capacity at the same time. Our models can be applicable to minimise either the expected backorders (EBOs) under a certain budget restriction or spending over certain availability. The proposed model relaxes those two assumptions by applying queueing theory and conditional Poisson probability distribution on demand rate. A numerical study shows the precision improvement. The EBO variation of our proposed model is decreased more than 50% when comparing to that of vari-METRIC.

An Improved Algorithm for Multi-Echelon Inventory Models in Consideration of Changing Demand Rates

An Improved Algorithm for Multi-Echelon Inventory Models in Consideration of Changing Demand Rates

Positioning Inventory in Clinical Trial Supply Chains

As a result of slow patient recruitment and high patient costs in the United States, clinical trials are increasingly going global. While recruitment efforts benefit from a larger global footprint, the supply chain has to work harder at getting the right drug supply, to the right place, at the right time. Certain clinical trial supply chains, especially those supplying biologics, have a combination of unique attributes that have yet to be addressed by existing supply chain models. These attributes include a fixed patient horizon, an inflexible supply process, a unique set of service-level requirements, and an inability to transfer drug supplies among testing sites. In this paper, we provide a new class of multi-echelon inventory models to address these unique aspects. The resulting mathematical program is a nonlinear integer programming problem with chance constraints. Despite this complexity, we develop a solution method that transforms the original formulation into a linear integer equivalent. By analyzing special cases and through numerical study of both real-life and simulated examples, we develop novel insights into inventory positioning and the cost drivers in clinical trial supply chains.

Quantifying the Effect of Transportation Practices in Military Supply Chains

Traditional multi-echelon inventory and readiness-based models have not fully examined the ability of effective transportation utilization to reduce cost, delay times, and improve readiness in the overall military logistics network. In this paper, we develop a simulation-based methodology for quantifying the effect of transportation options (i.e., truckload shipping, less-than-truckload shipping, transshipments, and express air shipping) on shipping costs, customer wait times, abort rates, and operational availability. Simulation was used to develop a multi-echelon (depots, bases) model of regional supply chain support for aircraft spare part maintenance activities. The resulting model was used for experimentation and to develop response surface equations for the behavior of the system. The logistics implications of the results are discussed as well as managerial insights into the behavior of such systems. Our analysis indicates that focusing more on local inventory and local repair can have a significant impact on the operational availability of the system. This shift should be looked at in terms of the cost of local repair resources compared to transportation costs.

Modelling Approaches to Optimise Spares in Multi-echelon Systems

Spare parts optimisation requires an integrated approach that starts with the removal of factors that create noise: bad coding, resulting in parts proliferation; lack of classification and thus of focus; poor network practices (uncoupled warehouses, poor relation with key suppliers); and poor data integrity (non-centralised, non-real time data). Emphasis is also placed on improving forecasts and the application of multi-echelon inventory models for repairable items. The METRIC model is then applied to a hypothetical and two real cases, an underground system and a mobile telephone company in Venezuela.

A two-echelon inventory model with lost sales

Almost all multi-echelon inventory models assume that demand not satisfied immediately can be backordered. In some situations this assumption may not be realistic. For example, it may be more representative to model stockouts as lost sales when the retailers are in a competitive market and customers can easily turn to another firm when purchasing the good. Assuming lost sales at the retailers, we consider a one warehouse several retailers inventory system. Using the well-known METRIC-approximation as a framework, we present a heuristic for finding cost effective base-stock policies. In a numerical study we find that the cost of the policies suggested by the heuristic is on average 0.40% above the cost of the optimal ( S−1, S) policy.

Editorial Objectives Supply Chain Management

It is tempting to say that, for a very long time, supply chain management has been a central topic in the field of management science and operations management. In fact, however, it has evolved from the seminal work done in the 1960s on multiechelon inventory models to recent studies of various mechanisms for coordinating supply chain decisions. In this evolution, one sees a clear shift from studying centralized planning models, in which a central planner makes all the decisions to optimize a systemwide objective, to focusing on decentralized systems with independent decision makers. This is no trival change, for it is one step closer to many real life situations, it has brought about another layer of complexity, and it often requires the use of new analytical tools. The department of supply chain management was created to recognize, emphasize, and encourage this change, and it will continue to do so. Organizing supply chain activities is about determining who does what (in the case of managers, who decides what), who knows what, and the economic incentives motivating supply chain members. This suggests that the management of supply chains can be addressed along three dimensions: allocation of decision rights, information elicitation and sharing, and incentive alignment. This framework matches what we observe in practice: vendor-managed inventory is a supply chain partnership to reallocate stocking decision rights; the creation of corporate communication networks is an example of information sharing; and the myriad of contracts signed among supply chain partners are attempts to align incentives. Moreover, the above three dimensions are likely to characterize the research frontier in supply chain management for the years to come. The Department of Supply Chain Management welcomes papers that are motivated by real-world operations problems and contribute to the understanding of supply chain management issues. The contributions can be methodological, conceptual, empirical, application-oriented, etc. The department especially welcomes papers that present novel models that may open up new directions of research. Needless to say, all submitted manuscripts must follow the guidelines of Management Science, and they will be rigorously refereed according to the normal standards of the journal. Please send four copies of the paper to the departmental editor of supply chain management at the address printed above. The associate editors for the department are: Sven Axsater, Lund University Gerard P. Cachon, University of Pennsylvania Gary Eppen, University of Chicago Stephen C. Graves, MIT Albert Y. Ha, Yale University Martin A. Lariviere, Northwestern University Evan L. Porteus, Stanford University Ananth Raman, Harvard University Kaj Rosling, Lund University Jeannette Song, University of California, Irvine Sridhar Tayur, Carnegie Mellon University Seungjin Whang, Stanford University

On multi-stage production/inventory systems under stochastic demand

This paper was presented at the 1992 Conference of the International Society of Inventory Research in Budapest, as a tribute to professor Andrew C. Clark for his inspiring work on multi-echelon inventory models both in theory and practice. It reviews and extends the work of the authors on periodic review serial and convergent multi-echelon systems under stochastic stationary demand. In particular, we highlight the structure of echelon cost functions which play a central role in the derivation of the decomposition results and the optimality of base stock policies. The resulting optimal base stock policy is then compared with an MRP system in terms of cost effectiveness, given a predefined target customer service level. Another extension concerns an at first glance rather different problem; it is shown that the problem of setting safety leadtimes in a multi-stage production-to-order system with stochastic lead times leads to similar decomposition structures as those derived for multi-stage inventory systems. Finally, a discussion on possible extensions to capacitated models, models with uncertainty in both demand and production lead time as well as models with an aborescent structure concludes the paper.

Modelling and analysis of a multi-echelon inventory system A case study

In this study we discuss multi-echelon inventory models dealing with the goods within the finished goods section of a product division of Philip's Industries. A model study has been carried out in order to compare several alternatives for the way in which goods are forwarded from factory, via stores to the customers. The results have been compared with the outcomes of the model describing the actual way of forwarding. Based on the positive results of the study some recommendations could be made.