Newsvendor characterizations for one-warehouse multi-retailer inventory systems with descrete demand under the balance assumption

This paper considers a one-warehouse multi-retailer inventory system that faces discrete stochastic demand of the customers. Under the so-called balance assumption (also known as the allocation assumption), base stock policies are optimal. Our main contribution is to show that the optimal base stock levels satisfy newsvendor characterizations, which are in terms of inequalities, and to extend the newsvendor equalities known for the continuous demand model. These characterizations are appealing because they (i) are easy to explain to nonmathematical oriented people like managers and MBA students, (ii) contribute to the understanding of optimal control, (iii) help intuition development by providing direct relation between cost and optimal policy parameters

Synchronizing the Retail Supply Chain

Dit proefschrift ontwerpt een retail supply chain, die beter en goedkoper is dan de gangbare. Dit wordt bereikt door de distributie te synchroniseren op de productie¬momenten. Goederen zouden direct uit productie al stroomafwaarts moeten bewegen, van fabrikant naar retailer, tegen lage kosten, in volle pallets en in volle auto’s en in hoeveel¬heden die groot genoeg zijn om de vraag tot het volgende productiemoment te dekken. Door de formules van de "Krantenverkoper" en die van de economische ordergrootte (EOQ) aan te passen aan een multi-echelon divergerend distributienetwerk, kan ook theoretisch worden bewezen dat het stroomafwaarts positioneren van voorraden inderdaad optimaal is en dat de voorraden daardoor zullen dalen. De huidige magazijnen van de leveranciers kunnen worden gereduceerd tot overslagpunten, waar goederen van de verschillende fabrieken van een leverancier worden samengebracht om rijden met vollere vrachtwagens mogelijk maken. Kleinere hoeveelheden kunnen leveranciers beter afleveren bij het dichtstbijzijnde distributiecentrum van een retailer, waarna de retailer zelf het deel met bestemming elders verder vervoert. Tenslotte kan de winkelbevoorrading worden aangepast aan de schapruimte, waardoor de werkwijze in de distributiecentra kan worden gerationaliseerd.Piet van der Vlist (1947) was born in Ouderkerk aan den IJssel. He received his high-school diploma from the Marnix Gymnasium in Rotterdam. Also in Rotterdam he graduated as Electronics Engineer at the University of Applied Sciences. He obtained a Master of Science in Electronics at the Delft University of Technology and one in Management Sciences at the University of Twente. He worked 15 years with the Dutch Ministry of Defense on the design and realization of the first generation digital communications systems. Then he joined Bakkenist Management Consultants and later Deloitte Consultancy, together for over 20 years. As consultant he was involved in numerous projects on Data exchange and Supply Chain redesign. Besides that, he was for 11 years (part-time) professor in ICT and Logistics at the Eindhoven University of Technology. Piet wrote and edited several books on data exchange and published numerous articles in business and scientific journals. A fairly good overview of his scientific career can be found in the "Liber Amicorum" that his friends wrote when he left Eindhoven University1. His current research interests lie in the design and management of retail supply chains, all the way from production down to the shelves. He found that the supply chain with the overall lowest costs requires synchronization of distribution to production and not the other way around as current practice seems to dictate. When he had to quit his jobs for health reasons, he finally found the opportunity to devote his time to research and extend the theory that supports Supply Chain Synchronization. He programmed built to purpose simulation models to get a better insight in the dynamics of synchronized supply chains. He joined both the Rotterdam Erasmus University to work with Professor Jo van Nunen and the Eindhoven University of Technology to work with Professor Ton de Kok. This PhD thesis is the result of that effort.This thesis is a design of a retail supply chain that is better and cheaper than the usual one. This is achieved by synchronizing distribution to production. Right from production goods should move downstream the supply chain at low cost in full pallets and in full truckloads, in quantities large enough to cover the needs till the next production run. By extending both the Newsvendor- and the EOQ-formulae to a multi-echelon divergent network, it can be proved that such forward positioning of inventory indeed is optimal and that overall supply chain inventories will drop. The suppliers’ warehouses become stockless cross docking points, where goods from the supplier’s various sourcing plants are brought together to consolidate them into full truckloads. Whenever suppliers deliver lower volumes, they better bring these goods to the nearest retailer’s facility; thereafter the retailer himself should move these goods onward to the proper destination within the retailer’s network. And finally shop replenishment should be rationalized based on shelf coverage, so as to enhance the retailer’s warehouse operations

Performance Evaluation of Stochastic Multi-Echelon Inventory Systems: A Survey

Globalization, product proliferation, and fast product innovation have significantly increased the complexities of supply chains in many industries. One of the most important advancements of supply chain management in recent years is the development of models and methodologies for controlling inventory in general supply networks under uncertainty and their widefspread applications to industry. These developments are based on three generic methods: the queueing-inventory method, the lead-time demand method and the flow-unit method. In this paper, we compare and contrast these methods by discussing their strengths and weaknesses, their differences and connections, and showing how to apply them systematically to characterize and evaluate various supply networks with different supply processes, inventory policies, and demand processes. Our objective is to forge links among research strands on different methods and various network topologies so as to develop unified methodologies.Masdar Institute of Science and TechnologyNational Science Foundation (U.S.) (NSF Contract CMMI-0758069)National Science Foundation (U.S.) (Career Award CMMI-0747779)Bayer Business ServicesSAP A

Optimal control of serial, multi-echelon inventory/production systems with periodic batching

We consider a single-item, periodic-review, serial, multi-echelon inventory system, with linear inventory holding and penalty costs. In order to facilitate shipment consolidation and capacity planning, we assume the system has implemented periodic batching: each stage is allowed to order at given equidistant times. Further, for each stage except the most downstream one, the reorder interval is assumed to be an integer multiple of the reorder interval of the next downstream stage. This reflects the fact that the further upstream in a supply chain, the higher setup times and costs tend to be, and thus stronger batching is desired. Our model with periodic batching is a direct generalization of the serial, multi-echelon model of Clark and Scarf (1960). For this generalized model, we prove the optimality of basestock policies, we derive Newsboy-type characterizations for the optimal basestock levels, and we describe an efficient exact solution procedure for the case with mixed Erlang demands. Finally, we present extensions to assembly systems and to systems with a modified fill rate constraint instead of backorder costs. Subject classification: Inventory/Production: Multi-echelon, stochastic demand, periodic batching, optimal policies.

A Multi-echelon Inventory System with Supplier Selection and Order Allocation under Stochastic Demand

This article addresses the development of an integrated supplier selection and inventory control problems in supply chain management by developing a mathematical model for a multi-echelon system. In particular, a buyer firm that consists of one warehouse and N identical retailers wants to procure a type of product from a group of potential suppliers, which may require different price, ordering cost, lead time and have restriction on minimum and maximum total order size, to satisfy the stochastic demand. A continuous review system that implements the order quantity, reorder point (Q, R) inventory policy is considered in the model. The objective of the model is to select suppliers and to determine the optimal inventory policy that coordinates stock level between each echelon of the system while properly allocating orders among selected suppliers to maximize the expected profit. The model has been solved by decomposing the mixed integer nonlinear programming model into two sub-models. Numerical experiments are conducted to evaluate the model and some managerial insights are obtained by performing some sensitivity analysis

Modeling inventory and responsiveness costs in a supply chain

Evaluation of supply chain performance is often complicated by the various interrelationships that exist within the network of suppliers. Currently many supply chain metrics cannot be analytically determined. Instead, metrics are derived from monitoring historical data, which is commonly referred to as Supply Chain Analytics. With these analytics it is possible to answer questions such as: What is the inventory cost distribution across the chain? What is the actual inventory turnover ratio? What is the cost of demand changes to individual suppliers? However, this approach requires a significant amount of historical data which must be continuously extracted from the associated Enterprise Resources Planning (ERP) system. In this dissertation models are developed for evaluating two Supply Chain metrics, as an alternative to the use of Supply Chain Analytics. First, inventory costs are estimated by supplier in a deterministic (Q , R, δ )2 supply chain. In this arrangement each part has two sequential reorder (R) inventory locations: (i) on the output side of the seller and (ii) on the input side of the buyer. In most cases the inventory policies are not synchronized and as a result the inventory behavior is not easily characterized and tends to exhibit long cycles. This is primarily due to the difference in production rates ( δ), production batch sizes, and the selection of supply order quantities (Q) for logistics convenience. The (Q , R, δ )2 model that is developed is an extension of the joint economic lot size (JELS) model first proposed by Banerjee (1986). JELS is derived as a compromise between the seller\u27s and the buyer\u27s economic lot sizes and therefore attempts to synchronize the supply policy. The (Q , R, δ )2 model is an approximation since it approximates the average inventory behavior across a range of supply cycles. Several supply relationships are considered by capturing the inventory behavior for each supplier in that relationship. For several case studies the joint inventory cost for a supply pair tends to be a stepped convex function. Second, a measure is derived for responsiveness of a supply chain as a function of the expected annual cost of making inventory and production capacity adjustments to account for a series of significant demand change events. Modern supply chains are expected to use changes in production capacity (as opposed to inventory) to react to significant demand changes. Significant demand changes are defined as shifts in market conditions that cannot be buffered by finished product inventory alone and require adjustments in the supply policy. These changes could involve a ± 25% change in the uniform demand level. The research question is what these costs are and how they are being shared within the network of suppliers. The developed measure is applicable in a multi-product supply chain and considers both demand correlations and resource commonality. Finally, the behavior of the two developed metrics is studied as a function of key supply chain parameters (e.g., reorder levels, batch sizes, and demand rate changes). A deterministic simulation model and program was developed for this purpose

Effective Multi-echelon Inventory Systems for Supplier Selection and Order Allocation

Successful supply chain management requires an effective sourcing strategy to counteract uncertainties in both the suppliers and demands. Therefore, determining a better sourcing policy is critical in most of industries. Supplier selection is an essential task within the sourcing strategy. A well-selected set of suppliers makes a strategic difference to an organization\u27s ability to reduce costs and improve the quality of its end products. To discover the cost structure of selecting a supplier, it is more interesting to further determine appropriate levels of inventory in each echelon for different suppliers. This dissertation focuses on the study of the integrated supplier selection, order allocation and inventory control problems in a multi-echelon supply chain. First, we investigate a non-order-splitting inventory system in supply chain management. In particular, a buyer firm that consists of one warehouse and N identical retailers procures a type of product from a group of potential suppliers, which may have different prices, ordering costs, lead times and have restriction on minimum and maximum total order size, to satisfy stochastic demand. A continuous review system that implements the order quantity, reorder point (Q, R) inventory policy is considered in the proposed model. The model is solved by decomposing the mixed integer nonlinear programming model into two sub-models. Numerical experiments are conducted to evaluate the model and some managerial insights are obtained with sensitivity analysis. In the next place, we extend the study to consider the multi-echelon system with the order-splitting policy. In particular, the warehouse acquisition takes place when the inventory level depletes to a reorder point R, and the order Q is simultaneously split among m selected suppliers. This consideration is important since it could pool lead time risks by splitting replenishment orders among multiple suppliers simultaneously. We develop an exact analysis for the order-splitting model in the multi-echelon system, and formulate the problem in a Mixed Integer Nonlinear Programming (MINLP) model. To demonstrate the solvability and the effectiveness of the model, we conduct several numerical analyses, and further conduct simulation models to verify the correctness of the proposed mathematical model