Johan Marklund

Decentralized inventory control in a two-level distribution system

Abstract We consider a model for decentralized inventory control in a two-level distribution system with one central warehouse and N non-identical retailers. All installations use continuous review installation stock ( R , Q )-policies for replenishing their inventories. Our approach is based on an approximate cost evaluation technique, where the retailers replace their stochastic lead-times by correct averages. By introducing a modified cost-structure at the warehouse, the multi-level inventory control problem can be decomposed into N +1 single level sub-problems, one problem for each installation. The sub-problems are then solved in an iterative manner by a simple coordination procedure, which can be interpreted as a negotiation process. In the case of normally distributed demand we show that the procedure converges to a near optimal solution. To assess the quality of the involved approximation an upper bound for the relative cost increase of using the obtained solution is derived. We also provide a numerical study illustrating the performance of our approach.

Research Note---Vertical Information Sharing in a Volatile Market

When demand is uncertain, manufacturers and retailers often have private information on future demand, and such information asymmetry impacts strategic interaction in distribution channels. In this paper, we investigate a channel consisting of a manufacturer and a downstream retailer facing a product market characterized by short product life, uncertain demand, and price rigidity. Assuming the firms have asymmetric information about the demand volatility, we examine the potential benefits of sharing information and contracts that facilitate such cooperation. We conclude that under a wholesale price regime, information sharing might not improve channel profits when the retailer underestimates the demand volatility but the manufacturer does not. Although information sharing is always beneficial under a two-part tariff regime, it is in general not sufficient to achieve sharing, and additional contractual arrangements are necessary. The contract types we consider to facilitate sharing are profit sharing and buyback contracts.

Controlling Inventories in Divergent Supply Chains with Advance-Order Information

This paper considers a generic one-warehouse multiple-retailer inventory system under continuous review, where customers provide perfect advance-order information. More specifically, each customer order entails a due date specifying when the customer wants the item delivered. The information is perfect in the sense that a placed order cannot be revised. With the intent of using the advance-order information fully throughout the supply chain, each installation replenishes its stock using order base-stock policies (see Hariharan and Zipkin 1995). As for stock allocation, the presence of advance-order information at the central warehouse raises important questions regarding when reservations should be made for different retailers, i.e., how to make best use of the available temporal information to allocate items to retailers. Exact and approximate cost evaluation techniques are presented for the general case, the general reservation policy, as well as for the two special cases of reserving as early as possible, the complete reservation policy, and as late as possible, the last-minute allocation policy. A numerical study illustrates the performance of the proposed heuristics and provides insights on the value of using advance-order information in supply chain inventory control.

Optimal Position-Based Warehouse Ordering in Divergent Two-Echelon Inventory Systems

A continuous-review two-echelon inventory system with one central warehouse and a number of nonidentical retailers is considered. The retailers face independent Poisson demand and apply standard (R, Q) policies. The retailer order quantities are fixed integer multiples of a certain batch size, representing the smallest pallet or container size transported in the system. A warehouse order may consist of one or several such batches. We derive a new policy for warehouse ordering, which is optimal in the broad class of position-based policies relying on complete information about the retailer inventory positions, transportation times, cost structures, and demand distributions at all facilities. The exact analysis of the new policy includes a method for determining the expected total inventory holding and backorder costs for the entire system. The class of position-based policies encompasses both the traditional installation-stock and echelon-stock (R, Q) policies, as well as the more sophisticated policies recently analyzed in the literature. The value of more carefully incorporating a richer information structure into the warehouse ordering policy is illustrated in a numerical study.

Evaluation of stock allocation policies in a divergent inventory system with shipment consolidation

In this paper we consider a one-warehouse N-retailer inventory system characterized by access to real-time point-of-sale data, and a time based dispatching and shipment consolidation policy at the warehouse. More precisely, inventory is reviewed continuously, while a consolidated shipment (for example, a truck) to all retailers is dispatched from the warehouse at regular time intervals. The focus is on investigating the cost benefits of using state-dependent myopic allocation policies instead of a simple FCFS (First-Come-First-Serve) rule to allocate shipped goods to the retailers. The analysis aims to shed some light on when, if ever, FCFS is a reasonable policy to use in this type of system? The FCFS allocations of items to retailers are determined by the sequence in which retailer orders (or equivalently customer demands) arrive to the warehouse. Applying the myopic policy enables the warehouse to postpone the allocation decision to the moment of shipment (from the warehouse) or the moments of delivery (to the different retailers), and to base it on the inventory information available at those times. The myopic allocation method we study is often used in the literature on periodic review systems.

Lower Bounds and Heuristics for Supply Chain Stock Allocation

Assume that m periods with stochastic demand remain until the next replenishment arrives at a central warehouse. How should the available inventory be allocated among N retailers? This paper presents a new policy and a new lower bound for the expected cost of this problem. The lower bound becomes tight as N → ∞. The infinite horizon problem then decomposes into N independent m-period problems with optimal retailer ship-up-to levels that decrease over the m periods, and the warehouse is optimally replenished by an order-up-to level that renders zero (local) warehouse safety stock at the end of each replenishment cycle. Based on the lower bound solution, we suggest a heuristic for finite N. In a numerical study it outperforms the heuristic by Jackson [Jackson, P. L. 1988. Stock allocation in a two-echelon distribution system or what to do until your ship comes in. Management Sci.34(7) 880--895], and the new lower bound improves on Clark and Scarfs [Clark, A. J., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Management Sci.6(4) 475--490] bound when N is not too small. Moreover, the warehouse zero-safety-stock heuristic is comparable to Clark and Scarfs warehouse policy for lead times that are not too long. The suggested approach is quite general and may be applied to other logistical problems. In the present application it retains some of the risk-pooling benefits of holding central warehouse stock.

Inventory Control in a Spare Parts Distribution System with Emergency Stocks and Pipeline Information

Motivated by collaboration with a global spare parts service provider, we consider a two-echelon inventory system with multiple local warehouses, a so-called support warehouse, and a central warehouse with ample capacity. In case of stock-outs, the local warehouses can receive emergency shipments from the support warehouse or the central warehouse at an extra cost. Our focus is on using information on orders in the replenishment pipeline, i.e., pipeline information, to achieve cost-efficient policies for requesting emergency shipments. We introduce a policy where the request for an emergency shipment is based on the time until an outstanding order will reach the stock point considered. The goal is to determine how long one should wait for stock in the replenishment pipeline before requesting an emergency shipment, and the cost effects of using pipeline information in this manner. The analysis utilizes results from queuing theory and provides a decomposition technique for optimizing the policy parameters that reduces the complex multiechelon problem to more manageable single-echelon problems. The performance of our policy indicates that there can be a significant benefit in using pipeline information.

Multi-Echelon Inventory Control - A Normal Demand Model for Implementation in Practice

This paper presents an approximation model for coordinated control of one-warehouse multiple-retailer inventory systems, where all locations use continuous review (R, nQ) policies. The motivation stems from close collaboration with a supply chain management software company, Syncron International, and one of their customers. A core objective has been to develop an accurate method for determining near-optimal reorder points that can be directly applied to real-life systems. The approach is based on decomposing the complex multi-echelon problem into N + 1 single-echelon problems, using a near-optimal-induced backorder cost at the central warehouse. Important extensions made compared to earlier work include the addition of procedures to adjust for lead-time variability, and for undershooting the reorder point when customers’ order sizes vary. The result is a flexible model that is computationally and conceptually simple enough to be implemented in practice. A numerical study, including real data from the case company, illustrates that the new model outperforms existing methods in the literature. Compared to the current methods used by the case company, it offers significant improvements in both service-level fulfilment and system-wide inventory holding costs. Implementations of the model into the Syncron software are in progress.

A model for heuristic coordination of real life distribution inventory systems with lumpy demand

This paper presents an approximation model for optimizing reorder points in one-warehouse N-retailer inventory systems subject to highly variable lumpy demand. The motivation for this work stems from close cooperation with a supply chain management software company, Syncron International, and one of their customers, a global spare parts provider. The model heuristically coordinates the inventory system using a near optimal induced backorder cost at the central warehouse. This induced backorder cost captures the impact that a reorder point decision at the warehouse has on the retailers’ costs, and decomposes the multi-echelon problem into solving N+1 single-echelon problems. The decomposition framework renders a flexible model that is computationally and conceptually simple enough to be implemented in practice.

Exact Analysis of Divergent Inventory Systems with Time-Based Shipment Consolidation and Compound Poisson Demand

Sustainable and efficient management of a distribution system requires coordination between transportation planning and inventory control decisions. In this context, we consider a one warehouse multi-retailer inventory system with a time-based shipment consolidation policy at the warehouse. This means that there are fixed costs associated with each shipment, and retailer orders are consolidated and shipped periodically to groups of retailers sharing the same delivery routes. Customer demand is compound Poisson distributed and unsatisfied demand at each stock point is backordered and allocated on a first-come first-served basis. The system is centralized and inventory levels are reviewed continuously. The warehouse has access to real-time inventory information from the retailers, and uses a (R, nQ) policy to replenish from an outside supplier/manufacturer. We derive the exact probability distributions for the inventory levels at the retailers, and use these to obtain exact expressions for the system’s expe...