(This article originally appeared in Management Science, April 1997, Volume 43, Number 4, pp. 546-558, published by The Institute of Management Sciences.)

Consider a series of companies in a supply chain, each of whom orders from its immediate upstream member. In this setting, inbound orders from a downstream member serve as a valuable informational input to upstream production and inventory decisions. This paper claims that the information transferred in the form of "orders" tends to be distorted and can misguide upstream members in their inventory and production decisions. In particular, the variance of orders may be larger than that of sales, and distortion tends to increase as one moves upstream-a phenomenon termed "bullwhip effect." This paper analyzes four sources of the bullwhip effect: demand signal processing, rationing game, order batching, and price variations. Actions that can be taken to mitigate the detrimental impact of this distortion are also discussed.

Information distortion in a supply chain: the bullwhip effect

Publisher Summary This chapter reviews the supply chain coordination with contracts. Numerous supply chain models are discussed. In each model, the supply chain optimal actions are identified. The chapter extends the newsvendor model by allowing the retailer to choose the retail price in addition to the stocking quantity. Coordination is more complex in this setting because the incentives provided to align one action might cause distortions with the other action. The newsvendor model is also extended by allowing the retailer to exert costly effort to increase demand. Coordination is challenging because the retailer's effort is noncontractible—that is, the firms cannot write contracts based on the effort chosen. The chapter also discusses an infinite horizon stochastic demand model in which the retailer receives replenishments from a supplier after a constant lead time. Coordination requires that the retailer chooses a large basestock level.

Supply Chain Coordination with Contracts

List of notations Preface to the second edition Preface to the first edition 1. Stochastic programming models 2. Two-stage problems 3. Multistage problems 4. Optimization models with probabilistic constraints 5. Statistical inference 6. Risk averse optimization 7. Background material 8. Bibliographical remarks Bibliography Index.

Lectures on Stochastic Programming: Modeling and Theory

In traditional supply chain inventory management, orders are the only information firms exchange, but information technology now allows firms to share demand and inventory data quickly and inexpensively. We study the value of sharing these data in a model with one supplier, N identical retailers, and stationary stochastic consumer demand. There are inventory holding costs and back-order penalty costs. We compare a traditional information policy that does not use shared information with a full information policy that does exploit shared information. In a numerical study we find that supply chain costs are 2.2% lower on average with the full information policy than with the traditional information policy, and the maximum difference is 12.1%. We also develop a simulation-based lower bound over all feasible policies. The cost difference between the traditional information policy and the lower bound is an upper bound on the value of information sharing: In the same study, that difference is 3.4% on average, and no more than 13.8%. We contrast the value of information sharing with two other benefits of information technology, faster and cheaper order processing, which lead to shorter lead times and smaller batch sizes, respectively. In our sample, cutting lead times nearly in half reduces costs by 21% on average, and cutting batches in half reduces costs by 22% on average. For the settings we study, we conclude that implementing information technology to accelerate and smooth the physical flow of goods through a supply chain is significantly more valuable than using information technology to expand the flow of information.

Supply Chain Inventory Management and the Value of Shared Information

Supply chain design and analysis:: Models and methods

In the last several years there have been a number of papers discussing optimal policies for the inventory problem. Almost without exception these papers are devoted to the determination of optimal purchasing quantities at a single installation faced with some pattern of demand. It has been customary to make the assumption that when the installation in question requests a shipment of stock, this shipment will be delivered in a fixed or perhaps random length of time, but at any rate with a time lag which is independent of the size of the order placed. There are, however, a number of situations met in practice in which this assumption is not a tenable one. An important example arises when there are several installations, say 1, 2,..., N, with installation 1 receiving stock from 2, with 2 receiving stock from 3, etc. In this example, if an order is placed by installation 1 for stock from installation 2, the length of time for delivery of this stock is determined not only by the natural lead time between these two sites, but also by the availability of stock at the second installation. In this paper we shall consider the problem of determining optimal purchasing quantities in a multi-installation model of this type.

Optimal Policies for a Multi-Echelon Inventory Problem

Approximate Solutions to a Simple Multi-Echelon Inventory Problem

I all came together on a Friday morning in midApril 1959. Just the two of us, in a conference room at Planning Research Corporation in Westwood, CA. The paper was a direct result of this meeting. At the time, we did not think much about what impact the paper would have on future work in this area, but we are pleased and honored that it has been selected as one of the influential papers published in the 50-year history of Management Science. I had been at Planning Research Corporation for just a short time after being in the Logistics Department at the RAND Corporation for five years. During my first couple of years at RAND, I helped in the design and implementation of inventory control procedures based on the Wilson lot size formula and a variable safety level concept to allow for demand uncertainty and differences in unit prices, factors not considered in the stock policies then current in the Air Force. However, I became generally disturbed that each facility (Air Force bases and a depot) was being considered independently, ignoring the fact that they were intimately connected in the real world. In particular, supply performance at the bases was being significantly degraded by lack of proper support from the depot. So, I decided to attack this multiechelon problem from an analytic point of view based on the classical AHM (Arrow-Harris-Marschak) model, particularly in order to accommodate time-dependent factors resulting from the phase-in and phase-out of weapon systems. Starting with the most simplifying assumptions and a single-user activity supported by one higher-level facility (depot), I was able to formulate a procedure by which levels at the user facility could be determined by the AHM model, results of which were then used as inputs to a similar calculation at the depot level. With this basic approach, I was able to then consider nonzero resupply time due to the work of Karlin and Scarf and fixed reorder costs at the depot due to the work of Scarf. Also, the approach was easily

https://pubsonline.informs.org/doi/pdf/10.1287/mnsc.1040.0292

Andrew J. Clark

Papers

Optimal Policies for a Multi-Echelon Inventory Problem

Approximate Solutions to a Simple Multi-Echelon Inventory Problem

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