David Simchi-Levi

The impact of exponential smoothing forecasts on the bullwhip effect

An important phenomenon often observed in supply chain management, known as the bullwhip effect, implies that demand variability increases as one moves up the supply chain, i.e., as one moves away from customer demand. In this paper we quantify this effect for simple, two-stage, supply chains consisting of a single retailer and a single manufacturer. We demonstrate that the use of an exponential smoothing forecast by the retailer can cause the bullwhip effect and contrast these results with the increase in variability due to the use of a moving average forecast. We consider two types of demand processes, a correlated demand process and a demand process with a linear trend. We then discuss several important managerial insights that can be drawn from this research. c 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 269{286, 2000

Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case

We analyze a finite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon. We show that when the demand model is additive, the profit-to-go functions arek-concave and hence an ( s, S, p) policy is optimal. In such a policy, the period inventory is managed based on the classical ( s, S) policy and price is determined based on the inventory position at the beginning of each period. For more general demand functions, i.e., multiplicative plus additive functions, we demonstrate that the profit-to-go function is not necessarilyk-concave and an ( s, S, p) policy is not necessarily optimal. We introduce a new concept, the symmetrick-concave functions, and apply it to provide a characterization of the optimal policy.

Risk Aversion in Inventory Management

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multiperiod inventory models as well as multiperiod models that coordinate inventory and pricing strategies. We show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. These structural results are extended to models in which the decision maker has access to a (partially) complete financial market and can hedge its operational risk through trading financial securities. Computational results demonstrate that the optimal policy is relatively insensitive to small changes in the decision-makers level of risk aversion.

Coordination of Pricing and Inventory Decisions: A Survey and Classification

Recent years have seen scores of retail and manufacturing companies exploring innovative pricing strategies in an effort to improve their operations and ultimately the bottom line. Firms are employing such varied tools as dynamic pricing over time, target pricing to different classes of customers, or pricing to learn about customer demand. The benefits can be significant, including not only potential increases in profit, but also improvements such as reduction in demand or production variability, resulting in more efficient supply chains.

Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case

We analyze an infinite horizon, single-product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are identically distributed random variables that are independent of each other, and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period, and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to maximize expected discounted, or expected average, profit over the infinite planning horizon. We show that a stationary ( s,S,p) policy is optimal for both the discounted and average profit models with general demand functions. In such a policy, the period inventory is managed based on the classical ( s,S) policy, and price is determined based on the inventory position at the beginning of each period.

New worst-case results for the bin-packing problem

In this note we consider the familiar bin-packing problem and provide new worst-case results for a number of classical heuristics. We show that the first-fit and best-fit heuristics have an absolute performance ratio of no more than 1.75, and first-fit decreasing and best-fit decreasing heuristics have an absolute performance ratio of 1.5. The latter is the best possible absolute performance ratio for the bin-packing problem, unless P = NP.

A Location Based Heuristic for General Routing Problems

We present a general framework for modeling routing problems based on formulating them as a traditional location problem called the capacitated concentrator location problem. We apply this framework to two classical routing problems: the capacitated vehicle routing problem and the inventory routing problem. In the former case, the heuristic is proven to be asymptotically optimal for any distribution of customer demands and locations. Computational experiments show that the heuristic performs well for both problems and, in most cases, outperforms all published heuristics on a set of standard test problems.

Effective Zero-Inventory-Ordering Policies for the Single-Warehouse Multiretailer Problem with Piecewise Linear Cost Structures

We analyze the problem faced by companies that rely on TL (Truckload) and LTL (Less than Truckload) carriers for the distribution of products across their supply chain. Our goal is to design simple inventory policies and transportation strategies to satisfy time varying demands over a finite horizon, while minimizing system wide cost by taking advantage of quantity discounts in the transportation cost structures. For this purpose, we study the cost effectiveness of restricting the inventory policies to the class of zero-inventory-ordering (ZIO) policies in a single-warehouse multiretailer scenario in which the warehouse serves as a cross-dock facility. In particular, we demonstrate that there exists a ZIO inventory policy whose total inventory and transportation cost is no more than 4/3 (5.6/4.6 if transportation costs are stationary) times the optimal cost. However, finding the best ZIO policy is an NP hard problem as well. Thus, we propose two algorithms to find an effective ZIO policy: An exact algorithm whose running time is polynomial for any fixed number of retailers, and a linear-programming-based heuristic whose effectiveness is demonstrated in a series of computational experiments. Finally, we extend the worst-case results developed in this paper to systems in which the warehouse does hold inventory.

The Bullwhip Effect: Managerial Insights on the Impact of Forecasting and Information on Variability in a Supply Chain

An important observation in supply chain management, popularly known as the bull-whip effect, suggests that demand variability increases as one moves up a supply chain. For example, empirical evidence suggests that the orders placed by a retailer tend to be much more variable than the customer demand seen by that retailer. This increase in variability propagates up the supply chain, distorting the pattern of orders received by distributors, manufacturers and suppliers.

Dispatching vehicles in a mega container terminal

Abstract.We consider a container terminal discharging and uploading containers to and from ships. The discharged containers are stored at prespecified storage locations in the terminal yard. Containers are moved between the ship area and the yard using a fleet of vehicles, each of which can carry one container at a time. The problem is to dispatch vehicles to the containers so as to minimize the total time it takes to serve a ship, which is the total time it takes to discharge all containers from the ship and upload new containers onto the ship. We develop easily implementable heuristic algorithms and identify both the absolute and asymptotic worst-case performance ratios of these heuristics. In simple settings, most of these algorithms are optimal, while in more general settings, we show, through numerical experiments, that these algorithms obtain near-optimal results for the dispatching problem.