Frank Y. Chen

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

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.

A newsvendor pricing game

This paper considers a horizontal market of multiple firms that face stochastic price-dependent demand. The firms make joint pricing/inventory decisions and use price to compete for market demand. With fairly general demand models that are price-dependent, stochastic, and substitutable among firms, we prove the existence and uniqueness of the pure-strategy Nash equilibrium. The market at the equilibrium exhibits a bias toward under-pricing caused by competition; specifically, raising prices at any equilibrium of the game increases the total system profit, and at any joint-optimal set of pricing levels each self-interested firm has an incentive to lower its price. This result closely parallels that obtained in the inventory competition games in which prices are fixed and the bias is toward overstocking.

Inventory models with minimal service level constraints

Abstract This paper investigates inventory models in which the stockout cost is replaced by a minimal service level constraint (SLC) that requires a certain level of service to be met in every period. The minimal service level approach has the virtue of simplifying the computation of an optimal ordering policy, because the optimal reorder level is solely determined by the minimal SLC and demand distributions. It is found that above a certain “critical” service level, the optimal (s,S) policy “collapses” to a simple base-stock or order-up-to level policy, which is independent on the cost parameters. This shows the minimal SLC models to be qualitatively different from their shortage cost counterparts. We also demonstrate that the “imputed shortage cost” transforming a minimal SLC model to a shortage cost model does not generally exist. The minimal SLC approach is extended to models with negligible set-up costs. The optimality of myopic base-stock policies is established under mild conditions.

Value of a put option to the risk-averse newsvendor

In this paper we consider an extension of the single-period inventory model with stochastic demand where a put option can be purchased to reduce losses resulting from low demand. The newsvendor not only chooses the order quantity but also determines the “strike price” and/or the “strike quantity” of the put option. As the buyer of the put option, the newsvendor pays the option writer an amount that equals the expected option payoff plus a risk premium and receives from the option writer the strike price (adjusted for salvage value) for each unit that the demand falls below the strike quantity. The newsvendor is risk-averse and attempts to maximize an expected utility function. We show that: (i) the same order quantity maximizes the expected profit with or without the option; and (ii) the strike price and strike quantity do not affect the newsvendors maximum expected profit but they do affect the variance of the profit. We use concepts from stochastic dominance theory to prove the following result: if the newsvendor uses the expected profit maximizing order quantity and if she has a quadratic utility function, then maximizing her expected utility is equivalent to minimizing the variance of the profit. Sensitivity analysis results indicate that under poor economic conditions (low sale price/high purchase cost) it may not be optimal to purchase the option. We also find that when the option writer assumes a higher risk/return for the random option payoff (that he pays the newsvendor) the newsvendor can reduce her profit uncertainty by choosing the strike price or strike quantity optimally.

Improving Supply Chain Performance and Managing Risk Under Weather-Related Demand Uncertainty

We consider a manufacturer-retailer supply chain for a seasonal product whose demand is weather sensitive. The retailer orders from the manufacturer (supplier) prior to the selling season and then sells to the market. We examine how a manufacturer can structure a weather-linked rebate to improve his expected profit. The proposed class of rebate contracts offers several advantages over many other contract structures, including no required verification of leftover inventory and/or markdown amounts, and no adverse effect on sales effort by the retailer. We provide a thorough analysis of the manufacturers and retailers decisions in this context. We show that the weather-linked rebate can take many different forms, and this flexibility allows the supplier to design contracts that are Pareto improving and/or limit his risk in offering the contract and the retailers risk in accepting it. For weather rebates with certain characteristics, the manufacturer can fully hedge his risks of offering a weather rebate by paying a risk premium; we show how this can be accomplished. We also show that the basic structural results extend to settings in which the two parties would like to limit their risk.

Analysis of third-party warehousing contracts with commitments

Abstract This paper considers multi-period warehousing contracts under random space demand. A typical contract is specified by a starting space commitment plus a certain number of times at which the commitment can be further modified. Three forms of contracts are analysed: (1) there is a restriction on the range of commitment changes and the schedule for the changes is preset by the warehouser; (2) the same as form (1) but there is no restriction on the range; (3) the same as form (2) but the schedule for the changes is chosen by the user. We explore properties and algorithms for the three problems from the users perspective. Solutions of simple form are obtained for the first two models and an efficient dynamic programming (DP) procedure is proposed for the last. A numerical comparison of the total expected leasing costs suggests that under certain demand patterns, contract forms (2) and (3) could be cost effective.

Integrated Inventory Replenishment and Temporal Shipment Consolidation: A Comparison of Quantity-Based and Time-Based Models

In this paper we present two models for joint stock replenishment and shipment consolidation decisions which arise in the context of vendor managed inventory. Stock replenishment from suppliers or shipment to customers each incurs a lump-sum cost to the vendor. We assume the vendor uses the reorder point, lot-size policy to replenish stock and one of two schemes to dispatch shipment: the time-based and quantity-based consolidation schemes. Under the time-based (quantity-based) scheme, a shipment is dispatched periodically (when a certain quantity of outstanding demand is accumulated). The basic finding is that the quantity-based scheme can outperform the time-based counterpart while the reverse never occurs.

Analysis of supply contracts with minimum total order quantity commitments and non-stationary demands

Abstract In this paper we address a buyer–supplier arrangement of particular importance: total order quantity commitment (TOQC). Under the TOQC contract that has been negotiated between the buyer and the supplier, the former agrees to an obligation to procure a certain quantity of an item from the latter over the predetermined period of time (additional quantity can be obtained maybe at a different price). The optimal inventory replenishment policy is shown to be dual order-up-to levels under a given TOQC, and the optimal TOQC is also demonstrated to be mathematically straightforward to obtain.