Inventory Management for Customers with Alternative Lead Times

It is common for suppliers operating in batch‐production mode to deal with patient and impatient customers. This paper considers inventory models in which a supplier provides alternative lead times to its customers: a short or a long lead time. Orders from patient customers can be taken by the supplier and included in the next production cycle, while orders from impatient customers have to be satisfied from the on‐hand inventory. We denote the action to commit one unit of on‐hand inventory to patient or impatient customers as the inventory‐commitment decision, and the initial inventory stocking as the inventory‐replenishment decision. We first characterize the optimal inventory‐commitment policy as a threshold type, and then prove that the optimal inventory‐replenishment policy is a base‐stock type. Then, we extend our analysis to models to consider cases of a multi‐cycle setting, a supply‐capacity constraint, and the on‐line charged inventory‐holding cost. We also evaluate and compare the performances of the optimal inventory‐commitment policy and the inventory‐rationing policy. Finally, to further investigate the benefits and pitfalls of introducing an alternative lead‐time choice, we use the customer‐choice model to study the demand gains and losses, known as demand‐induction and demand‐cannibalization effects, respectively.     

Misplaced Inventory and Radio‐Frequency Identification (RFID) Technology: Information and Coordination

Misplaced inventory is a major operational problem in many supply chains. Radio‐frequency identification (RFID) technology has been publicized as a promising solution for the misplaced inventory. Adoption of this technology has a fixed cost and variable cost of implementation, which can cause incentive issues in the supply chain. In this paper, we consider a supply chain under misplacement of inventory subject to uncertain demand. We study both centralized and decentralized cases and identify the conditions to coordinate the supply chain under implementation of RFID. We show that the incentives of the parties for investing in the technology are not perfectly aligned in the existence of the fixed cost of investment. Based on the relative payments of the parties for the fixed cost of investment, the incentives to adopt RFID can be characterized into regions, where we observe only one party or two parties benefiting from the technology when the tag price falls in a region specified in the paper. We further establish the effects of changes in mean and variance of a uniform demand on the incentives for investing in RFID and find that the incentives of the firms may indeed decrease as demand becomes more variable.     

Optimal Sourcing and Lead‐Time Reduction under Evolutionary Demand Risk

We develop a real‐options model for optimizing production and sourcing choices under evolutionary supply‐chain risk. We model lead time as an endogenous decision and calculate the cost differential required to compensate for the risk exposure coming from lead time. The shape of the resulting cost‐differential frontier reveals the term structure of supply‐chain risk premiums and provides guidance as to the potential value of lead‐time reduction. Under constant demand volatility, the break‐even cost differential increases in volatility and lead time at a decreasing rate, making incremental lead‐time reduction less valuable than full lead‐time reduction. Stochastic demand volatility increases the relative value of incremental lead‐time reduction. When demand has a heavy right tail, the value of lead‐time reduction depends on how extreme values of demand are incorporated into the forecasting process. The cost‐differential frontier is invariant to discount rates, making the cost of capital irrelevant for choosing between lead times. We demonstrate the managerial implications of the model by applying it first to the classic Sport‐Obermeyer case and then to a supplier‐selection problem faced by a global manufacturer.     

Inventory Rationing for Multiple Class Demand under Continuous Review

We consider how a firm should ration inventory to multiple classes in a stochastic demand environment with partial, class‐dependent backlogging where the firm incurs a fixed setup cost when ordering from its supplier. We present an infinite‐horizon, average cost criterion Markov decision problem formulation for the case with zero lead times. We provide an algorithm that determines the optimal rationing policy, and show how to find the optimal base‐stock reorder policy. Numerical studies indicate that the optimal policy is similar to that given by the equivalent deterministic problem and relies on tracking both the current inventory and the rate that backorder costs are accumulating. Our study of the case of non‐zero lead time shows that a heuristic combining the optimal, zero lead time policy with an allocation policy based on a single‐period profit management problem is effective.     

P2P Marketplaces and Retailing in the Presence of Consumers' Valuation Uncertainty

Can peer‐to‐peer (P2P) marketplaces benefit traditional supply chains when consumers may experience valuation risk? P2P marketplaces can mitigate consumers' risk by allowing them to trade mismatched goods; yet, they also impose a threat to retailers and their suppliers as they compete over consumers. Further, do profit‐maximizing marketplaces always extract the entire consumer surplus from the online trades? Our two‐period model highlights the effects introduced by P2P marketplaces while accounting for the platform's pricing decisions. We prove that with low product unit cost, the P2P marketplace sets its transaction fee to the market clearing price, thereby extracting all of the seller surplus. In this range of product unit cost, the supply chain partners are worse off due to the emergence of a P2P marketplace. However, when the unit cost is high, the platform sets its transaction fee to be less than the market clearing price, intentionally leaving money on the table, as a mechanism to stimulate first period demand for new goods in expectation for some of them to be traded later, in the second period, via the marketplace. It is not until the surplus left with the sellers is sufficiently high that the supply chain partners manage to extract some of this surplus, ultimately making them better off due to a P2P marketplace. We further analyze the impact of a P2P marketplace on consumer surplus and social welfare. In addition, we consider model variants accounting for a frictionless platform and consumer strategic waiting.     

A SIMULATION GAME FOR TEACHING SERVICE‐ORIENTED SUPPLY CHAIN MANAGEMENT: DOES INFORMATION SHARING HELP MANAGERS WITH SERVICE CAPACITY DECISIONS?*

For decades, the Beer Game has taught complex principles of supply chain management in a finished good inventory supply chain. However, services typically cannot hold inventory and can only manage backlogs through capacity adjustments. We propose a simulation game designed to teach service‐oriented supply chain management principles and to test whether managers use them effectively. For example, using a sample of typical student results, we determine that student managers can effectively use end‐user demand information to reduce backlog and capacity adjustment costs. The game can also demonstrate the impact of demand variability and reduced capacity adjustment time and lead times.     

Managing Supply Risk for Vertically Differentiated Co‐Products

The manufacturing complexity of many high‐tech products results in a substantial variation in the quality of the units produced. After manufacturing, the units are classified into vertically differentiated products. These products are typically obtained in uncontrollable fractions, leading to mismatches between their demand and supply. We focus on product stockouts due to the supply–demand mismatches. Existing literature suggests that when faced with product stockouts, firms should satisfy all unmet demand of a low‐end product by downgrading excess units of a high‐end product (downward substitution). However, this policy may be suboptimal if it is likely that low‐end customers will substitute with a higher quality product and pay the higher price (upward substitution). In this study, we investigate whether and how much downward substitution firms should perform. We also investigate whether and how much low‐end inventory firms should withhold to strategically divert some low‐end demand to the high‐end product. We first establish the existence of regions of co‐production technology and willingness of customers to substitute upward where firms adopt different substitution/withholding strategies. Then, we develop a managerial framework to determine the optimal selling strategy during the life cycle of technology products as profit margins shrink, manufacturing technology improves, and more capacity becomes available. Consistent trends exist for exogenous and endogenous prices.     

Flexible Backup Supply and the Management of Lead‐Time Uncertainty

We consider replenishment decisions for a constant rate demand environment from a supplier with uncertain lead times. We study the potential use of a flexible backup supplier as an emergency response to accurate lead‐time information arriving at (or close after) the beginning of the demand interval and well after an original order with the stochastic lead‐time supplier has been placed. The emergency response decisions involve whether to order and how much from the flexible backup supplier, with the objective of minimizing the cost of meeting demand. We derive the optimal emergency‐response policy and clearly outline its implications on the optimized safety lead time of the original order placement and on the cost of meeting demand. We examine the impact on the use of the flexible backup supplier of factors like the arrival time of accurate lead‐time information and the response lead time of the backup supplier. We further study the potential benefits of the use of the flexible backup supplier in a dual role: as one of the two suppliers in a redundant supply system assigned to originally meet the demand and as an emergency response to later‐arriving lead‐time information. Our numerical studies illustrate the benefits from the use of the flexible backup supplier as an emergency response, but for reasonable purchase premiums and short lead times of flexible backup supply options, their use in a dual (regular and emergency response) role often leads to improved performance over safety lead‐time single and uncertain lead‐time supplier‐replenishment strategies. The benefits of the backup supply options are accentuated the higher the lead‐time uncertainty of the stochastic lead‐time supplier is.     

Contracting Under Vendor Managed Inventory Systems Using Holding Cost Subsidies

Vendor managed inventory systems are becoming increasingly popular. An important issue in implementing a vendor managed inventory scheme is the contracting terms that dictate the ownership of the inventory and the responsibility of inventory replenishment decisions. Thus the performance of a vendor managed system crucially depends on these terms and on how inventory‐related costs are shared in a supply chain. We consider a system where a manufacturer supplies a single product to a retailer who faces random demand in a competitive market. The retailer incurs a fixed cost per order, inventory holding cost, and a penalty cost for a stockout (unsatisfied demand is back‐ordered). Further, the manufacturer incurs a penalty cost when there is a stockout at the retailer and a fixed replenishment cost. We assume that the players are rational and act noncooperatively. We compare the performance of retailer managed inventory systems, where the retailer places orders and makes replenishment decisions, with vendor managed inventory systems, wherein the vendor or manufacturer makes inventory and replenishment decisions. Specifically, in the vendor managed inventory system, we propose and evaluate holding cost subsidy‐type contracts on inventories offered by the retailer to improve system performance. We evaluate this contract in the context of three widely used inventory systems—deterministic economic order quantity, continuous review (Q, r) policies, and periodic review policies—and show when such contracts may improve channel performance.     

UPSTREAM VOLATILITY IN THE SUPPLY CHAIN: THE MACHINE TOOL INDUSTRY AS A CASE STUDY

Cyclicality is a well‐known and accepted fact of life in market‐driven economies. Less well known or understood, however, is the phenomenon of amplification as one looks “upstream” in the industrial supply chain. We examine the amplification phenomenon and its implications through the lens of one upstream industry that is notorious for the intensity of the business cycles it faces: the machine tool industry. Amplification of demand volatility in capital equipment supply chains, e. g., machine tools, is particularly large relative to that seen in distribution and component parts supply chains. We present a system dynamics simulation model to capture demand volatility amplification in capital supply chains. We explore the lead‐time, inventory, production, productivity, and staffing implications of these dynamic forces. Several results stand out. First, volatility hurts productivity and lowers average worker experience. Second, even though machine tool builders can do little to reduce the volatility in their order streams through choice of forecast rule, a smoother forecasting policy will lead companies to retain more of their skilled work force. This retention of skilled employees is often cited as one of the advantages that European and Japanese companies have had relative to their U. S. competitors. Our results suggest some insights for supply chain design and management: downstream customers can do a great deal to reduce the volatility for upstream suppliers through their choice of order forecast rule. In particular, companies that use smoother forecasting policies tend to impose less of their own volatility upon their supply base and may consequently enjoy system‐wide cost reduction.     

Supply Performance in Multi‐Echelon Inventory Systems with Intermediate Product Demand: A Perspective on Allocation

In this article, we study the performance of multi‐echelon inventory systems with intermediate, external product demand in one or more upper echelons. This type of problem is of general interest in inventory theory and of particular importance in supply chain systems with both end‐product demand and spare parts (subassemblies) demand. The multi‐echelon inventory system considered here is a combination of assembly and serial stages with direct demand from more than one node. The aspect of multiple sources of demands leads to interesting inventory allocation problems. The demand and capacity at each node are considered stochastic in nature. A fixed supply and manufacturing lead time is used between the stages. We develop mathematical models for these multi‐echelon systems, which describe the inventory dynamics and allow simulation of the system. A simulation‐based inventory optimization approach is developed to search for the best base‐stock levels for these systems. The gradient estimation technique of perturbation analysis is used to derive sample‐path estimators. We consider four allocation schemes: lexicographic with priority to intermediate demand, lexiographic with priority to downstream demand, predetermined proportional allocation, and proportional allocation. Based on the numerical results we find that no single allocation policy is appropriate under all conditions. Depending on the combinations of variability and utilization we identify conditions under which use of certain allocation polices across the supply chain result in lower costs. Further, we determine how selection of an inappropriate allocation policy in the presence of scarce on‐hand inventory could result in downstream nodes facing acute shortages. Consequently we provide insight on why good allocation policies work well under differing sets of operating conditions.     

Optimal Dynamic Order Scheduling under Capacity Constraints Given Demand‐Forecast Evolution

We consider a manufacturer without any frozen periods in production schedules so that it can dynamically update the schedules as the demand forecast evolves over time until the realization of actual demand. The manufacturer has a fixed production capacity in each production period, which impacts the time to start production as well as the production schedules. We develop a dynamic optimization model to analyze the optimal production schedules under capacity constraint and demand‐forecast updating. To model the evolution of demand forecasts, we use both additive and multiplicative versions of the martingale model of forecast evolution. We first derive expressions for the optimal base stock levels for a single‐product model. We find that manufacturers located near their market bases can realize most of their potential profits (i.e., profit made when the capacity is unlimited) by building a very limited amount of capacity. For moderate demand uncertainty, we also show that it is almost impossible for manufacturers to compensate for the increase in supply–demand mismatches resulting from long delivery lead times by increasing capacity, making lead‐time reduction a better alternative than capacity expansion. We then extend the model to a multi‐product case and derive expressions for the optimal production quantities for each product given a shared capacity constraint. Using a two‐product model, we show that the manufacturer should utilize its capacity more in earlier periods when the demand for both products is more positively correlated.     

On the Preference to Avoid Ex Post Inventory Errors

The value of demand information underlies many supply chain strategies that aim at better matching supply and demand. This study reports on the results of a laboratory experiment designed to estimate the behavioral value of demand information. Relative to the commonly assumed benchmark of a rational risk‐neutral decision maker, we find that decision makers are consistently willing to pay too much for the option to eliminate the risk of supply not matching demand. Contrary to intuition, we show that risk aversion does not explain this result. We posit that demand information provides behavioral value because it mitigates regret from ex post inventory errors.     

Pricing Decisions During Inter‐Generational Product Transition

How should companies price products during an inter‐generational transition? High uncertainty in a new product introduction often leads to extreme cases of demand and supply mismatches. Pricing is an effective tool to either prevent or alleviate these problems. We study the optimal pricing decisions in the context of a product transition in which a new‐generation product replaces an old one. We formulate the dynamic pricing problem and derive the optimal prices for both the old and new products. Our analysis sheds light on the pattern of the optimal prices for the two products during the transition and on how product replacement, along with several other dynamics including substitution, external competition, scarcity, and inventory, affect the optimal prices. We also determine the optimal initial inventory for each product and discuss a heuristic method.     

Optimal Planning Quantities for Product Transition

The replacement of an existing product with a new one presents many challenges. In particular, uncertainties in a new product introduction often lead to extreme cases of demand and supply mismatches. This paper addresses inventory planning decisions for product upgrades when there is no replenishment opportunity during the transition period. We allow product substitution: when a company runs out of the old product, a customer may be offered the new product as a substitute. We show that the optimal substitution decision is a time‐varying threshold policy and establish the optimal planning policy. Further, we determine the optimal delay in a new product introduction, given the initial inventory of the old product.     

Combined Pricing and Portfolio Option Procurement

In this paper, we study a single‐product periodic‐review inventory system that faces random and price‐dependent demand. The firm can purchase the product either from option contracts or from the spot market. Different option contracts are offered by a set of suppliers with a two‐part fee structure: a unit reservation cost and a unit exercising cost. The spot market price is random and its realization may affect the subsequent option contract prices. The firm decides the reservation quantity from each supplier and the product selling price at the beginning of each period and the number of options to exercise (inventory replenishment) at the end of the period to maximize the total expected profit over its planning horizon. We show that the optimal inventory replenishment policy is order‐up‐to type with a sequence of decreasing thresholds. We also investigate the optimal option‐reservation policy and the optimal pricing strategy. The optimal reservation quantities and selling price are shown to be both decreasing in the starting inventory level when demand function is additive. Building upon the analytical results, we conduct a numerical study to unveil additional managerial insights. Among other things, we quantify the values of the option contracts and dynamic pricing to the firm and show that they are more significant when the market demand becomes more volatile.     

库存成本变化的VMI供应链协调

提出了库存成本变化的经济订货批量(EOQ)模型，基于该模型研究了库存成本变化时供应商管理库存(VMI)系统的最优协议问题。在该系统中，订货商和供应商达成缺货成本共担协议：当缺货发生时，供应商需要向订货商支付缺货补偿。订货商和供应商分散决策，订货商通过设计协议来减少其成本，而供应商通过制定补货决策来缩小自身成本。通过与传统系统和整合系统的比较，得出了库存成本变化时VMI系统的最优补货决策和缺货成本共担协议。采用数值算例验证了分析结果。结果表明，当且仅当供应商预期成本等于整合系统的最小总成本与固定缺货罚金之和时，VMI系统与整合系统具有相同的补货决策和系统绩效，即能够实现供应链协调。     

Centralization versus decentralization: Risk pooling,risk diversification,and supply chain disruptions

We investigate optimal system design in a multi-location system in which supply is subject to disruptions. We examine the expected costs and cost variances of the system in both a centralized and a decentralized inventory system. We show that, when demand is deterministic and supply may be disrupted, using a decentralized inventory design reduces cost variance through the risk diversification effect, and therefore a decentralized inventory system is optimal. This is in contrast to the classical result that when supply is deterministic and demand is stochastic, centralization is optimal due to the risk-pooling effect. When both supply may be disrupted and demand is stochastic, we demonstrate that a risk-averse firm should typically choose a decentralized inventory system design.     

Order Stability in Supply Chains: Coordination Risk and the Role of Coordination Stock

The bullwhip effect describes the tendency for the variance of orders in supply chains to increase as one moves upstream from consumer demand. We report on a set of laboratory experiments with a serial supply chain that tests behavioral causes of this phenomenon, in particular the possible influence of coordination risk. Coordination risk exists when individuals' decisions contribute to a collective outcome and the decision rules followed by each individual are not known with certainty, for example, where managers cannot be sure how their supply chain partners will behave. We conjecture that the existence of coordination risk may contribute to bullwhip behavior. We test this conjecture by controlling for environmental factors that lead to coordination risk and find these controls lead to a significant reduction in order oscillations and amplification. Next, we investigate a managerial intervention to reduce the bullwhip effect, inspired by our conjecture that coordination risk contributes to bullwhip behavior. Although the intervention, holding additional on‐hand inventory, does not change the existence of coordination risk, it reduces order oscillation and amplification by providing a buffer against the endogenous risk of coordination failure. We conclude that the magnitude of the bullwhip can be mitigated, but that its behavioral causes appear robust.     

VMI供应链下考虑补货策略的的契约设计

结合(r,Q)和(s,S)两种库存补货策略,提出了货权属供应商的VMI供应链的契约设计问题。采用风险分担的思想,给出了两种可行的风险分担的契约形式。在离散需求下,通过参数试验的形式,分别研究了两种契约形式对供应链效率的影响。研究结果表明,两种契约能够使得供应链的效率达到满意,同时对于影响效率的参数有一定的鲁棒性,并且在一定情况下能协调供应链。相比收益分享契约,引入风险分享的契约形式能够使得供应链协作的效率更高。研究结论对VMI契约设计有参考意义。