Multi‐Echelon Inventory Management under Short‐Term Take‐or‐Pay Contracts

We extend the Clark–Scarf serial multi‐echelon inventory model to include procuring production inputs under short‐term take‐or‐pay contracts at one or more stages. In each period, each such stage has the option to order/process at two different cost rates; the cheaper rate applies to units up to the contract quantity selected in the previous period. We prove that in each period and at each such stage, there are three base‐stock levels that characterize an optimal policy, two for the inventory policy and one for the contract quantity selection policy. The optimal cost function is additively separable in its state variables, leading to conquering the curse of dimensionality and the opportunity to manage the supply chain using independently acting managers. We develop conditions under which myopic policies are optimal and illustrate the results using numerical examples. We establish and use a generic one‐period result, which generalizes an important such result in the literature. Extensions to cover variants of take‐or‐pay contracts are included. Limitations are discussed.     

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

We consider a periodic‐review inventory system with regular and expedited supply modes. The expedited supply is faster than the regular supply but incurs a higher cost. Demand for the product in each period is random and sensitive to its selling price. The firm determines its order quantity from each supply in each period as well as its selling price to maximize the expected total discounted profit over a finite or an infinite planning horizon. We show that, in each period if it is optimal to order from both supplies, the optimal inventory policy is determined by two state‐independent thresholds, one for each supply mode, and a list price is set for the product; if only the regular supply is used, the optimal policy is a state‐dependent base‐stock policy, that is, the optimal base‐stock level depends on the starting inventory level, and the optimal selling price is a markdown price that decreases with the starting inventory level. We further study the operational impact of such supply diversification and show that it increases the firm's expected profit, reduces the optimal safety‐stock levels, and lowers the optimal selling price. Thus that diversification is beneficial to both the firm and its customers. Building upon these results, we conduct a numerical study to assess and compare the respective benefit of dynamic pricing and supply diversification.     

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

It is common for a firm to make use of multiple suppliers of different delivery lead times, reliabilities, and costs. In this study, we are concerned with the joint pricing and inventory control problem for such a firm that has a quick‐response supplier and a regular supplier that both suffer random disruptions, and faces price‐sensitive random demands. We aim at characterizing the optimal ordering and pricing policies in each period over a planning horizon, and analyzing the impacts of supply source diversification. We show that, when both suppliers are unreliable, the optimal inventory policy in each period is a reorder point policy and the optimal price is decreasing in the starting inventory level in that period. In addition, we show that having supply source diversification or higher supplier reliability increases the firm's optimal profit and lowers the optimal selling price. We also demonstrate that, with the selling price as a decision, a supplier may receive even more orders from the firm after an additional supplier is introduced. For the special case where the quick‐response supplier is perfectly reliable, we further show that the optimal inventory policy is of a base‐stock type and the optimal pricing policy is a list‐price policy with markdowns.     

End‐of‐Life Inventory Problem with Phaseout Returns

We consider the service parts end‐of‐life inventory problem of a capital goods manufacturer in the final phase of its life cycle. The final phase starts as soon as the production of parts terminates and continues until the last service contract expires. Final order quantities are considered a popular tactic to sustain service fulfillment obligations and to mitigate the effect of obsolescence. In addition to the final order quantity, other sources to obtain serviceable parts are repairing returned defective items and retrieving parts from phaseout returns. Phaseout returns happen when a customer replaces an old system platform with a next‐generation one and returns the old product to the original equipment manufacturer (OEM). These returns can well serve the demand for service parts of other customers still using the old generation of the product. In this study, we study the decision‐making complications as well as cost‐saving opportunities stemming from phaseout occurrence. We use a finite‐horizon Markov decision process to characterize the structure of the optimal inventory control policy. We show that the optimal policy consists of a time‐varying threshold level for item repair. Furthermore, we study the value of phaseout information by extending the results to cases with an uncertain phaseout quantity or an uncertain schedule. Numerical analysis sheds light on the advantages of the optimal policy compared to some heuristic policies.     

A New Two‐Bin Policy for Inventory Systems with Differentiated Demand Classes

We consider an inventory system under continuous review with two demand classes that are different in terms of service level required (or penalty cost incurred for backordering of demand). Prior literature has proposed the critical level rationing (CLR) policy under which the demand from the lower priority class is backordered once inventory falls below the critical level. While this reduces the penalty cost for the higher demand class, the fill rate achieved for the lower priority demand class gets compromised. In this study, we propose a new class of two‐bin (2B) policy for the problem. The proposed 2B policy assigns separate bins of inventory for the two demand classes. The demand for each class is fulfilled from its assigned bin. However, when the bin intended for the higher demand class is empty, the demand from the higher class can still be fulfilled with the inventory from the other bin. The advantage of the 2B policy is that better fill rates are achieved, especially for the lower demand class. Computational results show that the proposed policy is able to provide a much higher service level for the lower priority class demand without increasing the total cost too much and without affecting the service level for the higher priority class. When a service level constrained optimization problem is considered, the 2B policy dominates the CLR policy when the service level difference for the two classes is not too high or the service levels required for both the classes are relatively lower.     

Inventory Rationing in a Make‐to‐Stock System with Batch Production and Lost Sales

We address an inventory rationing problem in a lost sales make‐to‐stock (MTS) production system with batch ordering and multiple demand classes. Each production order contains a single batch of a fixed lot size and the processing time of each batch is random. Assuming that there is at most one order outstanding at any point in time, we first address the case with the general production time distribution. We show that the optimal order policy is characterized by a reorder point and the optimal rationing policy is characterized by time‐dependent rationing levels. We then approximate the production time distribution with a phase‐type distribution and show that the optimal policy can be characterized by a reorder point and state‐dependent rationing levels. Using the Erlang production time distribution, we generalize the model to a tandem MTS system in which there may be multiple outstanding orders. We introduce a state‐transformation approach to perform the structural analysis and show that both the reorder point and rationing levels are state dependent. We show the monotonicity of the optimal reorder point and rationing levels for the outstanding orders, and generate new theoretical and managerial insights from the research findings.     

Optimal Inventory Control with Dual‐Sourcing,Heterogeneous Ordering Costs and Order Size Constraints

We consider a dual‐sourcing inventory system, where procuring from one supplier involves a high variable cost but negligible fixed cost whereas procuring from the other supplier involves a low variable cost but high fixed cost, as well as an order size constraint. We show that the problem can be reduced to an equivalent single‐sourcing problem. However, the corresponding ordering cost is neither concave nor convex. Using the notion of quasi‐convexity, we partially characterize the structure of the optimal policy and show that it can be specified by multiple thresholds which determine when to order from each supplier and how much. In contrast to previous research, which does not consider order size constraints, we show that it is optimal to simultaneously source from both suppliers when the beginning inventory level is sufficiently low. We also show that the decision to source from the low‐cost supplier is not monotonic in the inventory level. Our results require that the variable costs satisfy a certain condition which guarantees quasi‐convexity. However, extensive numerical results suggest that our policy is almost always optimal when the condition is not satisfied. We also show how the results can be extended to systems with multiple capacitated suppliers.     

End‐of‐Life Inventory Decisions for Consumer Electronics Service Parts

We consider a consumer electronics manufacturer's problem of controlling the inventory of spare parts in the final phase of the service life cycle. The final phase starts when the part production is terminated and continues until the last service contract or warranty period expires. Placing final orders for service parts is considered to be a popular tactic to satisfy demand during this period and to mitigate the effect of part obsolescence at the end of the service life cycle. Previous research focuses on repairing defective products by replacing the defective parts with properly functioning spare ones. However, for consumer electronic products there typically is considerable price erosion while repair costs stay steady over time. As a consequence, there might be a point in time at which the unit price of the product drops below the repair costs. If so, it is more cost effective to adopt an alternative policy to meet service demands toward the end of the final phase, such as offering customers a new product of the similar type or a discount on a next generation product. This study examines the cost trade‐offs of implementing alternative policies for the repair policy and develops an exact expression for the expected total cost function. Using this expression, the optimal final order quantity and switching time from repair to an alternative policy can be determined simultaneously. Numerical analysis of a real world case sheds light on the cost benefits of these policies and also yields insights into the quantitative importance of the various cost parameters.     

Profitability of Service‐Level‐Based Price Differentiation with Inventory Rationing

In this paper, we study the profitability of service‐level‐based price differentiation (SLBPD) in an inventory‐rationing context. SLBPD implies that a company offers several combinations of prices and guaranteed service levels, from which customers self‐select; different customers choose different offerings because they incur different shortage costs if an order is not fulfilled immediately. We develop an analytical model for SLBPD and explore if and when such a service differentiation strategy yields higher profits than a single undifferentiated offering. The results of our analyses suggest that SLBPD is profitable only if a company faces pricing restrictions, e.g., because of competitive pressure or regulatory restrictions. We develop necessary and sufficient conditions under which a specific and relevant form of SLBPD (called “service‐level‐based upselling”) is profitable, and provide an algorithm to compute the optimal parameters of such a policy. Based on this algorithm we carry out numerical analyses that allow us to characterize the profit increment of service‐level‐based upselling. We derive managerial insights into the attractiveness of SLBPD and explain how our basic analytical framework can be extended to account for more complex practical features.     

Customer‐Base Concentration and Inventory Efficiencies: Evidence from the Manufacturing Sector

What is the link between customer‐base concentration and inventory efficiencies in the manufacturing sector? Using hand‐collected data from 10‐K Filings, we find that manufacturers with more concentrated customer bases hold fewer inventories for less time and are less likely to end up with excess inventories, as indicated by the lower likelihood and magnitude of inventory write‐downs and reversals. Using disaggregated inventory disclosures, we find that inventory efficiencies primarily flow through the finished goods inventory account, while raw material efficiencies are offset by higher work‐in‐process holdings and longer work‐in‐process cycles. In additional analysis, we document a valuation premium for more concentrated manufacturers after controlling for other firm characteristics, including default risk and cost of capital estimates. We conclude that investors trade off the costs and benefits of relationships with a limited number of major customers and, on balance, consider customer‐base concentration as a net positive for firm valuation. Overall, our study adds to interdisciplinary research in accounting and operations management by shedding new light on the relevance of major customer disclosures for fundamental analysis and valuation in the manufacturing sector.     

Pool‐Point Distribution of Zero‐Inventory Products

We study zero‐inventory production‐distribution systems under pool‐point delivery. The zero‐inventory production and distribution paradigm is supported in a variety of industries in which a product cannot be inventoried because of its short shelf life. The advantages of pool‐point (or hub‐and‐spoke) distribution, explored extensively in the literature, include the efficient use of transportation resources and effective day‐to‐day management of operations. The setting of our analysis is as follows: A production facility (plant) with a finite production rate distributes its single product, which cannot be inventoried, to several pool points. Each pool point may require multiple truckloads to satisfy its customers' demand. A third‐party logistics provider then transports the product to individual customers surrounding each pool point. The production rate can be increased up to a certain limit by incurring additional cost. The delivery of the product is done by identical trucks, each having limited capacity and non‐negligible traveling time between the plant and the pool points. Our objective is to coordinate the production and transportation operations so that the total cost of production and distribution is minimized, while respecting the product lifetime and the delivery capacity constraints. This study attempts to develop intuition into zero‐inventory production‐distribution systems under pool‐point delivery by considering several variants of the above setting. These include multiple trucks, a modifiable production rate, and alternative objectives. Using a combination of theoretical analysis and computational experiments, we gain insights into optimizing the total cost of a production‐delivery plan by understanding the trade‐off between production and transportation.     

Durability,Transit Lags,and Optimality of Inventory Management Decisions

Two laboratory experiments on a single‐echelon inventory task show that inventory durability interacts with transit lags to create order volatility that exceeds demand volatility. Thus, inventory durability and transit lags cause managers to deviate from inventory decision optimality. Durability creates a large increase in order volatility because players adjust orders insufficiently to reflect current inventory and backlogs, much as they adjust orders insufficiently to reflect holding and backlog costs in newsvendor studies (e.g., Schweitzer and Cachon 2000). Transit lags exacerbate non‐optimal ordering by interfering with players' ability to correct prior errors. Our results suggest that non‐optimal inventory decisions can be driven by inventory and supply chain characteristics, even in the absence of the coordination and information sharing problems studied by Croson et al. (2005) and Sterman (1989a,b). We also examine the influence of features related to personality. We find little evidence that the interactive effects of durability and transit lags are altered by need for cognition, impulsiveness, or locus of control, suggesting that these features make supply chain management extremely difficult. These results imply that retailers and their upstream partners must consider the characteristics of their product and supply chains when interpreting demand signals received from downstream partners.     

Bayesian Inventory Management with Potential Change‐Points in Demand

We consider the inventory management problem of a firm reacting to potential change points in demand, which we define as known epochs at which the demand distribution may (or may not) abruptly change. Motivating examples include global news events (e.g., the 9/11 terrorist attacks), local events (e.g., the opening of a nearby attraction), or internal events (e.g., a product redesign). In the periods following such a potential change point in demand, a manager is torn between using a possibly obsolete demand model estimated from a long data history and using a model estimated from a short, recent history. We formulate a Bayesian inventory problem just after a potential change point. We pursue heuristic policies coupled with cost lower bounds, including a new lower bounding approach to non‐perishable Bayesian inventory problems that relaxes the dependence between physical demand and demand signals and that can be applied for a broad set of belief and demand distributions. Our numerical studies reveal small gaps between the costs implied by our heuristic solutions and our lower bounds. We also provide analytical and numerical sensitivity results suggesting that a manager worried about downside profit risk should err on the side of underestimating demand at a potential change point.     

Flexible‐Duration Extended Warranties with Dynamic Reliability Learning

Frequent technological innovations and price declines adversely affect sales of extended warranties (EWs) as product replacement upon failure becomes an increasingly attractive alternative. To increase sales and profitability, we propose offering flexible‐duration EWs. These warranties can appeal to customers who are uncertain about how long they will keep the product as well as to customers who are uncertain about the product's reliability. Flexibility may be added to existing services in the form of monthly billing with month‐by‐month commitments or by making existing warranties easier to cancel with pro‐rated refunds. This paper studies flexible warranties from perspectives of both customers and the provider under customers' reliability learning. We present a model of customers' optimal coverage decisions and show that customers' optimal coverage policy has a threshold structure under some mild conditions. We further show that flexible warranties can result in higher profits and higher attach rates in a homogeneous market as well as in a heterogeneous market with multiple segments differing in various dimensions.     

Replenishment Policies for Multi‐Product Stochastic Inventory Systems with Correlated Demand and Joint‐Replenishment Costs

This study analyzes optimal replenishment policies that minimize expected discounted cost of multi‐product stochastic inventory systems. The distinguishing feature of the multi‐product inventory system that we analyze is the existence of correlated demand and joint‐replenishment costs across multiple products. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real‐world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class (s, c, d, S)‐policies, and also develop an algorithm to compute good policies in this class, for large multi‐product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective.     

考虑供应链信用水平的存货质押率研究

供应链融资可以提高中小企业的信用水平和贷款能力。考虑单一核心企业和单一零售商构成的二级供应链,产品市场需求为典型的报童模型,给出了供应链信用和信用乘数的概念,建立了考虑供应链信用水平的银行质押率决策模型,得到供应链存货质押融资情况下银行的最优质的押率,研究了信用乘数、存货质押量、回购价、回购率、银行的损失规避程度等诸多要素对银行质押率的影响。研究表明:供应链融资情况下的最优质押率高于零售商单独融资情况下的最优质押率;一定条件下,银行质押率与核心企业信用乘数、回购参数正相关;质押率和存货质押量、银行风险厌恶程度负相关;举例并进行了灵敏度分析。     

Beyond Information Sharing: An Empirical Analysis of Vendor‐Managed Inventory

Using a unique, item‐level data set, we examined benefits to downstream firms (distributors) from the decision‐transfer component of vendor‐managed inventory (VMI), the feature that distinguishes VMI from other information‐sharing, collaborative supply chain programs. Our major findings are that the decision‐transfer component of VMI adds significant benefits to the downstream firm in terms of inventory and stockout reductions above and beyond information sharing, and that these two benefits may be realized at different times following VMI implementation; that is, inventory reduction, initially, may be the major benefit to distributors from VMI, while the benefits of stockout reduction may more likely be realized after the first year of implementation. In addition, VMI provides benefits to the upstream firm (manufacturer) by reducing the downstream firm's inventory variability, a likely contributor to the bullwhip effect. Based on our empirical analysis, the decision‐transfer component of VMI, on average, reduces inventory levels by 7%, stockouts by 31%, and inventory variability by 9%.     

Looking Upstream: Optimal Policies for a Class of Capacitated Multi‐Stage Inventory Systems

We consider a multi‐stage inventory system with stochastic demand and processing capacity constraints at each stage, for both finite‐horizon and infinite‐horizon, discounted‐cost settings. For a class of such systems characterized by having the smallest capacity at the most downstream stage and system utilization above a certain threshold, we identify the structure of the optimal policy, which represents a novel variation of the order‐up‐to policy. We find the explicit functional form of the optimal order‐up‐to levels, and show that they depend (only) on upstream echelon inventories. We establish that, above the threshold utilization, this optimal policy achieves the decomposition of the multidimensional objective cost function for the system into a sum of single‐dimensional convex functions. This decomposition eliminates the curse of dimensionality and allows us to numerically solve the problem. We provide a fast algorithm to determine a (tight) upper bound on this threshold utilization for capacity‐constrained inventory problems with an arbitrary number of stages. We make use of this algorithm to quantify upper bounds on the threshold utilization for three‐, four‐, and five‐stage capacitated systems over a range of model parameters, and discuss insights that emerge.     

Lead Time Management through Expediting in a Continuous Review Inventory System

We consider a continuous review inventory system where delivery lead times can be managed by expediting in‐transit orders shipped from the supplier. First, we propose an ordering/expediting policy and derive expressions for evaluating the operating characteristics of such systems. Second, using extensive numerical experiments, we quantify the benefits of such an expediting policy. Third, we investigate a number of managerial issues. Specifically, we analyze the impact of the number of expediting hubs and their locations along the shipment network on the performance of such systems and offer insights into the design of the shipment network. We show (i) a single expediting hub that is optimally located in a shipment network can capture the majority of cost savings achieved by a multi‐hub system, especially when expediting cost is not low or demand variability is not high; (ii) when expediting time is proportional to the time to destination, for small‐enough or large‐enough demand variations, a single expediting hub located in the middle of the shipment network can capture the majority of cost savings of an optimally located hub; and (iii) in general, hubs close to the retailer significantly drive down costs, whereas hubs close to the supplier may not offer much cost savings.