应对突发事件的库存共享策略

以包含两个销售商的库存系统为例,构建了一个描述库存共享应对突发事件的非合作博弈模型,证明了其纳什均衡解是唯一存在的。研究结果显示库存共享策略总有可能使得销售商的期望利润得以改进。另外,比较静态分析反映了转载价格和转载成本显著影响库存共享销售商的最优订货量和最优期望利润。最后,提出了一个简单的求解模型纳什均衡解的启发式算法。     

Building Supply Chain Resilience through Virtual Stockpile Pooling

Stockpiling inventory is an essential strategy for building supply chain resilience. It enables firms to continue operating while finding a solution to an unexpected event that causes a supply disruption or demand surge. While extremely valuable when actually deployed, stockpiles incur large holding costs and usually provide no benefits until such a time. To help to reduce this cost, this study presents a new approach for managing stockpiles. We show that if leveraged intelligently, stockpiles can also help an organization better meet its own regular demand by enabling a type of virtual pooling we call virtual stockpile pooling (VSP). The idea of VSP is to first integrate the stockpile into several locations’ regular inventory buffers and then dynamically reallocate the stockpile among these locations in reaction to the demand realizations to achieve a kind of virtual transshipment. To study how to execute VSP and determine when it can provide the most value, we formulate a stylized multi‐location stochastic inventory model and solve for the optimal stockpile allocation and inventory order policies. We show that VSP can provide significant cost savings: in some cases nearly the full holding cost of the stockpile (i.e., VSP effectively maintains the stockpile for free), in other cases nearly the savings of traditional physical inventory pooling. Last, our results prescribe implementing VSP with many locations for large stockpiles, but only a few locations for small stockpiles.     

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.     

Risk Pooling Advantages of Manufacturing Network Configuration

The decision of a firm to set up a plant network is influenced by a number of factors, including demand fluctuations across its portfolio of products, logistics costs, and service level requirements. Product plant networks offer the benefits of consolidated production and reduced transshipment costs; on the other hand, process plant networks allow intensive dedication to process expertise and economies of scale. In this paper, we show that, aside from these benefits, process plant networks offer significant risk pooling advantages under a wide range of conditions. We analytically demonstrate that, even without accounting for economies of scale advantages, firms may prefer the process plant network configuration due to the risk pooling benefits offered.     

供应链库存协调策略研究

研究和分析了直运型供应链通过共同补给期协调库存的策略问题。在该供应链中,单一供应商提供单一产品给面临随机需求的单一零售商。在所提出的库存协调策略条件下,供应商指定共同补给期,当零售商按供应商指定的共同补给期作为其订货周期时,供应商提供零售商一定的价格折扣。这种协调策略可以视为Stackelberg博弈。在阐述了解决该博弈问题的方法后,进行了数值实验,分析了采用这种协调策略的利益。     

考虑多种安全库存策略的选址-库存问题研究

考虑多种安全设置策略的物流网络的选址-库存问题,不仅是选址、订货、运输和库存的集成优化,还需要考虑多种不同的安全库存设置和转运策略。因此,本文深入讨论了二级物流网络中的六种安全库存设置策略,构建了六种考虑不同安全库存设置的选址-库存模型。在考虑集中设置安全库存时,集中安全库存需要通过转载运输实现,因此需要将转载运输成本引入选址-库存模型之中,使新的选址-库存模型更加科学合理。另外,针对六种新的选址-库存模型,提出了基于个体成本差异分配的遗传算法,迭代搜索选址、分配、库存设置策略的优化组合。最后,通过数据实验验证了模型的有效性：（1）安全库存与转载运输之间存在此消彼长的背反关系;（2）安全库存设置和转载运输策略对总成本的影响取决于两种费率权重情况。本文的研究可以为二级物流网络的选址、订货和安全库存策略集成优化决策提供参考依据。     

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.     

Analysis and Management of Periodic Review,Order‐Up‐To Level Inventory Systems with Order Crossover

In this article, we investigate the (R, S) periodic review, order‐up‐to level inventory control system with stochastic demand and variable leadtimes. Variable leadtimes can lead to order crossover, in which some orders arrive out of sequence. Most theoretical studies of order‐up‐to inventory systems under variable leadtimes assume that crossovers do not occur and, in so doing, overestimate the standard deviation of the realized leadtime distribution and prescribe policies that can inflate inventory costs. We develop a new analytic model of the expected costs associated with this system, making use of a novel approximation of the realized (reduced) leadtime standard deviation resulting from order crossovers. Extensive experimentation through simulation shows that our model closely approximates the true expected cost and can be used to find values of R and S that provide an expected cost close to the minimum cost. Taking account of, as opposed to ignoring, crossovers leads, on average, to substantial improvements in accuracy and significant cost reductions. Our results are particularly useful for managers seeking to reduce inventory costs in supply chains with variable leadtimes.     

Inventory Sharing with Transshipment: Impacts of Demand Distribution Shapes and Setup Costs

We study a firm's optimal transshipment problem considering the impacts of setup costs for transshipment and demand distribution shapes. We assume that the demand follows a three‐point distribution, which changes from a degenerate distribution, to a unimodal distribution, and to a bimodal distribution as the demand shape parameter increases. We find that as the demand shape parameter increases, the optimal transshipment strategy changes from no transshipment to transshipment, and finally to no transshipment. The firm would use two‐way transshipment when the shape parameter is relatively small, while it would use one‐way transshipment when the shape parameter is relatively large. When the optimal strategy is one‐way transshipment, the transshipment direction depends on the contribution margin as well as the demand shape, when the difference between the two demand uncertainties is small. Our study of a dual‐channel retail system shows that the additional benefit of two‐way transshipment is negligible when there are many retail stores.     

A Note on the Relationship Among Capacity,Pricing, and Inventory in a Make‐to‐Stock System

We address the simultaneous determination of pricing, production, and capacity investment decisions by a monopolistic firm in a multi‐period setting under demand uncertainty. We analyze the optimal decision with particular emphasis on the relationship between price and capacity. We consider models that allow for either bi‐directional price changes or models with markdowns only, and in the latter case we prove that capacity and price are strategic substitutes.     

风险偏好和需求不确定性对销售努力和补货决策库存系统的影响

研究风险偏好和需求不确定性对库存和销售努力决策库存系统的影响.运用应用概率中的随机比较方法,分别在一阶和二阶随机占优的意义下给出比较需求分布不同两个系统的最优利润和努力水平的充分条件或充分必要条件.证明存在一类需求分布在一定条件下系统的最优利润和努力水平都随需求可变性的增加而增大.数值例子验证了获得的研究结果.     

Shelf Space Management When Demand Depends on the Inventory Level

Two factors that their influence on the demand has been investigated in many papers are (i) the shelf space allocated to a product and to its complement or supplement products and (ii) the instantaneous inventory level seen by customers. Here we analyze the joint shelf space allocation and inventory decisions for multiple items with demand that depends on both factors. The traditional approach to solve inventory models with a state‐dependent demand rate uses a time domain approach. However, this approach often does not lead to closed‐form expressions for the profit rate with both dependencies. We analyze the problem in the inventory domain via level crossing theory. This approach leads to closed‐form expressions for a large set of demand rate functions exhibiting both dependencies. These closed‐form expressions substantially simplify the search for optimal solutions; thus we use them to solve the joint inventory control and shelf space allocation problem. We consider examples with two products to investigate the significance of capturing both demand dependencies. We show that in some settings it is important to capture both dependencies. We consider two heuristics, each one of them ignores one of the two dependencies. Using these heuristics it seems that ignoring the dependency on the shelf space might be less harmful than ignoring the dependency on the inventory level, which, based on computational results, can lead to profit losses of more than 6%. We demonstrate that retailers should use their operational control, e.g., reorder point, to promote higher demand products.     

考虑成本和收益净现值的确定性存储决策模型研究

净现值是企业决策中需要考虑的重要宏观经济因素.本文建立了考虑成本和收益净现值的连续时间有限时段确定性库存系统的最优存储和定价决策模型,证明了给定价格下最优策略中任意两个相邻订货周期之间的递推关系,分析了该关系的解析性质,并得出订货周期长度的上下限.在此基础上提出求解最优存储策略和最优价格的两步优化算法.最后通过数值算例对本文模型及结果做出说明.     

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.     

A Bayesian Inventory Model Using Real‐Time Condition Monitoring Information

Lack of coordination between machinery fault diagnosis and inventory management for spare parts can lead to increased inventory costs and disruptions in production activity. We develop a framework for incorporating real‐time condition monitoring information into inventory decisions for spare parts. We consider a manufacturer who periodically replenishes inventory for a machine part that is subject to deterioration. The deterioration is captured via condition monitoring and modeled using a Wiener process. The resulting degradation model is used to derive the life distribution of a functioning part and to estimate the demand distribution for spare parts. This estimation is periodically updated, in a Bayesian manner, as additional information on part deterioration is obtained. We develop an inventory model that incorporates this updated demand distribution and demonstrate that a dynamic base‐stock policy, in which the optimal base‐stock level is a function of some subset of the observed condition monitoring information, is optimal. We propose a myopic critical fractile policy that captures the essence of the optimal policy, but is easier to compute. Computational experiments indicate that this heuristic performs quite well relative to the optimal policy. Adaptive inventory policies such as these can help manufacturers to increase machine availability and reduce inventory costs.     

Integrality in Stochastic Inventory Models

We study several finite‐horizon, discrete‐time, dynamic, stochastic inventory control models with integer demands: the newsvendor model, its multi‐period extension, and a single‐product, multi‐echelon assembly model. Equivalent linear programs are formulated for the corresponding stochastic dynamic programs, and integrality results are derived based on the total unimodularity of the constraint matrices. Specifically, for all these models, starting with integer inventory levels, we show that there exist optimal policies that are integral. For the most general single‐product, multi‐echelon assembly system model, integrality results are also derived for a practical alternative to stochastic dynamic programming, namely, rolling‐horizon optimization by a similar argument. We also present a different approach to prove integrality results for stochastic inventory models. This new approach is based on a generalization we propose for the one‐dimensional notion of piecewise linearity with integer breakpoints to higher dimensions. The usefulness of this new approach is illustrated by establishing the integrality of both the dynamic programming and rolling‐horizon optimization models of a two‐product capacitated stochastic inventory control system.     

Dependency of Crop Production between Global Breadbaskets: A Copula Approach for the Assessment of Global and Regional Risk Pools

As recent events have shown, simultaneous crop losses in different parts of the world can cause serious risks to global food security. However, to date, little is known about the spatial dependency of lower than expected crop yields from global breadbaskets. This especially applies in the case of extreme events, i.e., where one or more breadbaskets are experiencing far below average yields. Without such information, risk management approaches cannot be applied and vulnerability to extremes may remain high or even increase in the future around the world. We tackle both issues from an empirical perspective focusing on wheat yield. Interdependencies between historically observed wheat yield deviations in five breadbaskets (United States, Argentina, India, China, and Australia) are estimated via copula approaches that can incorporate increasing tail dependencies. In doing so, we are able to attach probabilities to interregional as well as global yield losses. To address the robustness of our results, we apply three different methods for constructing multivariate copulas: vine copulas, ordered coupling using a minimax approach, and hierarchical structuring. We found interdependencies between states within breadbaskets that led us to the conclusion that risk pooling for extremes is less favorable on the regional level. However, notwithstanding evidence of global climatic teleconnections that may influence crop production, we also demonstrate empirically that wheat production losses are independent between global breadbaskets, which strengthens the case for interregional risk pooling strategies. We argue that through interregional risk pooling, postdisaster liabilities of governments and international donors could be decreased.     

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.     

直接配送下随机需求库存-路径问题最优平稳策略及其算法

直接配送策略下随机需求库存-路径问题（Stochastic Demand Inventory Routing Problem with Direct Deliveries, SDIRPDD）由于其需求的不确定性、决策的长期性以及其最优策略形式对求解其他库存-路径问题（IRP）的参考价值,使得对SDIPRDD问题的研究成为物流、供应链优化领域研究的一个热点。文章首先证明了无约束SDIRPDD的最优平稳策略为（s,S）形式,并通过分析车辆数约束对客户单阶段期望成本函数的影响,给出了存在车辆数和客户库存容量约束时SDIRPDD问题的最优平稳策略形式,进而提出了一种求解有约束SDIRPDD问题最优平稳策略的近似算法。最后,通过数值算例验证了算法的有效性并分析了结果的现实意义。     

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.