Loss-averse newsvendor problem with supply risk

Modeling the manufacturer as a newsvendor, in this paper we study the ordering decisions of a loss-averse newsvendor with supply and demand uncertainties. Using the stylized newsvendor models, we analyse several key issues, including the effect of the newsvendor’s loss aversion, the effect of demand uncertainty, and the effect of supply uncertainty on the decision maker’s optimal decision under the procurement model, in which the decision maker only pays for the actual quantity received. Through our analysis, we find the following facts: the optimal order quantity decreases with respect to the degree of loss-aversion; the supply uncertainty induces the decision maker to order more than that in a deterministic environment; a stochastically larger demand always results in a larger order quantity and a larger expected utility; the optimal expected utility decreases in the demand volatility while the optimal order quantity may increase or decrease. Moreover, with numerical experiments, we demonstrate that the supply risk negatively affects the utility more than the demand risk does.     

The risk-averse newsvendor problem with random capacity

We study the effect of capacity uncertainty on the inventory decisions of a risk-averse newsvendor. We consider two well-known risk criteria, namely Value-at-Risk (VaR) included as a constraint and Conditional Value-at-Risk (CVaR). For the risk-neutral newsvendor, we find that the optimal order quantity is not affected by the capacity uncertainty. However, this result does not hold for the risk-averse newsvendor problem. Specifically, we find that capacity uncertainty decreases the order quantity under the CVaR criterion. Under the VaR constraint, capacity uncertainty leads to an order decrease for low confidence levels, but to an order increase for high confidence levels. This implies that the risk criterion should be carefully selected as it has an important effect on inventory decisions. This is shown for the newsvendor problem, but is also likely to hold for other inventory control problems that future research can address.     

Channel coordination under two-level trade credits and demand uncertainty

This study considers a decentralized supply chain where a retailer has an opportunity to order a product from a supplier prior to the sales season to satisfy uncertain demand. The retailer provides trade credit to end customers and makes credit period and order quantity decisions to maximize profits. The end demand is both random and credit period-dependent. On the basis of the newsvendor model, this paper focuses on channel coordination when a retailer provides trade credit to end customers. When the supplier also provides trade credit to the retailer, we show that the traditional trade credit contract cannot coordinate the channel. Four composite contracts based on trade credit (trade credit cost sharing with buy back or quantity flexibility; modified trade credit with buy back or quantity flexibility) are provided to induce the retailer to make decisions while optimizing the channel profit. This paper shows that the retailer provides a longer credit period to its customers and orders a larger quantity from the supplier under the composite contracts. With these contracts, the profit sharing between both parties depends on the wholesale price (Pareto improvement) for the fixed retail price and the purchasing cost.     

Probability-free solutions to the non-stationary newsvendor problem

This paper concerns the multi-period newsvendor problem. In this problem, the decision maker has to decide the order quantity of an item in the subsequent period in which the demand is usually unknown. No statistical assumptions are made about the unknown demand. We adopt an online learning method from the field of prediction with expert advice to study the non-stationary newsvendor problem. We propose newsvendor strategies for both real-valued and integer order quantities. Taking the non-stationary strategies that can switch between different order quantities as benchmark, we prove that our proposed strategies can guarantee that the newsvendor’s cumulative gains are almost as large as those of the best switching strategies with not too many switches. Simple computational experiments are further performed to illustrate the effectiveness of our strategies.     

On the value of customer information for an independent supplier in a continuous review inventory system

We consider the inventory control problem of an independent supplier in a continuous review system. The supplier faces demand from a single customer who in turn faces Poisson demand and follows a continuous review (R, Q) policy. If no information about the inventory levels at the customer is available, reviews and ordering are usually carried out by the supplier only at points in time when a customer demand occurs. It is common to apply an installation stock reorder point policy. However, as the demand faced by the supplier is not Markovian, this policy can be improved by allowing placement of orders at any point in time. We develop a time delay policy for the supplier, wherein the supplier waits until time t after occurrence of the customer demand to place his next order. If the next customer demand occurs before this time delay, then the supplier places an order immediately. We develop an algorithm to determine the optimal time delay policy. We then evaluate the value of information about the customer’s inventory level. Our numerical study shows that if the supplier were to use the optimal time delay policy instead of the installation stock policy then the value of the customer’s inventory information is not very significant.     

风险厌恶条件下竞争报童问题的二层规划模型

有效应用数学规划方法研究报童类产品的库存管理,能够降低企业的成本和风险,从而提高企业的经济效益.此类问题的研究,目前主要集中在应用Nash博弈研究竞争报童问题以及零售商所持风险态度对供应链库存水平的影响.试图研究序贯决策下的竞争报童问题模型以及零售商所持风险态度对供应链库存水平的影响.由此建立了二层规划模型.算例表明序贯决策的竞争报童问题中,总订购量随风险厌恶程度的提高而降低.     

Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions

This paper provides an approximating programming technique to solve the multi-product newsvendor model in which product demands are independent and stocking quantities are subject to two or more ex-ante linear contraints, such as budget or volume constraints. Previous research has attempted to solve this problem with Lagrange relaxation techniques or by limiting the distribution of demand. However, by taking advantage of the separable nature of the problem, a close approximation of the optimal solution can be found using convex separable programming for any demand distribution in the traditional newsvendor model and extensions. Sensitivity analysis of the linear program provides managerial insight into the effects of parameters of the problem on the optimal solution and future decisions.     

Buyer-supplier currency exchange rate flexibility contracts in global supply chains

This paper analyzes a decentralized global supply chain under a newsvendor setting, where a supplier delivers a certain quantity of a single product to a buyer in accordance with the terms of a mutually agreed upon contract. This contract is signed prior to the delivery of the product and subsequent payment, thus, exposing the supply chain to the risk of currency exchange rate fluctuations. We propose two types of currency exchange rate flexibility contracts to explore the characteristics of exchange rate risk mitigation policies for the buyer and the supplier. Furthermore, we investigate the effects of the contract structures on the optimal order quantity, as well as the expected profits of both supply chain members. Our results show that the optimal order quantity of the buyer decreases when the wholesale price is uncertain due to exchange rate volatility. Also, both our proposed contracts tend to improve the expected profits of both the buyer and the supplier, when the payment is made in the supplier’s currency, indicating the desirability of adopting such contractual agreements from the perspective of both parties. On the other hand, when the payment is made in the buyer’s currency, our suggested contracts do not yield such win-win scenarios. Finally, we examine the effectiveness of availing the services of a local vendor, which is capable of satisfying any demand in excess of the quantity ordered from the foreign source with short notice, in order to mitigate the risks associated with an overseas order.     

价格数量折扣下多阶段报童问题的在线策略

价格数量折扣可以提高订购量, 是库存决策中的一个重要因素. 特别地, 当订购量达到一定水平时, 价格折扣才会发生. 应用理论计算机科学兴起的弱集成算法, 研究具有这种价格数量折扣的多阶段报童问题的在线策略. 弱集成算法是一种在线序列决策算法, 其主要特点是不对未来输入做任何统计假设, 克服了报童问题研究中需要对需求做概率假设的困难. 主要将弱集成算法应用到固定订购量的专家策略, 给出了价格数量折扣下多阶段报童问题的具体在线策略;得到了该在线策略相对于最优专家策略的理论保证. 进一步将回收价值和缺货损失费引入, 给出了推广的在线策略及其理论结果. 最后应用数值算例说明了给出的在线策略具有较好的竞争性能.     

Copula-CVaR下考虑随机成本和需求的单周期订货决策研究

不确定环境下的单周期最优订货量决策具有重要且广泛的应用价值。与传统的仅考虑需求不确定性的报童模型不同,本文考虑市场价格恒定,但成本和需求随机变化且相关联下的报童决策问题。为此,采用Copula函数构建成本和需求之间的关联,考虑决策者可能具有的风险态度,建立了相应的Copula-CVaR模型,证明了模型解的存在性和唯一性,并将模型离散化为易求解的线性规划问题。最后,通过不同的风险水平和多种Copula函数下的仿真,分析了随机成本与需求的相关性和波动性对最优决策结果影响,并得到相关结论,为相关企业决策提供依据。     

Robust distribution planning for supplier-managed inventory agreements when demand rates and travel times are stationary

Supplier-managed inventory (SMI) is a partnering agreement between a supplier and his customers. Under this SMI agreement, inventory monitoring and ordering responsibilities are entirely transferred to the supplier. Subsequently, the supplier decides both the quantity and timing of his customer deliveries. The inventory routing problem is an underlying optimization model for SMI partnerships to cost-effectively coordinate and manage customer inventories and related replenishments logistics. This paper discusses the case where customer demand rates and travel times are stochastic but stationary, and proposes a version of the inventory routing optimization model that generates optimal robust distribution plans. The approach proposed to obtain and deploy these robust plans combines optimization and Monte Carlo simulation. Optimization is used to determine the robust distribution plan and simulation is used to fine-tune the plan's critical parameters such as replenishment cycle times and safety stock levels. Results of a simplified real-life case implementing the proposed optimization-simulation approach are shown and discussed in detail.     

Newsvendor with multiple options of expediting

We consider a manufacturer facing single period inventory planning problem with uncertain demand and multiple options of expediting. The demand comes at a certain time in the future. The manufacturer may order the product in advance with a relatively low cost. She can order additional amount by expediting after the demand is realized. There are a number of expediting options, each of which corresponds to a certain delivery lead time and a unit procurement price. The unit procurement price is decreasing over delivery lead time. The selling price is also decreasing over time. In this paper, we assume that the manufacturer must deliver all products to the customer in a single shipment. The problem can be formulated as a profit maximization problem. We develop structural properties and show how the optimal solution can be identified efficiently. In addition, we compare our model with the classical newsvendor model and obtain a number of managerial insights.     

基于报童模型的过度自信零售商的订货决策与协调研究

根据以往过度自信的研究,我们借用报童模型,设定了一个期望需求及方差预测都存在偏差的过度自信零售商,探究了该零售商与理性零售商在订购量及利润方面的差别,算出了过度自信零售商的利润损失。并且分情况讨论,供应商是否能采取契约机制实现有过度自信零售商的供应链利润最大化。     

随机需求下基于供应中断的备份供应商决策分析

假定需求服从随机分布,研究由零售商主导的供应链中,采用一个战略供应商和一个备份供应商模式,零售商与备份供应商通过能力期权建立订货契约:首先,零售商向备份供应商预订能力,支付预订成本;接着,向战略供应商订货,如果没有发生突发事件则其供货量等于订货量,否则供货量变为零;然后,零售商基于战略供应商的供货量和备份供应商的能力预订确定向备份供应商的订货量,支付执行成本;最后,零售商用战略供应商和备份供应商的总供货量满足顾客需求。备份供应商在考虑自己的能力维持成本和制造成本后决定是否接受零售商提供的能力期权契约。针对零售商可选择的四种不同策略,求得采取不用策略所满足的条件,并给出相应的最优订货量、能力预订量和能力执行量和最优利润等的解析解。     

Demand uncertainty and supplier's returns policies for a multi-store style-good retailer

As demand uncertainty grows in the marketplace, a critical issue today in most purchase contract negotiations between an independent retailer of a style-good and its supplier is the provision of a returns policy, i.e., a commitment by the supplier to buy back unsold inventory of the good at the end of its selling season. Management science research on the strategic role and optimal design of returns policies has grown in recent years but so far offers little treatment of how exactly the retailer's optimal order quantity decisions are affected by demand uncertainty and how a supplier's returns policy can influence these decisions. Employing the traditional “newsboy problem” modeling framework, the authors investigate these issues considering a supplier who faces a retailer with two or more store outlets with normally distributed and possibly correlated demands. To facilitate their analyses, the authors employ a methodology based on special error function representations of the highly nonlinear objective functions of the retailer and supplier. Utilizing this approach, the authors are able to provide explicit insights into how: (a) the buyer's total order quantity decision is affected by the variability in demand; (b) buyback prices in combination with wholesale prices can influence the buyer's order quantity response to demand uncertainty; (c) demand uncertainty moderates the effects of the buyback and wholesale prices; (d) supplier's optimal combination of actions are affected by demand variability; (e) retailer's and supplier's expected profits behave in response to changes in the supplier's actions under different levels of demand variability.     

Sensitivity analysis of the newsvendor model

Quality of decisions in inventory management models depends on the accuracy of parameter estimates used for decision making. In many situations, error in decision making is unavoidable. In such cases, sensitivity analysis is necessary for better implementation of the model. Though the newsvendor model is one of the most researched inventory models, little is known about its robustness. In this paper, we perform sensitivity analysis of the classical newsvendor model. Conditions for symmetry/skewness of cost deviation (i.e., deviation of expected demand–supply mismatch cost from its minimum) have been identified. These conditions are closely linked with symmetry/skewness of the demand density function. A lower bound of cost deviation is established for symmetric unimodal demand distributions. Based on demonstrations of the lower bound, we found the newsvendor model to be sensitive to sub-optimal ordering decisions, more sensitive than the economic order quantity model. Order quantity deviation (i.e., deviation of order quantity from its optimum) is explored briefly. We found the magnitude of order quantity deviation to be comparable with that of parameter estimation error. Mean demand is identified as the most influential parameter in deciding order quantity deviation.     

Monotonicity properties of wholesale price contracts

This paper contributes to the supply chain contracts literature in economics and operations by performing qualitative sensitivity analysis of a wholesale price contract in a two-echelon supply chain setting. Order-theory tools are used to derive sufficient conditions for monotonicity of contract parameters.The upstream supplier is modeled as a Stackelberg leader. The supplier is assumed to have complete information about the costs and revenue function of the downstream retailer. It is shown that an equilibrium wholesale price weakly increases with an increase in the supplier production cost rate, but it may increase or decrease with an increase in the retailer cost rate. As either the supplier production cost or the retailer cost increases, the supplier profit decreases weakly. Additional sensitivity analysis is performed assuming certain properties of the retailer revenue function.Several well-known results in the supply chain contracting literature can be considered as special cases of the more general theorems developed here. In particular, this paper reexamines the analysis of a newsvendor supply chain problem by Lariviere and Porteus [Lariviere, M.A., Porteus, E.L., 2001. Selling to the newsvendor: An analysis of price-only contracts. Manufacturing & Service Operations Management 3, 293–305]. This paper generalizes and extends their work, by establishing properties of the newsvendor demand distribution that guarantee monotonicity of the contract parameters, without requiring a unique contract solution.     

A fuzzy newsvendor approach to supply chain coordination

In the absence of a clear command and control structure, a key challenge in supply chain management is the coordination and alignment of supply chain members who pursue divergent and often conflicting goals. The newsvendor model is typically used as a framework to quantify the cost of misalignment and to assess the impact of various coordination initiatives. The application of the newsvendor framework, however, requires the specification of some probability distribution for the sources of uncertainty, and in particular, for the market demand. The specification of an adequate demand distribution becomes difficult in the absence of statistical data. We therefore consider a fuzzy approach to the newsvendor problem. We use several fuzzy parameters in the model for the demand, the wholesale price, and the market sales price. We solve the fuzzy newsvendor problem to study three coordination policies: quantity discounts, profit sharing, and buyback. For each coordination policy, the optimal order quantity of the retailer is computed. The possible profits of the members in the supply chain are calculated with minimum sharing of private information. We further extend the fuzzy newsvendor model to a setting with a single manufacturer and multiple retailers under the assumption of ample capacity for the manufacturer. Detailed numerical examples are also provided.     

Stability and monotonicity in newsvendor situations

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization. However, we assume that the retailers impose some level of stock that should be dedicated to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where several model cost parameters and the retailers’ dedicated stock levels can change. We investigate how the profit division might be affected by these changes. We focus on four monotonicity properties. We identify several classes of games with retailers, where some of the monotonicity properties hold. Moreover, we show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general, when changes in dedicated stock levels are in concern.