Risk-sensitive capacity control in revenue management

Both the static and the dynamic single-leg revenue management problem are studied from the perspective of a risk-averse decision maker. Structural results well-known from the risk-neutral case are extended to the risk-averse case on the basis of an exponential utility function. In particular, using the closure properties of log-convex functions, it is shown that an optimal booking policy can be characterized by protection levels, depending on the actual booking class and the remaining time. Moreover, monotonicity of the protection levels with respect to the booking class and the remaining time are proven.     

First- and second-price sealed-bid auctions applied to push and pull supply contracts

We investigate a newsvendor-type retailer sourcing problem under demand uncertainty who has the option to source from multiple suppliers. The suppliers’ manufacturing costs are private information. A widely used mechanism to find the least costly supplier under asymmetric information is to use a sealed-bid reverse auction. We compare the combinations of different simple auction formats (first- and second-price) and risk sharing supply contracts (push and pull) under full contract compliance, both for risk-neutral and risk-averse retailer and suppliers. We show the superiority of a first-price push auction for a risk-neutral retailer. However, only the pull contracts lead to supply chain coordination. If the retailer is sufficiently risk-averse, the pull is preferred over the push contract. If suppliers are risk-averse, the first-price push auction remains the choice for the retailer. Numerical examples illustrate the allocation of benefits between the retailer and the (winning) supplier for different number of bidders, demand uncertainty, cost uncertainty, and degree of risk-aversion.     

CVaR准则下两条供应链的促销努力竞争与链内协调研究

研究两条供应链相互竞争下决策者风险厌恶程度的影响和链内协调问题。针对两条分别由风险中性制造商和风险厌恶零售商组成、进行订货与促销竞争的可替代产品供应链,假定需求随机且依赖于促销努力水平与产品合格率,利用条件风险值(CVaR)方法和博弈理论建立了对应两条供应链均为分散式供应链(DD模式)、均为集中式供应链(II模式)、一条为分散式供应链一条为集中式供应链(DI模式)的EPEC、Nash和MPEC竞争决策模型,给出了三种模式下的竞争均衡决策、以及零售商为风险厌恶者时可实现链内协调的回购加促销补贴契约。进一步分析了零售商风险中性情况。最后的算例验证了模型的合理性和协调契约的有效性。研究表明,零售商越厌恶风险,其订货量越低;产品合格率越高,零售商的促销努力水平越大;供应链协调是供应链竞争下的占优策略。     

On the comparison of risk-neutral and risk-averse newsvendor problems

The objective of this paper is to investigate and compare the relationship between risk-neutral and risk-averse newsvendor problems under three different decision criteria: expected utility (EU) maximization, mean-variance (MV) analysis, and conditional value-at-risk (CVaR) minimization. Several models in the literature have shown that for special cases of the newsvendor problem (eg, no salvage value, no shortage penalty, and with recourse option), a risk-averse newsvendor orders less than a risk-neutral newsvendor. First, we present an observation about the EU maximization models with such special cases where a risk-averse newsvendor orders less than a risk-neutral one. We note that this observation does not extend to the newsvendor problem with positive shortage penalty. Using several counterexamples, we demonstrate that the common wisdom that a risk-averse newsvendor orders less than a risk-neutral newsvendor is not true in general. Second, we demonstrate, analytically where possible and numerically if not, that the comparison of the optimal order quantities of risk-neutral and risk-averse newsvendors depends on the key assumptions regarding the model inputs, namely, the decision criterion, the demand distribution and the cost parameters such as shortage penalty and unit ordering cost. Third, we show that EU and the MV criteria yield consistent results while EU and CVaR criteria may yield consistent or conflicting results depending on the loss function used for the CVaR criterion.     

常数相对风险厌恶多单位拍卖的比较静态与定价结构

考虑竞价者具有常数相对风险厌恶时的多单位拍卖问题,讨论均衡出价与风险偏好以及价值分布之间的关系.在竞价者具有相同的风险偏好的对称拍卖情形,利用风险中性等价导出了比较静态的充要条件,这一充要条件综合了风险偏好和价值分布的变化.在竞价者具有不同的风险偏好的非对称拍卖中,导出了均衡出价关于风险偏好的线性定价结构,依据这一结构,对任意给定出价,竞价者要求的剩余是其风险厌恶参数的线性函数,并且可以分解为竞争性剩余和风险厌恶剩余.     

The effect of risk aversion on a supply chain with postponed pricing

We consider a supply chain consisting of a supplier and a risk-averse retailer operating under endogenous demand in retail pricing. The demand potential is uncertain and is revealed at the beginning of the selling season when it is too late to order products. The product price, on the other hand, is not determined in advance and can be postponed until the demand is revealed. The goal is to study the effect of risk-aversion and postponed pricing on both the retailer’s decisions and the overall supply chain. We find that the risk-averse retailer does not necessarily order less than the risk-neutral one and may introduce a bias by choosing a specific demand distribution. We contrast two specific choices. One is symmetric (balanced) with respect to the mean demand potential. The other is skewed (pessimistic) with most observations expected below the mean demand potential. Our numerical results show that the binding downside risk constraint deteriorates the supply chain performance when the forecast is balanced and improves it when the forecast is pessimistic.     

产出不确定条件下“公司+农户”型订单农业供应链协商模型研究

在农产品产出不确定性及零售价格受农产品产出率影响的条件下,研究了一类由风险规避农户和风险中性公司组成“公司+农户”型订单农业农产品供应链协调问题。在该农产品供应链中,农户和公司通过Nash协商谈判来分别决策最优的生产量和订单价格。研究结果表明,在农产品产出不确定及零售市场价格受农产品产出率影响的条件下,风险规避型农户和公司的Nash协商合作博弈存在均衡解。Nash协商谈判所达成的最优农产品产出量和订单价格均高于分散决策情形下的最优农产品产出量和订单价格。最优农产品产出量是关于农户风险规避度的单调增函数,而最优的订单价格是关于农户风险规避度的单调减函数。最后,通过与分散决策情形相比,证明了Nash协商谈判机制能够促使风险规避型农户和风险中性型公司均达到帕累托改进。     

Optimal ordering and pricing strategies in the presence of a B2B spot market

In the current paper, we examine the effect of a B2B spot market on the strategic behavior and the performance of a reseller who continues to use the traditional channel while participating in a B2B spot market. We analyze the case in which a risk-neutral reseller faces an additive or multiplicative demand function and identify sufficient conditions under which the optimal order quantity and retail price exist and are unique. We then analytically examine the case in which a risk-averse reseller participates in a fully liquid spot market. We also study numerically how varying liquidity, spot price volatility, demand variability, and correlation coefficient affect a firm’s strategies and performance. We find that demand variability significantly affects both pricing and ordering strategies, whereas the spot price volatility has less influence on pricing decisions. Our results also show that for a risk-averse reseller to charge a lower retail price when the spot market liquidity increases is desirable. We further show that a B2B spot market cannot always improve a reseller’s utility. These findings shed light on how resellers can adjust their procurement and pricing strategies to align with the new business environment created by the emergence of B2B spot markets, as well as have obvious implications for the development of a B2B spot market.     

A recourse certainty equivalent for decisions under uncertainty

We propose a new criterion fordecision-making under uncertainty. The criterion is based on acertainty equivalent (CE) of a (monetary valued) random variable Z, $$S_\upsilon (Z) = \mathop {\sup }\limits_z \{ z + E_Z \upsilon (Z - z)\} ,$$ wherev(·) is the decision maker'svalue-risk function. This CE is derived from considerations ofstochastic optimization with recourse, and is calledrecourse certainty equivalent (RCE). We study (i) the properties of the RCE, (ii) the recoverability ofv(·) fromS _v (·) (in terms of the rate of change in risk), (iii) comparison with the “classical CE”u ^?1 Eu(·) inexpected utility (EU) theory, (iv) relation to risk-aversion, (v) connection with Machina'sgeneralized expected utility theory, and its use to explain theAllais paradox and other decision theoretic paradoxes, and (vi) applications to models ofproduction under price uncertainty, investment in risky and safe assets andinsurance. In these models the RCE gives intuitively appealing answers forall risk-averse decision makers, unlike the EU model which gives only partial answers, and requires, in addition to risk-aversion, also assumptions on the so-calledArrow-Pratt indices.     

基于CVaR风险测度标准的价格补贴策略下的协调研究

基于条件风险值模型(CVaR),探讨了在一个风险中性制造商和一个风险规避零售商组成的制造商领导的斯塔克伯格博弈供应链中,制造商如何与风险规避零售商订立批发价契约以最大化其期望利润的问题。设计了价格补贴的契约协调机制,给出了该机制下风险规避程度对零售商和制造商最优决策的影响。证明了在一定的实施条件下,制造商通过设立价格补贴机制,可改善供应链双方利润与供应链效率。最后,用算例验证了模型和理论分析的可行性。     

Optimal investment under operational flexibility, risk aversion, and uncertainty

Traditional real options analysis addresses the problem of investment under uncertainty assuming a risk-neutral decision maker and complete markets. In reality, however, decision makers are often risk averse and markets are incomplete. We confirm that risk aversion lowers the probability of investment and demonstrate how this effect can be mitigated by incorporating operational flexibility in the form of embedded suspension and resumption options. Although such options facilitate investment, we find that the likelihood of investing is still lower compared to the risk-neutral case. Risk aversion also increases the likelihood that the project will be abandoned, although this effect is less pronounced. Finally, we illustrate the impact of risk aversion on the optimal suspension and resumption thresholds and the interaction among risk aversion, volatility, and optimal decision thresholds under complete operational flexibility.     

风险规避型零售商资金约束下双渠道闭环供应链的定价决策

针对单一风险中性制造商和单一风险规避零售商组成的双渠道闭环供应链,建立制造商主导的Stackelberg博弈模型,讨论零售商分别通过银行贷款和延期支付解决资金约束问题时,各参与方的最优定价,分析回收率和零售商风险规避程度对决策结果的影响,并比较两种融资方式中决策结果的差异。研究表明:在双渠道闭环供应链中,零售商的资金约束不会影响批发价格、直销价格和零售价格随回收率的变化趋势。随着零售商风险规避程度的提高,银行贷款中批发价格的变化还与利率有关,直销价格始终降低;延期支付中批发价格始终提高,直销价格与之无关。当融资利率相等时,银行贷款中的批发价格始终高于延期支付,而直销价格和零售价格的相对大小还受利率和回收率的影响。     

Portfolio construction on the Athens Stock Exchange: a multiobjective optimization approach

In this research article, our purpose is to propose a single-period multiobjective mixed-integer programming model for equity portfolio construction, in order to generate the Pareto optimal portfolios, using a variant of the well-known ε-constraint method. The decision maker's investment policy, i.e. constraints regarding the portfolio structure, is strongly taken into account. An illustrative application in the Athens Stock Exchange market is also presented.     

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.     

A methodology for integrated critical spare parts and insurance management

Critical spare‐parts stock optimization has become a relevant topic for academy and industry. In most articles, the problem has been stated as a trade‐off between economic risks of shortages and financial costs. Risk optimization in this context has been mainly studied from a logistics point of view. The most common decision variables have been stock levels, stock location, and reorder points. In this context, buying insurance to cover shortage cost can be a complementary (or exclusive) measure for risk mitigation. Insurance optimization traditionally has been studied from a microeconomic and financial perspective. The main decision variable has been the indemnity function, and occasionally, the insurance premium. Its use in the context of physical asset management has not been observed to the best of our knowledge. This creates an opportunity to link inventory optimization techniques with insurance optimization for shortage losses. In this work, we present a novel approach to jointly manage the shortage risk of a critical non‐repairable component in a unique critical system. We develop an original model to integrate critical spare‐parts stock optimization with insurance optimization techniques. The result is a decision model to select the optimal stock and insurance policy that maximizes the decision maker's expected utility. This allows for a business‐centered integrated perspective in critical parts decisions. We present a case study representative of the mining industry, illustrating the complementary nature of selecting optimal stock levels and contracting an optimal insurance. Our results show that contracting an insurance can lead to policies preferred by a risk‐averse decision maker. The case study shows that this may even occur lowering stock levels and increasing profits. Copyright © 2015 John Wiley & Sons, Ltd.     

Capacity allocation for demand of different customer-product-combinations with cancellations, no-shows, and overbooking when there is a sequential delivery of service

We consider a problem where different classes of customers can book different types of services in advance and the service company has to respond immediately to the booking request confirming or rejecting it. Due to the possibility of cancellations before the day of service, or no-shows at the day of service, overbooking the given capacity is a viable decision. The objective of the service company is to maximize profit made of class-type specific revenues, refunds for cancellations or no-shows as well as the cost of overtime. For the calculation of the latter, information of the underlying appointment schedule is required. Throughout the paper we will relate the problem to capacity allocation in radiology services. Drawing upon ideas from revenue management, overbooking, and appointment scheduling we model the problem as a Markov decision process in discrete time which due to proper aggregation can be optimally solved with an iterative stochastic dynamic programming approach. In an experimental study we successfully apply the approach to a real world problem with data from the radiology department of a hospital. Furthermore, we compare the optimal policy to four heuristic policies, of whom one is currently in use. We can show that the optimal policy significantly improves the currently used policy and that a nested booking limit type policy closely approximates the optimal policy and is thus recommended for use in practice.     

“酒店+OTA”双渠道供应链超订策略研究

为解决市场需求不确定环境下,酒店和在线旅行网站(Online Travel Agency,OTA)合作时的能力超订量与在线房间预留量的决策问题,建立了基于佣金合作模式的数学模型,给出了实现酒店整体期望收益最大化的在线房间预留量与能力超订量。借助数值分析,进一步研究了佣金率与需求不确定性对最优决策的影响。结果表明,当佣金率与门店需求不确定性较小时,酒店采取双渠道策略并且实施超订;当佣金率与门店需求不确定性很大时,酒店采取门店单渠道策略但不实施超订。另外,在线房间预留量随着佣金率、门店需求不确定性的增大而减小。     

The value of rolling-horizon policies for risk-averse hydro-thermal planning

We consider the optimal management of a hydro-thermal power system in the mid and long terms. From the optimization point of view, this amounts to a large-scale multistage stochastic linear program, often solved by combining sampling with decomposition algorithms, like stochastic dual dynamic programming. Such methodologies, however, may entail prohibitive computational time, especially when applied to a risk-averse formulation of the problem. We propose instead a risk-averse rolling-horizon policy that is nonanticipative, feasible, and time consistent. The policy is obtained by solving a sequence of risk-averse problems with deterministic constraints for the current time step and future chance and CVaR constraints.The considered hydro-thermal model takes into account losses resulting from run-of-river plants efficiencies as well as uncertain demand and streamflows. Constraints aim at satisfying demand while keeping reservoir levels above minzones almost surely. We show that if the problem uncertainty is represented by a periodic autoregressive stochastic process with lag one, then the probabilistic constraints can be computed explicitly. As a result, each one of the aforementioned risk-averse problems is a medium-size linear program, easy to solve.For a real-life power system we compare our approach with three alternative policies. Namely, a robust nonrolling-horizon policy and two risk-neutral policies obtained by stochastic dual dynamic programming, implemented in nonrolling- and rolling-horizon modes, respectively. Our numerical assessment confirms the superiority of the risk-averse rolling-horizon policy that yields comparable average indicators, but with reduced volatility and with substantially less computational effort.     

Quality investment and price decision in a risk-averse supply chain

In this paper, we investigate quality investment and price decision of a make-to-order (MTO) supply chain with uncertain demand in international trade. Due to volatility of orders from buyers, the supplier and the manufacturer in the supply chain are subject to financial risk. In contrast to the general assumption that players in a supply chain are risk neutral in quality investment and price decision, we consider the risk-averse behavior of the players in three different supply chain strategies: Vertical Integration (VI), Manufacturer’s Stackelberg (MS) and Supplier’s Stackelberg (SS). The study shows that both supply chain strategy and risk-averse behavior have significant impacts on quality investment and pricing. Compared to a risk-neutral supply chain, a risk-averse supply chain has lower, same and higher quality of products in VI, MS and SS, respectively. Also, we derive the conditions under which the supply chain strategy is implemented in a decentralized setting. A numerical study is used to illustrate some related issues.