A PRICE-SETTING NEWSVENDOR MODEL UNDER CVAR DECISION CRITERION WITH EMERGENCY PROCUREMENT

In this paper, we consider a newsvendor model in which a risk-averse manager faces a stochastic price-dependent demand in either an additive or a multiplicative form. An emergency purchase option is allowed after the realization of demand to satisfy the units that are short. By adopting Conditional value-at-risk （CVaR） as the decision criterion, we aim to investigate the optimal pricing and ordering decisions, and the effects of parameter changes in such a setting. We provide sufficient conditions for the uniqueness of the optimal policy for both demand models. We perforl~, comparative statics analysis to show how the optimal pricing and ordering decision behaves when changing parameters. We also compare our results with those of the newsvendor with a general utility function and with CVaR criterion under lost sales assumption. Our key results include： （i） For both demand models, the optimal selling price is decreasing in risk aversion. Hence, the optimal price of a risk-averse newsvendor is not greater than the optimal price of a risk-neutral newsvendor. （it） In contrary to the lost sales case, for the multiplicative demand model, the optimal order quantity may not be monotonic in risk aversion. Consequently, the optimal risk-averse order quantity may be lower or higher than the optimal risk- neutral counterpart. （iii） For the additive model, the optimal order quantity is strictly increasing in the emergency purchase price, while for the multiplicative model the optimal order quantity has no such a monotonic property. Some numerical examples are conducted to verify our claims and gain more insights about the risk-averse decision-making behaviors.

OPTIMAL DECISIONS WHEN BALANCING EXPECTED PROFIT AND CONDITIONAL VALUE-AT-RISK IN NEWSVENDOR MODELS

This paper investigates a risk-averse inventory model by balancing the expected profit and conditional value-at-risk （CVaR） in a newsvendor model setting. We find out that： i） The optimal order quantity is increasing in the shortage cost for both the CVaR only criterion and the tradeoff objective, ii） For the case of zero shortage cost, the optimal order quantity to the CVaR criterion or tradeoff objective is increasing in the selling price, respectively. However, it may not be monotonic in the selling price when incorporating a substantial shortage cost. Moreover, it may be larger or less than the risk-neutral solution, iii） Under the tradeoff objective function, although the optimal order quantity for the model without shortage cost is increasing in the weight put on the expected profit, this property may not be true in general for the model with a substantial shortage cost. Some numerical examples are conducted to verify our results and observations.

A RISK-AVERSE NEWSVENDOR MODEL WITH LIMITED CAPACITY AND OUTSOURCING UNDER THE CVAR CRITERION

For seasonal products, the retailers usually launch various marketing ettorts, llKe aaverusmg tmu promotion, to promote them in a selling season. While facing large demand from the customers, one should take the capacity constraint and outsotlrcing into consideration. Considering the shorten life cycles of most products, in this paper we adopt the traditional newsvendor model to investigate the optimal marketing effort along with optimal order quantity. We address the risk aversion issue and characterize the influence of the sellers＇ risk propensity with CVaR criterion, and we develop an effective algorithm to obtain the optimal strategy. The impact of sellers＇ risk propensity on the performance of the system is illustrated via numerical examples, The innovation of this paper is threefold. First, the optimal joint strategy of the marketing effort and order quantity is investigated and an efficient algorithm to find the optimal strategy is developed. Second, the capacity constraint option and an outsourcing strategy are studied jointly for excess products. Finally, the risk propensity of the seller and its influence are investigated by using the CVaR criterion, through which we obtain some new managerial insights.

Joint Bidding Decision of Wind Farms and Energy Storage Based on Newsvendor Model

Currently,renewable energy generation has received more and more attention.This article focuses on wind energy generation,one of the renewable energy sources.Aiming at the intermittent and unpredictable wind power problems,according to the day ahead bidding mechanism in the power market,this paper introduces the energy storage system to maximize wind power merchants profit based on the newsvendor model.First,this paper focuses on the wind farms combined with storage system to put forward the optimal bidding decision of selling or buying electricity to the market one day in advance and the optimal bidding amount.Then,we analyze the relationship between the optimal bid amount and the market penalty price coefficient,government subsidy,storage system charge and discharge efficiency,and other parameters.Based on the analysis of various parameters,power generation companies can make reasonable bidding decisions and amount to maximize profits.

The newsvendor model revisited： the impacts of high unit holding costs on the accuracy of the classic model

The newsvendor problem has been applied in various business settings. It is often assumed that the decision variable, i.e., order-up-to level, has no impacts on the holding costs for average inventory cycled in a given period, which is the difference between beginning and ending inventory levels on hand in that period. The average holding cost for this portion of inventory is conveniently and approximately calcutated as half the product of the unit holding cost and the expectation of the demand in one period if it is assumed that the inventory is approximately evenly consumed. It is a good approximation when the unit holding cost is significantly lower than the unit backorder cost as this optimal solution to inventory level is able to guarantee a low probability of understocking. However, if this condition does not hold, the approximation may deviate from the actual cost and cannot measure the expected holding cost for this portion of inventory. This paper examines the impact of the cycle stock holding cost on the newsvendor model and the conditions under which this portion of cost is not negligible.

基于报童模型的供应链网络均衡决策研究

在不确定性需求下构建了基于报童模型的两层供应链网络,供应链网络是由原料供应商、产品生产商和需求市场构成。针对不确定性需求引入报童模型到供应链网络均衡模型中,用于供应链网络中厂商的产量和价格决策。模型构建了基于报童模型的变分不等式来表达供应链网络在不确定性需求下的均衡条件。最后,通过数值案例给出了需求均匀分布下,方差对于产品价格、原料供应商产品流量的影响分析。

考虑库存风险的服装行业新产品预售策略博弈研究

电子商务时代,服装行业线上销售的退货率居高不下。为缓解高退货率连带的库存风险,部分服装企业采用超长预售策略,在相对较长的预售期内次第发货满足顾客订单。在此现实背景下,文章基于报童模型,探讨商家在正常预售和超长预售中的策略选择,并求解两种策略的最优定价、产量、利润和可行条件。结果表明:当需求不确定性较大且产品残值较小,预售时长在合理的范围内且顾客更愿意等待时,应选择超长预售策略,反之选择正常预售策略;并且,超长预售策略能够显著降低库存剩余风险。研究结论对服装企业的预售决策和库存管理具有一定的现实参考价值。

“蔬菜类商品的自动定价与补货决策”问题解析

给出2023年“高教社杯”全国大学生数学建模竞赛C题“蔬菜类商品的自动定价与补货决策”的可行解法,并对赛题评阅中发现的问题作了简要的评述.该题旨在通过对6个典型蔬菜品类的交易数据进行分析,探索蔬菜类商品的订购和定价问题.蔬菜需求具有明显的时间趋势和价格敏感性,由于保鲜期短,通常采用每日补货的运营方式.首先,通过剥离销量的时间效应,揭示销量的分布规律、价格与销量的耦合关系以及品类之间的相关性;其次,利用随机优化,建立优化模型并对补货和定价策略进行求解;最后,基于成本预测并叠加销量的时间效应,得到最优的补货量和销售价格.

基于“两部制”背景的地下储气库库容优化

随着“两部制”收费模式的逐步推进,地下储气库运营面临着市场化资源配置、定价形成机制和运营机制等诸多方面的运营难题。其中合理调节地下储气库库容,对地下储气库推进市场化运营具有重要的意义,有利于地下储气库提高收益回收建设成本,实现资产的保值、增值。为此,基于需求不确定的报童模型,建立地下储气库库容新模型,计算了地下储气库对内对外2种业务的最优库容分配。研究结果表明:①地下储气库非市场化运营下内部用户的实际注气量大于市场化下理论最优注气量,在市场化运营时可以通过对内部用户注气量合理规划,获得更多利润;②内部企业最优注气量与工作气量呈现负相关关系,设置合理的工作气量,为对外业务保留合理的剩余注气能力可以为地下储气库增益增值;③地下储气库在定价时要充分考虑用户的承受能力和可操作性,通过库容优化配置和合理市场化定价的匹配组合,实现了更高收益。结论认为,以报童模型为基础构建储气库库容分配模型,得到了需求不确定情境下储气库的最优注气量,为地下储气库优化库容资源配置提供理论依据,有助于推动地下储气库市场化改革的进程,具有较好的理论意义和现实价值。

基于目标客户定位的销售商决策模型研究

基于目标客户定位,构建销售商的两阶段决策模型,研究消费者策略行为对决策的影响。根据理性预期理论,分析销售商在3个目标客户定位策略下的最优决策,为其选择最优策略提供依据。结果表明:若消费者的异质程度较大,同时将策略消费者和全部短视消费者视为目标客户的策略不可行;随着更多的策略或短视消费者被视为目标客户,销售商可以降低产品的价格,但不能过度减少和增加订货量;高单位订货成本、大规模策略消费者及其不显著的异质性均有助于销售商选择同时将大量策略和短视消费者视为目标客户的策略。

基于零售商销售努力的风险和模糊规避报童模型研究

本文基于零售商的销售努力研究了一类风险规避与模糊规避报童问题。本文运用最坏情况条件风险值(WCVa R)方法构建了决策模型,得到了零售商订货量及努力水平的最优决策,该决策可完全退化为风险中性及模糊规避型决策,并进一步刻画了风险规避及模糊规避行为对零售商决策和利润的影响。研究发现,虽然风险容忍度越低,零售商的最优订货量越低,但是对于成长性较好的企业,决策者在WCVa R模型中的“风险”及“模糊”双重规避行为并不会导致决策过度保守,甚至在市场需求分布信息不完备的情况下,该模型比模糊中性的CVa R模型有更好的绩效表现。

考虑退货影响的概率销售下的库存问题研究

在现在产品的销售过程中,销售商在面临库存问题时,除了要考虑制定最优的决策以满足需求量,还需重视退货的问题。文章从销售商的角度出发,针对产品需求量不确定的情况下,采用概率销售策略;应用贝叶斯信息更新方法获取库存量和期望利润的模型,根据数值分析观察顾客的退货率对库存管理水平的影响。研究结果表明,随着产品退货率的上升,销售商的期望利润会下降,但贝叶斯信息更新方法的引入和概率产品转换率的提高可以减少退货所带来的损失。

考虑缺货影响的企业产品满足率和价格均衡分析

本文考虑消费者对缺货的厌恶程度,构建由销售有区别产品的n个企业组成的竞争市场,利用随机效应理论建立MNL模型,分别在价格外生与价格内生条件下分析竞争市场的均衡情况。在价格外生情况下,本文分别证明了满足率竞争和市场份额竞争两种情形下纳什均衡的存在性和唯一性。本文通过对两种情形下纳什均衡的比较分析,得到满足率竞争情形下企业提供更高的产品满足率,企业产品的市场份额增加,但企业获得的利润更低;在价格内生情况下,分别证明了价格满足率同时竞争与市场份额满足率同时竞争两种情形下纳什均衡的存在性和唯一性。通过比较分析,本文发现两种竞争情形下的产品满足率相同,但在价格满足率同时竞争情形下企业会制定更低的价格,企业产品的市场份额增加,获得的利润更低。最后通过数值仿真,本文表明市场中的企业数量越多,企业的价格和利润越低。此外,降低消费者对缺货的厌恶程度、产品单位成本或提高消费者对产品的估值能够使企业获得更大的利润。

回购与缺货成本下的连续时间报童模型

对带回购策略与缺货成本的连续时间报童模型,研究了其最优订购策略与批发价策略,使得生产商和零售商期望收益最大化。在零售价格依赖需求过程与零售价格外生的两种情形下,讨论了带回购策略和缺货成本对连续时间报童均衡策略的共同影响。运用随机最大值原理研究了以上问题均衡策略的存在唯一性,讨论了均衡策略满足的条件,在价格外生情形下得出结论:回购策略与缺货成本的共同作用,使得零售商的最优订购量和供应商的最优批发价格均提高很多。最后,通过数值算例做了最优批发价格与最优订购策略的敏感度分析,具体例子验证了已得结论。

考虑零售商定价和库存决策的零售平台差异化补贴策略研究

文中研究了一个包含多个零售商定价与库存决策的零售平台补贴策略优化问题,并基于平台补贴这一新的运营模式,研究平台与零售商的决策优化问题。首先,通过一个单周期的报童模型刻画零售商对库存与定价的决策;然后,考虑零售平台对零售商的补贴和抽成,建立了一个双层规划模型,随后设计了一个启发式算法求解模型,并给出了详细的求解过程;最后通过数值仿真验证了算法的有效性。同时,文中还就存在多个零售商时平台的决策进行了内在原因分析。研究结果表明,文中提出的模型及算法对于求解零售商与零售平台的决策问题有一定效果。

基于顾客惰性行为的无理由退货策略研究

通过对加入了顾客惰性因素的无理由退货策略建立数学模型,发现当惰性顾客存在时,商家的最优销售价格为只考虑理性顾客时的标准价格与惰性损失之差;最优退货价格为产品的清货价格与边际惰性效用贡献率之和;与只考虑理性顾客的无理由退货策略相比,惰性在一定程度上会对销量产生负影响,但在相同环境下却能为商家带来更多的利润。

需求不确定环境下多个零售商竞争的鲁棒随机优化模型

在需求不确定环境下构建了由一个制造商和多个零售商组成的供应链系统,考虑不同产品的可替代性,建立了多个零售商竞争的随机优化模型。利用鲁棒优化方法研究了需求不确定环境下多个零售商竞争的绝对鲁棒优化问题、偏差鲁棒优化问题和相对鲁棒优化问题。最后通过数值算例比较分析了不同产品替代率下的绝对鲁棒优化解、偏差鲁棒优化解及相对鲁棒优化解。

零售业供应链企业RFID技术应用决策研究

采用RFID技术产生的成本是制约RFID应用的主要因素。通过采用报童模型分析了由1个生产商和1个零售商组成的供应链,考虑了零售商商品摆放错误对供应链利润的影响。分别研究了集中决策和分散决策情况下,采用RFID技术对生产商和零售商利润的影响,以及可以承担的最大RFID标签成本,为供应链成员企业采用RFID技术的决策提供了定量化、模型化的依据。

基于顾客策略行为的供货水平与供应链绩效

基于顾客策略行为,考虑报贩模型和分散式供应链模型。通过分析销售商与顾客的理性预期均衡,研究了批发价格契约、数量折扣契约和两部定价契约下的供货水平和供应链绩效。研究结果表明:两部定价契约能提升供应链利润,高利润同时伴随着高供货水平,而批发价格契约或数量折扣契约下的供应链绩效则小于一体化供应链绩效。由于顾客策略行为的存在,生产商应该把两部定价契约中的批发价设定在低于生产商边际生产成本,以增大供应链的供货水平,从而提高供应链利润。

过度自信的报童模型研究

将过度自信定义为报童对市场需求信息的过度精确,建立了过度自信的报童模型,得到了过度自信报童的最优订货量和理性报童最优订货量之间的线性解析关系,并分析了过度自信水平对订货偏差及利润损失的影响。研究发现,随着报童过度自信水平的增加,其订货量会越来越偏离理性的最优订货量,而且过度自信导致的利润损失是关于过度自信水平的递增的凸函数,最后通过算例对上述的模型和结论进行了分析验证。