带全量价格折扣的供应商最低免运费订货批量研究

本文从供应商角度,首先基于经济订货批量模型建立了使供应商利润最大化的最小订货量优化模型,并给出了解析解。然后,我们又将其拓展到商品带全量价格折扣和运费带全量折扣的情形,并基于折扣函数的非连续性,运用逆向归纳法建立了最优免运费最小订货量的数值算法。最后通过算例对最优免费送货策略的有效性及使用条件进行了理论分析。     

基于二阶段随机规划的城市医疗废弃物回收网络设计

城市医疗废弃物日益增加,且回收需求量受诸多因素的影响,难以准确预测,假定回收需求为确定值的医疗废弃物网络优化设计不能与实际需求相匹配。本文考虑了离散随机参数环境下,医疗回收网络设计中选址规划、分配计划及运输规划的协同优化问题,建立了以选址成本、运输成本最小为目标,设施与车辆能力限制为约束的二阶段随机规划模型。根据模型特点,设计了基于Benders decomposition的求解算法,同时,设计了一系列加速技术用于提高算法的求解效率。最后,以国内某城市医疗回收网络为背景设计算例,检验本文模型和求解策略的可行性和有效性。结果表明：相比确定性规划,随机规划的解能够节约总成本,结合一系列加速技术的Benders decomposition方法比CPLEX与纯的Benders decomposition更有优势。     

闭环供应链网络设施竞争选址模型研究

如何把握市场竞争趋势的变化,充分了解行业竞争状况,为企业新建设施选择具有竞争优势与发展前景的位置,是企业进入新市场要解决的首要问题。考虑一个大型企业计划开设一定数量的制造/再制造工厂和销售/回收中心以进入一个区域市场,在此市场上已存在若干同类设施的情况下,通过分析新进企业与这个区域内现有企业构成一主多从Stackelberg主从对策问题,将均衡模型捕捉的由新进企业引起的网络均衡态的变化引入位置决策过程,建立设施竞争选址模型决策在竞争环境中使新进企业利润最大化的位置,以及产品生产量、各层设施间的产品交易量和产品价格等决策。针对模型的特点,提出了遗传算法与QPADM算法相结合的求解策略,最后利用提出的模型和求解算法对算例进行计算与分析。     

网络购物平台最优价格促销策略：价格折扣还是现金券？

平台价格促销已成为平台营销中的重要问题，不同于传统模式下商家决定商品的价格促销，平台价格促销是以平台作为价格促销的决策者。本文建立了平台价格折扣和现金券两种由平台作为决策者的价格促销模型，探讨平台的最优价格促销策略，并在原有模型的基础上考虑商家广告投资决策并构建了扩展模型。研究结果表明，(1)只有当商品的基本需求、消费者价格敏感度和商品价格满足一定条件时，平台价格促销才能提升平台利润。(2)在两种价格促销都能提升平台利润情况下，平台的交易费率较高且商品价格较低则平台实施现金券策略的利润高于价格折扣策略；其他情况下平台实施价格折扣策略的利润高于现金券策略。(3)在平台交易费率较低的情况下，价格折扣策略下消费者能得到更多优惠；否则现金券策略下消费者得到更多优惠。(4)增加商家广告投资能够提高平台促销活动的利润，但是平台的价格优惠降低，且平台实施价格促销活动的条件区间减小。     

遗传算法在逆向物流网络选址问题中的应用研究

随着公众环保意识的增强、环保立法的出台和可观的经济利益的显现,企业开始关注逆向物流。而在逆向物流中,集中退货中心管理是企业逆向物流系统高品质运作的基础和前提。因此,本文构建了一个逆向物流网络中的选址模型,旨在研究从备选地址中选择建立配送中心或回收中心最佳策略,然后应用遗传算法讨论了该模型的具体解法。最后针对模拟算例,通过对比遗传算法和部分枚举法的效率及结果,说明遗传算法对于求解这类问题是一种有效的方法。     

库存水平影响需求的变质性产品的供应链协调模型

在考虑市场需求是库存水平线性分段函数、变质性产品和零售商采用(S,s)订货策略的情形下,本文研究了由一个供应商和一个零售商构成的供应链系统运作协调问题。给出了可以实现供应链完美协调的数量折扣策略,理论证明了模型最优解的存在性和唯一性,同时提供了相应的求解方法。数值算例结果表明该折扣模型对于改善供需双方绩效和供应链运作协调是十分有效的。     

基于二层规划的供应链契约谈判模型与求解

基于二层规划理论建立了一种形式化的契约谈判模型,并提供了基于模糊数学理论的交互式求解算法。以批量订货和价格折扣为例,分别研究了Stackclberg对策、集中式合作和基于二层规划的谈判合作三种策略下的契约机制。通过与另外两种策略的比较,初步得到采用谈判合作策略协调效果好、可执行性高的结论。     

基于随机p-鲁棒优化的国家血液战略储备库选址-库存模型

以往的救灾实践对建立国家血液战略储备体系提出了迫切要求。国家血液战略储备库的建设问题亟待解决。由于血液产品特性以及应急血液保障特性的存在,使得国家血液战略储备库的选址决策具有一定的复杂性。本文将问题定位为选址-库存问题。首先,以应急条件下血液保障及时度最高为目标,构建了一个不确定环境下考虑多情景、多血型、多阶段、带提前期、有容量限制、日常随机需求、有预算约束及协同定位的国家血液战略储备库选址-库存模型。同时,为了规避应急条件下的不确定风险,进一步构建了国家血液战略储备库选址-库存问题的随机p-鲁棒优化模型。该模型为离散非线性混合整数规划模型,难以快速精确求解。故基于模型性质,设计了相应的遗传算法。最后,设计了两组算例验证模型与算法的有效性。其中,第1组算例基于我国大陆地区31个省级血液中心与省级行政区的数据,并根据不同预算值给出6个算例,得到了国家血液战略储备库的选址-库存决策方案。第2组算例为6个不同规模的模拟算例,用来测试不同规模下的算法性能。算例结果表明：遗传算法的性能更好;鲁棒解与确定性模型最优值相差不大（最大差距≤1.08%）,可降低不确定性导致的风险。实践中,可对本文所建模型稍作改进,应用于具有类似特征的易腐品（药品、粮食等）应急物资储备库选址-库存决策。     

政府奖励机制下闭环供应链的利他关切性决策

考虑政府奖励机制的影响,文章对闭环供应链中的利他关切性决策进行研究。文章首先构建了制造商是否利他关切的两种分散决策和集中决策模型,并求解给出最优回收决策和政府最优奖励决策;然后,对各模型的最优决策进行比较分析,讨论制造商的利他关切对决策的影响。在此基础上,设计“数量折扣联合固定费用-成本共担”契约,对闭环供应链系统进行协调。最后,通过数值算例验证模型结论。研究表明：(1)政府奖励强度的设置存在阈值。只有当奖励强度大于阈值时,奖励机制才有效,才能促进废旧品的回收。(2)制造商的利他关切行为有利于系统获利,但不利于制造商利润的增长,但是这种利他行为扩大了制造商和零售商的谈判空间,有利于协调机制的实施;(3)政府最优奖励强度与WEEE回收价格和价格敏感系数正相关,与利他系数正相关。并且,政府奖励强度的增加有利于“数量折扣联合固定费用-成本共担”契约协调机制的达成。     

占线Bahncard问题的风险补偿模型

Bahncard 是德国 Decutsche Bundesbahn 铁路公司发行的一种优惠卡.这种因预先支付一定资金而在未来获得相应价格折扣的活动已经成为商家的主要价格折扣方式.但消费者选择最优的购买时机却具有较大的困难.因此,基于消费者对未来需求的有限预知,提出了风险补偿模型,应用竞争算法求解模型,得到最优的 TSUM 和 PSUM 策略及其相应的竞争性能比.实例证明所得的结论是对传统竞争算法的推广,最优的 TSUM 和 PSUM 策略具有现实的可行性.     

Optimal trade-in strategy of business-to-consumer platform with dual-format retailing model

B2C platforms are increasingly implementing trade-in programs to boost sales. Most of these platforms have adopted dual-format retailing model including both self-run stores and third-party stores. Under trade-in program framework, B2C platforms will determine the optimal trade-in rebate, and whether to offer the rebate to consumers with gift card (GC) or cash coupon (CC). GC can only be used in self-run stores, while CC can be used in both stores. To entice more consumers to trade-in products, platforms may launch trade-in efforts in the market. To address such decision-making challenges, we consider a B2C platform who owns a self-run store and hosts a third-party store, and examine the optimal trade-in strategy for the platform by developing four theoretical models. We first present two models without considering trade-in efforts, i.e., one model regarding GC payment, and one model regarding CC payment, and then extend them by taking trade-in efforts into consideration. Some interesting findings and insights are achieved. In particular, we find that both GC and CC do not always benefit the platform. Interestingly, offering high quality and low selling price for products in both the self-run store and the third-party store are also not always beneficial to the platform. So is the competition between both stores. Launching trade-in efforts may lead to a lower trade-in rebate but a higher profit for the platform. A counterintuitive finding is obtained that a higher gift card redemption rate is not beneficial to the platform, and vice versa.     

竞争环境下的以旧换新策略

企业通过对拥有旧产品的老消费者提供以旧换新补贴能够提升自身销量与利润。然而,面临竞争对手时企业的以旧换新决策是否会受到影响?本文求解了先后进入市场的双寡头竞争企业所面临的以旧换新与定价博弈均衡,并分析了竞争存在与否对于企业以旧换新策略产生的影响。研究结果表明,第一,面对竞争时企业的定价决策受到市场中老消费者比例、两家竞争企业各自新产品的创新提升水平、老产品的使用残值这四个因素的共同影响。第二,当老产品残值相对较低而市场中老消费者数量适中时,两企业均不提供以旧换新可能成为博弈均衡,而其他条件下,两企业均提供以旧换新为博弈均衡。第三,先进入的企业没有动机单独为消费者提供以旧换新补贴。第四,竞争对手的存在对于先进入企业自身的以旧换新决策与相应的定价策略都产生了显著的影响。     

基于非概率可靠性的铁路应急设施选址-路径鲁棒优化

鉴于铁路应急设施选址研究中很难合理估计参数的概率分布或确定其隶属函数的问题,将选址-路径问题与区间非概率可靠性方法结合起来,以复杂网络理论为基础,提出网络节点区间权重的确定方法,同时考虑节点权重、边权及径权区间不确定性的共同作用,构建铁路应急设施选址节点加权网络。基于区间非概率可靠性理论及区间运算规则,提出路径的非概率可靠性度量及最优时间可靠度路径选择方法,建立节点权重、边权及径权均为区间数的非概率可靠性铁路应急设施选址-路径鲁棒优化模型,并给出了求解算法,确定了基于区间模型的铁路应急设施鲁棒选址的最优方案。算例表明,本文的优化方案能更好地保证救援的时间鲁棒性,能有效地规避不确定因素波动对设施选址的长期风险,具有很好的实际应用价值。     

The comparison between trade-in and leasing of a product with technology innovations

Companies can adopt trade-in and/or leasing to shorten consumers׳ upgrade cycle and gain control over secondary markets. In this paper, we consider a monopolistic manufacturer who offers a technology product to a market consisting of heterogeneous consumers. We focus on an exogenous, stochastic innovation process that determines the availability of new technology and consequently, residual value of the current product. We derive the optimal pricing strategy of trade-in and leasing, respectively, examine its impact on the manufacturer׳s expected profit, and compare the performance of the two strategies. Trade-in protects the manufacturer against residual value risk and allows the flexibility of offering the option at different innovation states separately. Leasing, on the other hand, provides the manufacturer an opportunity to circumvent low new product prices and thus increases expected profit when product reuse profitability is high. The interplay between the two forces, product reuse profitability and new product price, determines the preference between trade-in and leasing. Our findings provide monopolistic manufacturers guidance on how to optimally employ the trade-in and leasing strategies.     

考虑市场细分的零售商自主以旧换新策略研究

在越来越多企业开始自主推行以旧换新业务的背景下,本文从供应链的视角出发,构建考虑市场细分和消费者效用的策略模型,研究零售商自主以旧换新策略选择及相应的供应链决策问题,着重分析市场细分和旧产品折旧程度对策略选择、决策和供应链效率的影响.研究发现:零售商的策略选择除了受产品制造成本影响外,还依赖于外部客户比例和旧产品折旧程度;当老客户占比和旧产品折旧度处于某区域时,自主以旧换新策略优于无以旧换新策略;在某些情况下,制造商的期望策略与零售商的最优策略相悖;供应链效率受客户比例和旧产品折旧度影响.此外,当老客户占比或旧产品折旧度高于某阈值时,老客户对主体的利润贡献大于新客户.本文的研究结论对企业在供应链环境下推行以旧换新政策有一定的理论指导意义.     

焕新计划下考虑消费者细分的产品定价策略

焕新计划是生产商为提升自身竞争优势而推出的一种促销手段，加入焕新计划的消费者在第一阶段可以享受全方位服务，在第二阶段可以享受以旧换新抵扣优惠。消费者将权衡加入焕新计划的费用、服务水平以及抵扣力度等因素决策是否在第一阶段加入焕新计划。本文假设时尚型消费者每阶段都会购买最新产品，而节俭型消费者第一阶段购买产品后在第二阶段继续使用，针对这两类消费者在实施焕新计划和不实施焕新计划两种情况下，构建两阶段模型以决策产品的最优定价；运用解析方法分析了产品的生产成本等参数对最优定价的影响；运用解析方法和数值算例方法对两模型进行对比。     

Strategyproof mechanism design for facility location games with weighted agents on a line

Approximation mechanism design without money was first studied in Procaccia and Tennenholtz (2009) by considering a facility location game. In general, a facility is being opened and the cost of an agent is measured by its distance to the facility. In order to achieve a good social cost, a mechanism selects the location of the facility based on the locations reported by agents. It motivates agents to strategically report their locations to get good outcomes for themselves. A mechanism is called strategyproof if no agents could manipulate to get a better outcome by telling lies regardless of any configuration of other agents. The main contribution in this paper is to explore the strategyproof mechanisms without money when agents are distinguishable. There are two main variations on the nature of agents. One is that agents prefer getting closer to the facility, while the other is that agents prefer being far away from the facility. We first consider the model that directly extends the model in Procaccia and Tennenholtz (2009). In particular, we consider the strategyproof mechanisms without money when agents are weighted. We show that the strategyproof mechanisms in the case of unweighted agents are still the best in the weighted cases. We establish tight lower and upper bounds for approximation ratios on the optimal social utility and the minimum utility when agents prefer to stay close to the facility. We then provide the lower and upper bounds on the optimal social utility and lower bound on the minimum distance per weight when agents prefer to stay far away from the facility. We also extend our study in a natural direction where two facilities must be built on a real line. Secondly, we propose an novel threshold based model to distinguish agents. In this model, we present a strategyproof mechanism that leads to optimal solutions in terms of social cost.     

基于旧件质量和“以旧换再”补贴的分级定价研究

以旧换再补贴政策已经在我国试点施行，相关原型新品和再制品的市场购买行为和企业定价决策受此影响。根据传统销售和售后渠道以及消费者持有旧件质量的不同细分市场，考虑到消费者的"以旧换再"偏好程度构建了制造商分级定价利润模型并分段优化，得到了"以旧换再"补贴下的最优分级定价决策，面向企业给出了旧件分级再制造的成本条件，面向政府给出了授予企业产品补贴资格的参考依据。考虑到再制造领先企业和一般企业再制造条件的不同，采用算例分析展示了补贴对领先企业及一般企业再制造分级定价决策的影响，并分析了消费者"以旧换再"偏好程度的变化对企业分级再制造决策的影响。结果表明，分级定价可以提高再制造系统的整体利润；换购补贴对促进再制造领先企业与一般企业再制造体系发展的积极作用不同，政府应根据产业及企业特点结合其他举措选择实施补贴的时机和补贴比例。     

Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns

In this paper we study a class of locations models where facilities are not perfectly reliable and failures may be correlated. We analyze problems with Median and Center objectives under complete and incomplete customer information regarding the state of facilities. The goal is to understand how failure probabilities, correlations, availability of information, and problem objective affect the optimal location patterns. In particular, we want to find analytical confirmations for location patterns observed in numerical experiments with network location models. To derive closed-form analytical results the analysis is restricted to a simple (yet classic) setting: a 2-facility problem on a unit segment, with customer demand distributed uniformly over the segment (results can be extended to other demand distributions as well). We derive explicit expressions for facility trajectories as functions of model parameters, obtaining a number of managerial insights. In addition we provide the decomposition of the optimal cost into the closed form components corresponding to the cost of travel, the cost of facility unreliability and the cost of incomplete information. Most of the theoretical insights are confirmed via numerical experiments for models with larger (3–5) number of facilities.     

Median problems with positive and negative weights on cycles and cacti

This paper deals with facility location problems on graphs with positive and negative vertex weights. We consider two different objective functions: In the first one (MWD) vertices with positive weight are assigned to the closest facility, whereas vertices with negative weight are assigned to the farthest facility. In the second one (WMD) all the vertices are assigned to the nearest facility. For the MWD model it is shown that there exists a finite set of points in the graph which contains the locations of facilities in an optimal solution. Furthermore, algorithms for both models for the 2-median problem on a cycle are developed. The algorithm for the MWD model runs in linear time, whereas the algorithm for the WMD model has a time complexity of  O(n²)\mathcal{O}(n^{2}) .