An inventory model with random discount offerings

We consider an inventory model in which a supplier makes deal offers with random discount prices at random points in time. Assuming that discount offerings follow a Poisson process and discount price is a discrete random variable with a known distribution, we propose a continuous-review control policy for the model and derive optimality conditions for the policy parameters. The model is then extended to the case of multiple suppliers that offer discount deals with supplier-specific Poisson processes and discount prices. Numerical examples are presented to demonstrate cost savings due to discount offers.     

提前期、构建成本和短缺量拖后率均可控的EOQ模型

传统库存模型通常将提前期和构建成本视为不可控制。事实上可以通过追加投资缩短提前期和降低构建成本。缺货期间,为减少订单丢失量和补偿顾客的损失,供应商会给予一定的价格折扣。现实库存系统中,容易得到需求的期望值和标准差,但较难得到其分布规律。基于此,考虑短缺量拖后率与价格折扣和缺货期间库存水平相关,提出了一种需求为任意分布且提前期和构建成本均可控的EOQ模型,证明了模型存在唯一最优解,给出了一种寻优算法。数值仿真分析表明,一般情况下,压缩提前期和降低构建成本能降低订购批量和安全库存,降低库存总成本;短缺量拖后系数和缺货概率对库存总成本影响较大,企业应尽量降低缺货概率,尤其在短缺量拖后系数较小时。     

基于期权的易逝品订购预售联合策略研究

由需求不确定所引起的库存过剩或产品脱销通常会给企业的正常运营带来极大风险,本文考虑一种运输时间影响损耗率的易逝品,在消费者估值不确定的情况下,从集成的角度出发,针对零售商的订购与预售联合策略展开研究。需求端零售商可通过批发价订购方式或组合订购方式采购易逝品,销售端可提供折扣预售和期权预售两种策略。通过模型构建详细分析了几种不同的订购预售联合策略,求解了不同策略下的最优订购量和最优预售价格以及不同策略的适用情形。研究发现柔性采购(组合订购方式)和期权预售联合决策可以有效降低需求波动带来的库存积压和产品短缺风险,且期权预售策略比折扣预售策略的应用范围更广。     

分段的延期支付条件下临时订货策略分析

商业活动中供应商时常会给采购商短期的价格折扣,目的是使采购商进行临时的大量采购;供应商为了鼓励采购商订货,会针对采购规模给予其不同的延期支付期限;而当价格恢复到定常时,延期支付的期限则为供求双方事先规定的常值,采购商按照允许延期支付的EOQ模型订货。将延期支付基本EOQ模型中存在的门槛式延期支付规则(只有当采购量大于特定值才可以延期支付货款)应用并推广到这种临时采购中:延期支付期限是临时采购量的分段函数。由于采购商可以采取按低价追加订货或者放弃这个机会,基于这2种策略年度成本差异最大化,分析了采购商最优的追加订货批量如何确定的问题,拓宽了允许延期支付的EOQ模型应用范围。     

考虑旅客跨区间流转的机票多预定区间折扣优化模型研究

多预定区间差异化折扣逐渐成为机票收益管理的重要分支。本文提出了一种新的收益管理模型：基于顾客跨区间流转的收益管理模型,并给出了二分法迭代求解方法。假设各个预订时间区间的潜在需求可以通过大数据手段进行预测,首先结合旅客的价格敏感和潜在需求跨时间段流转的特性分析了各区间的需求函数,然后结合需求函数构建了多预定区间折扣优化模型。由于该模型属于动态的收益管理模型,因此构建了一种动态求解方法——二分迭代法。最后,依据航空公司的实际情况设计了两个仿真实验。实验计算结果不仅验证了新模型和算法的有效性,而且得出一些比较有用的结论：（1）票价与提前购票时间不存在单调的线性关系;（2）预订区间远离离港日折扣逐渐变大,靠近离港日的折扣会逐渐减少,但是包含离港日的预订区间的折扣又会变大;（3）流转率越高则折扣越少;（4）价格敏感系数越高折扣越高;（5）流转率通过改变价格敏感系数而影响折扣的大小。本文给出的折扣优化决策模型符合旅游产品多预定区间折扣决策的实践,可以为机票、酒店、景区等多种旅游产品的票价决策提供有益参考。     

PRICE‐DEPENDENT INVENTORY MODELS WITH DISCOUNT OFFERS AT RANDOM TIMES*

We consider an inventory model with a supplier offering discounts to a reseller at random epochs. The offer is accepted when the inventory position is lower than a threshold level. We compare three different pricing policies in which demand is induced by the resellers price variation. Policy 1 is the EOQ policy without discount offers. Policy 2 is a uniform price, stock‐independent policy. Policy 3 is a stock level‐dependent, discriminated price policy. Assuming constant demand rates, expressions are obtained for the optimal order quantities, prices, and profits. The numerical experiments show that if it is better to accept a suppliers discount, then it benefits the reseller to transfer the discount to downstream customers.     

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。     

The resource constrained multi-item inventory problem with price discount: a geometric programming approach

In this paper we present a geometric programming approach for determining the inventory policy for multiple items having price discount and a limit on the total average inventory of all the items. An example is solved to illustrate the method.     

基于可控提前期和延迟供货的短生命周期产品库存模型

本文用斜坡型函数来描述短生命周期产品需求变化特征,用持有成本不断增加的形式来表示存货的无形变质所带来的损失,通过向供应商支付额外的赶工成本来缩短提前期,同时在允许缺货的情况下设置合理的缺货期价格折扣来控制订单的流失,即以价格折扣的损失来挽留住更多的顾客,使其总成本到达最优。本文在此基础上建立了短生命周期产品的库存模型,并提出了最优解的求解方法。     

短生命周期产品的三种库存模型的比较

讨论短生命周期产品库存模型,考虑无形变质因素,并假定无形变质率与需求率成反比关系.在线性需求和常数生产率的条件下,假设,若需求率为1,则视作产品的市场生命周期结束.并且,在产品生命周期的前期不存在缺货的情况下,给出了短生命周期产品分别在理想状态、允许缺货以及价格折扣导致需求率变化等3种状态下的库存模型,最后在相同参数条件下对这3种模型进行比较,找出了单位时间内平均总成本最小的最优库存模型,厂商可以根据自身的情况选择合适的库存策略.     

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。     

两级供应链Stackelberg主从对策的优化模型及其应用

本文研究了供应链的协调订货模式及其特例,提出了两级供应链Stackelberg主从对策问题模型,其中卖方作为主方给出最小补充期策略,买方作为从方以最优库存策略响应。建立了求解Stackelberg主从对策问题的成本优化模型,并考虑了累积价格折扣激励和买方库存成本合理化。对一个石油分销系统Stackelberg主从对策问题应用遗传算法离线仿真计算,得出Stackelberg均衡解,达到帕累托最优。     

考虑订货协调成本与数量折扣的改良品供应链水平协调

在单个供应商与多个销售商构成的二级改良品供应链中，销售商们采用联合补货方式不仅可以分摊订货成本，而且由于订货批量的增加从而更易获得供应商提供的数量折扣合同。建立多个销售商在独立补货与联合补货中的利润水平函数，推导联合补货优于独立补货的充要条件。将销售商之间的联合补货行为转化成多人合作博弈问题，证明博弈具有的基本性质，设计基于博弈核心的利润分配方法。通过数值算例和敏感性分析验证了文中所构建模型的正确性。     

消费者锚定效应下的动态定价与库存控制研究

在零售商-消费者两级供应链中, 零售商垄断销售市场, 研究基于消费者锚定效应的动态定价与库存问题。将消费者的锚定效应纳入决策模型中, 探讨消费者锚定的参考价格与产品的市场需求、价格的动态变化关系;利用动态规划理论建立了消费者锚定效应的动态定价与库存模型;在此基础上考虑利润折现和库存积压问题, 并分别构建了相应模型。数值分析表明, 消费者会根据市场价格的变化决定最佳的购买时机, 零售商的期望收益随着销售时间的延长而增加。     

Supply Chain Coordination in the Presence of Gray Markets and Strategic Consumers

The practice of diverting genuine products to unauthorized gray markets continues to challenge companies in various industries and creates intense competition for authorized channels. Recent industry surveys report that the abuse of channel incentives is a primary reason for the growth of gray market activities. Therefore, it is crucial that companies take the presence of gray markets into consideration when they design contracts to distribute products through authorized retailers. This issue has received little attention in the extensive literature on contracting and supply chain coordination. In this study, we analyze the impacts of gray markets on two classic contracts, wholesale price and quantity discount, in a supply chain with one manufacturer and one retailer when the retailer has the opportunity to sell to a domestic gray market. Our analysis provides interesting and counterintuitive results. First, a classic quantity‐discount contract that normally coordinates the supply chain can perform so poorly in the presence of a gray market that the supply chain would be better off using a wholesale price contract instead. Second, the presence of gray market can also degrade the performance of the wholesale price contract; therefore, a more sophisticated contract is needed for coordinating the supply chain. We show that contracts that solely depend on retailer's order quantity cannot coordinate the supply chain, and provide the conditions for coordinating the supply chain with price‐dependent quantity discount contracts. We also provide comparative statics and show that when there is a gray market, coordinating the supply chain enhances total consumer welfare.     

具有两阶段生产模式和需求信息更新的供应链契约研究

针对二级供应链,在基于Stackelberg博弈的批发价契约中,分析了折扣价格与零售商最优提前订购量的关系及对契约双方期望收益的影响;设计了价格折扣与回购联合的协调契约,分析了供应链系统的最优提前生产量、供应链协调条件及协调契约下制造商和零售商的期望收益变化,并在协调契约不满足制造商的个体理性约束时,提出采用不对称Nash谈判模型设计两阶段生产与订购的回购契约,在保证供应链系统整体绩效最优的条件下,使制造商和零售商利润都能得到满意增长。研究表明,三级供应链实行两阶段订购的必要条件是分销商与零售商的最优提前订购量相等,与二级供应链相比,价格折扣契约下三级供应链效率更低,但价格折扣与回购联合的契约同样能协调三级供应链,该协调契约满足零售商与分销商激励相容约束。     

两种激励条件下三级供应链产品质量控制策略研究

本文基于四阶段Stackelberg博弈分析,研究了在三级供应链中如何进行产品质量控制策略问题。构建了由制造商、零售商与最终顾客组成的三级供应链博弈模型,制造商进行产品质量决策,即生产高质量产品或者低质量产品,零售商进行产品采购决策和零售定价决策,最终顾客根据两种产品质量水平和零售价格的差异,决定产品的购买数量;当零售商采购高质量产品时,制造商将会向其提供价格折扣策略;当零售商采购低质量产品时,制造商将会向其提供延迟付款策略。运用最优化原理,求解了制造商的产品质量水平、价格折扣、延迟付款期限和零售商的零售价格、最终顾客的购买数量,及期望收益函数。进行了算例分析,结果表明:高质量产品零售价格关于价格折扣下降幅度更大,而低质量产品零售价格关于延迟付款期限下降幅度更大;制造商提供的价格折扣越大、延迟付款期限越长,其期望收益将会减少,此时零售商的期望收益将会增加,最终顾客产品需求量将会增加;制造商的总期望收益函数将呈现"倒U"型,求解了期望收益的最大值及各契约参数的值,结果证明所提出的产品质量控制策略是可行的。     

需求受销售价格与变质时间影响的时滞变质品供应链协调研究

在由单个生产商和单个销售商组成的两级时滞变质品供应链中,销售商面临的市场需求受销售价格和物品变质时间影响。分别建立分散决策与集中决策下的时滞变质品供应链定价与补货模型,得到两种决策模式下的销售价格与订货批量均衡解。通过比较两种决策模式发现,集中决策下的销售价格更低且订货批量和预期利润更高。引入数量折扣契约对时滞变质品供应链进行协调,并借助常相对风险规避型效用函数和纳什讨价还价理论来分配协调后的预期利润增量。通过数值算例演示了决策变量求解过程,敏感性分析给出了时滞变质品特性参数变动时对决策变量产生的影响。     

Quantity Flexibility Contract in the Presence of Discount Incentive

We design a new contract, which we refer to as the QFi contract, that combines the quantity flexibility (QF) mechanism and the price‐only discount incentive. Under the QF contract, the buyer does not assume full responsibility for the forecast, yet the supplier guarantees the availability of the forecasted quantity and extra buffer inventory. In contrast, the price‐only discount contract places full inventory burden on the buyer. We show that the proposed QFi contract effectively balances the inventory risk for both the buyer and the supplier considering both the QF and discount mechanisms. We also show that the QFi contract is able to achieve supply chain coordination. More importantly, the QFi contract's coordinating price scheme does not require knowledge of demand distribution. We identify areas where the buyer and supplier may both benefit from implementing the QFi contract as opposed to the extant QF or price‐only (wholesale) discount contractual decisions in a decentralized supply chain. We also specify the conditions under which supply chain coordination can be achieved in a win‐win manner. We conclude with managerial implications and provide directions for future research.     

To sell or not to sell to an off-price retailer in the presence of strategic consumers

In the newsvendor model, strategic consumers choose between buying the product at the regular price or waiting to try to buy the product at the discount price. Retailers can benefit from the ability to decrease strategic consumers’ perceived probability of finding a unit available at the discount price. Selling some inventory to an off-price retailer, who has a large number of thrift consumers, enables retailers to change consumers’ perceived probability of product availability at a reduced price, but at a cost of losing some strategic consumers to the off-price retailer. We show that without the off-price retailer’s exclusive consumers and even if the off-price retailer buys the product for a price below the retailer’s cost, the retailer can still be better-off with the off-price retailer. We also find that the retailer benefits more when the off-price retailer charges higher price for the product and has a large consumer segment of its own.