An EOQ model with deteriorating items in response to a temporary sale price

In economic order quantity models, it is often assumed that the unit purchase cost is constant. Such an assumption is usually not fulfilled in many practical situations. In practice, it is observed that suppliers sometimes offer temporary price discounts to stimulate demand, boost market share or decrease inventories of certain items. In this paper, a deteriorating inventory model with a temporary sale price has been developed. We shall be concerned with finding the optimal total cost saving for deteriorating items during the special replenishment period. Numerical examples are presented to illustrate the proposed model.     

随机需求环境下联产品系统价格与产量决策研究

基于固定比例生产技术和多产品随机需求的情形,研究了联产品制造商的两阶段产量和价格联合优化模型。通过反向倒推的优化求解,得到了联产品制造商的最优产量和价格决策以及变化规律。同时研究了需求服从均匀分布时,需求波动对均衡的影响。研究结果表明,在订货成本较低和一种产品的需求波动性较大时,当另外一种产品的波动增大,则该产品的最优订货量增大,同时价格下降。借助数值仿真,分析了价格敏感度和产出比例对最优决策和利润的影响。结果表明,在给定一种产品的价格敏感度时,另外一种的价格敏感度越大,那么该产品的价格就越低,制造商的订货量就下降。当一种产品的产出比例固定时,另一种产品的产出比例上升时,则该产品的价格下降,制造商的订货量下降,总利润上升。     

信息不对称下价格随机的应急数量折扣契约研究

以市场需求和市场价格随机波动的二级供应链为研究对象,寻找其在信息不对称条件下绩效优化的路径。通过显示原理分别构建生产成本和销售成本信息不对称时应急供应链的数量折扣契约模型,得到最优订货量与最佳批发价策略。通过具体的算例加以验证,分析了信息不对称程度对供应链上成员及整个供应链绩效的影响。研究结果表明：当突发事件造成市场价格随机波动和市场需求变化时,供应链上的跟随者能从隐瞒私人信息中获利。但当市场需求增大时,整个供应链绩效受损,反之则反是。这与以往研究在市场需求随机、市场价格固定和信息不对称条件下的结论迥异。     

全渠道零售下“Showrooms”对需求分布、定价和收益的影响研究

作为一种新兴的线下体验、线上购买的商业运作模式,展厅（Showrooms）在全渠道零售领域发展迅速。基于消费者效用分别建立单一网络渠道和"网络+实体"渠道下零售商开设Showrooms前后的利润模型,对比分析固定销售价格和优化定价两种情形下Showrooms对定价、市场需求、利润和退货率的影响。研究表明：（1）单一网络渠道下,网络渠道价格固定时,开设Showrooms可使市场总需求增加,总利润在展厅运营成本较低时增加;网络渠道价格优化时,开设Showrooms可使网络渠道价格、总需求和总利润在展厅运营成本较低时增加,但固定价格情形下总利润的增幅更大。（2）"网络+实体"渠道下,开设Showrooms可使总需求和总利润均在展厅运营成本较低及网络退货率和网购不便利成本较高时增加,而且仅优化网络渠道价格时的增幅最大,网络和实体渠道价格均固定时次之;价格优化的最终趋势是全渠道同款同价。（3）开设Showrooms可使零售商总的网络退货率和退货量都下降。     

An optimal replenishment model for inventory items with normally distributed deterioration

This paper deals with the inventory replenishment problem for deteriorating items with normally distributed shelf life, continuous time-varying demand, and shortages under the inflationary and time discounting environment. The reasons of choosing normal are twofold: it is one of the most important probability phenomena in the real world due to the classical central limit theorem, and it is also one of the most commonly used lifetime distributions in reliability contexts. The problem is formulated as a dynamic programming model and solved by numerical search techniques. The solutions of the model determine the optimal replenishment schedule over a finite planning horizon so that the present worth of the future costs associated with the system is minimized. In the extensive experiments, we validate the model, demonstrate the optimal replenishment schedule and lot-size, and carry out a comparative study to ascertain its contribution. In addition, sensitivity analysis was provided to help identify the most crucial factors that affect system performance. The experimental result shows that the deteriorating problem solved by an appropriate model (i.e. the proposed normal model) can save the total cost up to 2% approximately. It also identifies that the magnitudes of purchase cost per unit and demand rate are the most significant parameters that affect the replenishment decisions and cost.     

随机需求下考虑不同竞争情形的网约车平台动态定价

针对乘车需求波动下网约车平台间存在乘车需求竞争和乘运供应竞争的最优定价问题，以平台期望收益最大化为目标，运用最优控制论方法，构建不同竞争情形下的网约车平台动态定价模型，并利用哈密尔顿函数及模型推导，求得最优动态竞争价格解以及乘运供应率与需求率的变化轨迹。结果表明：平台最优动态竞争价格随市场需求的波动而动态变化，且最优价格可以有效调控平台供应能力，促使平台供需匹配，优化平台期望收益。此外，乘车需求市场竞争越激烈，平台最优价格越低，而乘运供应市场竞争越激烈，最优价格越高。平台间竞争的加剧将降低平台的期望收益，且平台期望收益随着固定佣金报酬率的提高先增大后减小。     

A decision support system for a third-party coordinator managing supply chain with demand uncertainty

Global supply chains reduce cost but increase lead times, complexities and uncertainties. Retailers in consumer products industry are getting shorter lead time to respond to market demand. To meet this challenge, many rely on third party supply chain managers (SCMs) for economically supplying required quantities of finished products quickly. However, due to shorter ‘time to market’, the SCM has to procure raw materials and start production process based on expected demand. Since SCM absorbs financial penalties associated with under- and over-estimation of demand from retailer, finding an optimal production lot size and product customisation strategy are essential to an SCM's operation. We develop a profit maximisation model and provide a close-form solution that allows an SCM to calculate optimal production lot size. The model is used to examine profitability of postponing product customisation. Finally, the effect of demand variation on SCM's profitability is explored.     

网络销售中退货担保与定价决策

本文采用退货担保期权综合完全退货策略与部分退货策略的优点,构建了网络销售中基于期权的退货与定价模型,以商品的价格、退货策略和退货担保期权价格为决策变量,讨论了存在退货期权和不存在退货期权两种情况下,最优决策存在的条件,求解出销售商最优价格、退货策略和退货担保期权价格,分析了各个市场参数变化对最优值的影响,通过对担保退货期权与退货策略同时存在和购买期权才能退货二种策略的比较,发现供应商最优策略是前者。算例验证了以上结论,做了敏感性分析,总结了相关管理启示与未来研究方向。所得结论对网络销售商开展网上销售有重要参考价值。     

考虑随机市场需求的双渠道供应链风险补偿策略研究——从质量与价格竞争视角

在由两个供应商和单个零售商构成的二级双渠道供应链系统中，分析了随机市场需求以及供应商之间同时存在价格与质量竞争的情形下的双渠道供应链协调问题。在供应链集中决策、无风险补偿及有风险补偿三种情境下，构建了基于质量和价格的风险补偿模型并求得纳什均衡解。研究结果表明：存在可行的需求风险补偿策略使得供应链达到协调水平，并且需求风险补偿策略对零售商更加有利；在需求风险补偿策略下，需求风险补偿价格与其对应批发价格正相关，与其产品质量水平负相关；价格竞争程度对零售商订货量具有负向影响作用，对供应链总利润影响作用随着竞争程度增加而减弱，质量竞争程度对零售商订货量和供应商产品质量水平具有正向影响作用，对供应链总利润影响呈倒U型关系；需求风险补偿策略能够激励零售商的订货行为，强化价格竞争程度和质量竞争程度对供应商订货量和供应链总利润的影响；在供应链系统中双渠道营销模式下的供应链总利润要优于单渠道营销模式下的供应链总利润。本文结论不仅详细剖析了风险补偿策略对双渠道供应链协调的影响关系，也理清了价格与质量竞争对各方行为策略的影响机理。     

Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: A geometric programming approach

A multi-item inventory model with constant demand and infinite replenishment is developed under the restrictions on storage area, total average shortage cost and total average inventory investment cost. These restrictions may be precise or imprecise. Here, it is assumed that inventory costs are directly proportional to the respective quantities, and unit purchase/production cost is inversely related to the demand. Restricted shortages are allowed but fully backlogged. First, the problem is formulated in crisp environment taking the deterministic and precise inventory parameters. It is solved by both geometric programming (GP) and gradient-based non-linear programming (NLP) methods. Later, the problem is formulated with fuzzy goals on constraints and objectives where impreciseness is introduced through linear membership functions. It is solved using the fuzzy geometric programming (FGP) method. The inventory models are illustrated with numerical values and compared with the crisp results. A sensitivity analysis on the optimum order quantity and average cost is also presented due to the variation in the tolerance of total average inventory investment cost and total average shortage cost following Dutta et al., 1993, Fuzzy Sets and Systems, 55, 133-142.     

Acquisition and Disclosure of Operational Information*

We study a firm's strategy for acquisition and disclosure of operational information by establishing linkages among information quality, managerial self‐interest, and production planning. We develop a multistage model in which a manager of a publicly traded firm first receives private information about the product demand and then uses it to make production and disclosure decisions. We consider two prevalent disclosure models employed in the accounting literature: all‐or‐nothing and cheap‐talk models. In the all‐or‐nothing model, it is assumed that any disclosure must be truthful, but the manager can strategically withhold information. We show that the manager commits to acquire the value‐added operational information if (i) the managerial self‐interest in the interim share price is low or (ii) the managerial self‐interest in the interim share price is high, but the fixed disclosure cost is either sufficiently low or sufficiently high. We demonstrate that the firm is better off if the production level is observable to the financial market because multidimensional signaling reduces costs. In the cheap‐talk model, we assume that the manager's disclosure may not be truthful. We show that the manager's incentive to acquire value‐added operational information increases along with the penalty cost for misleading investors. Therefore, a high penalty cost for misleading investors can encourage the manager to obtain more precise information, which in turn improves the firm's cash flow.     

Centralized versus Decentralized Competition for Price and Lead‐Time Sensitive Demand

We study two firms that compete on price and lead‐time decisions in a common market. We explore the impact of decentralizing these decisions, as made by the marketing and production departments, respectively, with either marketing or production as the leader. We compare scenarios in which none, one, or both of the firms are decentralized to see whether decentralization can be the equilibrium strategy. We find that under intense price competition, with intensity characterized by the underlying parameters of market demand, firms may suffer from a decentralized structure, particularly under high flexibility induced by high capacity, where revenue‐based sales incentives motivate sales/marketing to make aggressive price cuts that often erode profit margins. In contrast, under intense lead‐time competition, a decentralized strategy with marketing as the leader can not only result in significantly higher profits, but also be the equilibrium strategy. Moreover, decentralization may no longer lead to lower prices or longer lead‐times if the production department chooses capacity along with lead‐time.      

Optimal procurement of long-term contracts in the presence of imperfect spot market

B2B spot market has grown rapidly and become an effective trading channel for commodity products. Besides long-term contract procurement from conventional suppliers (forward and option), a buyer can procure or sell commodities at any time in B2B spot market to adjust her inventory level. However, spot prices are generally volatile and the market is imperfect in the sense that spot trading may be realized with uncertainty in a given period of time and often comes with extra transaction cost. This paper considers a commodity buyer who can order forward and option contracts in advance and trade in a B2B spot market when spot price and demand are observed stochastically. Based on a single-period newsvendor model, we discuss three optimal order strategies and derive respective expected profits when the buyer is risk-neutral. The sensitivity of purchase costs, market liquidity and transaction cost is investigated. We also compare the optimal expected profits for different strategies to illustrate the effects of the two long-term contracts in the presence of the B2B spot market. We then extend our model to a multi-period setting and derive the optimal strategy. Finally, we numerically compute the optimal order strategy for a risk-averse buyer and analyze the impact of spot market, risk aversion, as well as the correlation between customer demand and spot price.     

非对称信息下闭环供应链回购契约应对突发事件策略研究

研究了非对称信息下一个制造商和一个零售商组成的两级闭环供应链在回购契约下的协调问题。在考虑零售商销售成本信息为非对称信息和随机性市场需求基础上,首先,分析了在正常状态下分散式系统决策情况,通过重新设计可变参数解决了信息不对称的问题,实现了回购契约下的信息共享和供应链的完美协调;然后,探讨了闭环供应链回购契约应对突发事件的协调问题。研究结果表明：当突发事件造成市场规模和制造商生产成本同时扰动时,闭环供应链的销售活动将受影响,闭环供应链的协调将被打破,而闭环供应链的废旧品回收活动却不受突发事件的影响。为此,给出了闭环供应链回购契约的应急决策。最后通过数值算例验证了结论。     

考虑消费者预期的电动汽车分时租赁市场价格竞争模型

分时租赁平台作为电动汽车推广的主要方式，其特征与打车软件类似，在风险资本的推动下极易引发价格战。各租车公司的市场需求量不仅与自己的定价有关，也与竞争对手的定价策略相关，目标都是各自利润的最大化。本文在考虑消费者预期的基础上，研究了需求函数为线性情形下的多人博弈，证明了此博弈是超模博弈以及Nash均衡的存在性和唯一性。并进一步揭示了降价幅度、交叉价格和价格敏感消费群体占比对均衡价格、均衡需求量和利润的影响关系，讨论了价格竞争过程中各租车公司的决策过程与利弊关系。结果表明：任意租车公司的降价行为都会引发整个市场的降价反应，且降价幅度随着博弈阶段的推进逐渐减小，最终收敛于均衡价格；动态定价博弈存在最优组合策略，市场竞争时应当把握好降价幅度，避免过度的价格竞争；均衡价格是关于消费者预期的单调减函数，价格敏感的消费群体占比越大，租车公司间价格竞争越激烈，降价幅度会越大，均衡价格越低；对于市场份额大的租车公司利润是关于价格敏感型消费者占比的单调增函数，但对中小租车公司而言则是单调减函数，价格敏感的消费者越多，对大公司有利，对中小公司不利。     

基于逆向供应的V2G市场电价策略研究

本文讨论了电动汽车普及后电力公司借助V2G技术建立V2G市场的市场运行模式,对电力公司在不同价格策略下,电动汽车保有者参与V2G市场向电力公司反向供电的响应度进行对比、分析.结果表明:电力公司采取分时电价策略时,可以以较不采用分时电价情景低的反向购电价格获得更高的V2G市场响应度,在不损失电动汽车保有者效益的情况下,使电力公司获得更高的总收益.     

Supplier competition and its impact on firm׳s sourcing strategy

Most research on firms׳ sourcing strategies assumes that wholesale prices and reliability of suppliers are exogenous. It is of our interest to study suppliers׳ competition on both wholesale price and reliability and firms׳ corresponding optimal sourcing strategy under complete information. In particular, we study a problem in which a firm procures a single product from two suppliers, taking into account suppliers׳ price and reliability differences. This motivates the suppliers to compete on these two factors. We investigate the equilibria of this supplier game and the firm׳s corresponding sourcing decisions. Our study shows that suppliers׳ reliability often plays a more important role than wholesale price in supplier competition and that maintaining high reliability and a high wholesale price is the ideal strategy for suppliers if multiple options exist. The conventional wisdom implies that low supply reliability and high demand uncertainty motivate dual-sourcing. We notice that when the suppliers׳ shared market/transportation network is often disrupted and demand uncertainty is high, suppliers׳ competition on both price and reliability may render the sole-sourcing strategy to be optimal in some cases that depend on the format of suppliers׳ cost functions. Moreover, numerical study shows that when the cost or vulnerability (to market disruptions) of one supplier increases, its profit and that of the firm may not necessarily decrease under supplier competition.     

需求依赖于库存的易变质品在线采购问题研究

根据现实生活中常见的库存量越大越吸引消费者购买兴趣的现象，本文建立了需求依赖于库存的易变质品采购模型。在不假设价格服从任何分布的条件下，提出了采购价格不确定背景下的易变质品在线采购策略。本文采用在线问题及其竞争分析的方法来进行建模分析，设计出有效的在线竞争采购价格驱动的(s,S)策略，与离线最优策略进行比较，得出理论竞争比和最优经济采购数量和采购时间间隔。最后，通过数值算例说明该策略在现实中具有较好的实际竞争性能比，且在多个价格序列下都表现良好，从而说明了该策略是鲁棒的，可以为企业提供有价值的决策建议。     

The effects of the warranty cost on the imperfect EMQ model with general discrete shift distribution

In this paper, we investigate the effect of the warranty cost on optimization of the economic manufacturing quality (EMQ). This is done for a deteriorating process where the production process shifts from the in-control state to the out-of-control state following a general discrete probability distribution. Once the production process goes out of control, the production process produces some defective items. The defective item cost includes reworking and warranty costs. Thus, in order to economically operate a production-inventory system with products sold under warranty, the tradeoffs among the production setup, inventory, and defective item cost, including the reworked cost before sale and the warranty cost after sale, needed to be analysed. This objective in this paper is to determine the production lot size while minimizing the total cost per unit of time per unit of time. Various special cases are presented. Two of them are extensions of results obtained previously in the literature. Finally, a numerical example is given which uses a discrete Weibull probability distribution. Sensitivity analysis of the model with respect to cost and time parameters is also performed.     

静态市场下考虑重复购买的价格和质保期联合决策

本文研究静态市场下的以质保期和价格为决策变量的最优控制决策问题。考虑了初次购买和重复购买两个过程以及重复购买过程是否受价格影响两种情况。模型中的生产成本考虑了产品生产过程中的学习效应, 质保成本使用了免费维修质保策略并假设产品两次故障之间的时间服从韦伯分布。在完整建模的基础上, 应用最大化原理对基本模型进行了求解, 之后本文给出了一种基本模型的具体应用场景, 并运用Lingo11软件进行了数值试验。最后对主要研究结论进行了应用讨论。