Integrated inventory and transportation decision for ubiquitous supply chain management

We consider price-dependent demand and develop an integrated inventory and transportation policy with strategic pricing to maximize the total profit for a ubiquitous enterprise. The proposed policy provides the optimal ordering, shipment and pricing decision. We first assume that demand for a product is a linear function of the price. A mathematical model for the total profit under quantity based dispatch is developed in consideration of ordering, shipment and pricing variables. Optimality properties for the model are then obtained and an efficient algorithm is provided to compute the optimal parameters for ordering, shipment and pricing decision. Finally, we extend our results to a more general case where demand for the product is a convex or a concave function of the price.     

A reinforcement learning approach to competitive ordering and pricing problem

This study analyses simultaneous ordering and pricing decisions for retailers working in a multi‐retailer competitive environment for an infinite horizon. Retailers compete for the same market where the market demand is uncertain. The customer selects the winning agent (retailer) in each term on the basis of random utility maximization, which depends primarily on retailer price and random error. The complexity of the problem is increased by competitiveness, necessity for simultaneous decisions and uncertainty in the nature of increases, and is not conducive to examination using standard analytical methods. Therefore, we model the problem using reinforcement learning (RL), which is founded on stochastic dynamic programming and agent‐based simulations. We analyse the effects of competitiveness and performance of RL on three different scenarios: a monopolistic case where one retailer employing a RL agent maximizes its profit, a duopolistic case where one retailer employs RL and another utilizes adaptive pricing and ordering policies, and a duopolistic case where both retailers employ RL.     

Pricing and inventory management in a system with multiple competing retailers under (r, Q) policies

We consider a multi-retailer system operated on an infinite horizon, in which each retailer faces stochastic demand following a Poisson process and adopts a continuous-review (r, Q) policy for replenishing inventory to satisfy customer demand. The system involves decisions of pricing and inventory management with the goal of maximizing profit, which equals the sales revenue minus the purchase and inventory costs. Taking Cournot competition into account, models are formulated to optimize simultaneously the expected sales volumes and (r, Q) policies of all retailers. An efficient approach is proposed to calculate the approximate inventory cost. Based on this approach, solution methods for centralized and decentralized scenarios are developed. A great number of numerical computations are provided to evaluate the efficiency of the solution methods, and their performance in the two scenarios. Moreover, system performance under sequential decisions (first pricing and then inventory management) is also investigated.     

考虑参照价格效应的易逝品定价与订购策略

在考虑消费者参照价格效应的基础上,构建一个易逝品的定价与订购联合决策模型,其中产品的需求不仅依赖于销售价格还与该产品在消费者心目中的参照价格相关,变质率为常数,系统不允许缺货.分别讨论了对称参照价格效应和非对称参照价格效应两种情况下零售商的最优定价与订购决策问题,证明并得到关于模型结构的一些性质,进而设计了问题的求解算法.通过数值方法分析了参照价格效应参数和变质率对系统最优解的影响,以及两种情况下最优解之间的关系.结果显示:当面对具有参照价格依赖的消费者时,采用适当的营销策略来提高消费者的参照价格对零售商总是有利的;对高变质率产品而言,零售商可保持一个较稳定的订购策略,更多地关注产品的定价策略;面对损失厌恶型消费者,随着消费者参照价格的逐渐提高,零售商的定价与订购策略均应缓慢地改变,而不宜急剧变化.     

两种需求模式下过度自信零售商的最优定价和订货联合决策

以报童模型为背景,研究过度自信零售商对市场需求的信念存在偏差时的决策问题.在加法和乘法需求模式下,探讨需求依赖价格和缺货加急订货时零售商最优定价订货联合决策问题.证明最优决策的存在性及唯一性,并给出最优决策的解析式.讨论过度自信对最优决策和期望利润的影响,分析过度自信零售商和理性零售商的信念期望利润与实际利润对比变化情况.对比结果表明,过度自信导致零售商利润的损失,能够为现实中零售商的定价订货决策提供理论依据.     

需求信息不对称下的双渠道供应链合作广告投资决策分析

研究制造商主导的Stackelberg 博弈下双渠道供应链的合作广告策略, 分析信息不对称及双渠道对供应链合作广告投资决策的影响. 研究表明, 零售商在具有需求信息优势时会谎报需求信息, 并且在一定条件下其谎报决策会降低制造商的利润, 但能提高供应链的利润, 这种情况下制造商无法通过激励合同促使零售商共享信息. 另外, 在最优合作广告策略下, 当直销渠道与分销渠道所占市场份额的分配比例小于一定值时, 制造商采取双渠道会使供应链参与者均受益.

     

面对损失厌恶顾客的零售商订货定价策略及激励问题研究

考虑顾客存在损失厌恶, 研究零售商的订货和定价策略, 以及顾客损失厌恶程度对零售商决策行为的影响, 同时探讨零售商通过补偿契约对损失厌恶型顾客的激励问题, 得到如下主要结论: 顾客损失厌恶导致零售商利润和零售价格下降, 订货量和需求量增加; 零售商采取补偿契约能够提高零售商利润、零售价格、订货量和需求量, 有效弱化了顾客损失厌恶给企业带来的负面影响, 并且, 只要补偿额不超过一定限度, 补偿契约也会增加顾客的效用, 实现企业与顾客双赢.     

The impact of consumer behavior on preannounced pricing for a dual‐channel supply chain

This study discusses a dual‐channel supply chain in which a manufacturer sells a regular‐priced product through dual channels in the normal sales period and only sells overstocked products through the direct channel in the discounted sales period in the presence of strategic consumers. The manufacturer acts as a Stackelberg leader to adopt a preannounced pricing policy. This study first proposes demand functions for a two‐period dual‐channel model by incorporating consumer utility functions. Based on the demand functions, optimal pricing strategies for both manufacturer and retailer are established. The results show that the manufacturer prefers to raise prices in both periods for consumers with a short delivery lead time. However, counterintuitively, the selling prices set by the manufacturer do not decrease as the degree of consumer patience increases. Finally, there is a Pareto zone under a certain condition where both the manufacturer and the retailer in the two‐period dual‐channel model outperform their counterparts in terms of profit in the single‐period dual‐channel model.     

Combined optimal price and optimal inventory replenishment policies when a sale results in increase in demand

When a supplier reduces the price of a product temporarily a buyer might place a large order and offer a sale on these units to its customers. In most cases a price discount results in an increase in demand. In this paper we relax the constant demand assumption made in most studies of inventory systems with price changes. We analyze the options available to a buyer and develop profit functions for different combinations of sales period and replenishment time and present optimal ordering policies. The paper also presents a procedure to include any relationship between price and demand to determine the combined optimal price and optimal order quantity.     

Trade credit insurance in a capital‐constrained supply chain

We examine the role of trade credit insurance in a capital‐constrained supply chain with one (or two) loss‐neutral retailer(s) and one loss‐averse manufacturer. We model the interplay between these supply chain participants as a Stackelberg game and analyze their operating and financing decisions. In one capital‐constrained retailer case, we find that either the manufacturer's high loss aversion level or the retailer's low initial capital motivates the manufacturer to adopt insurance. Insurance drives more credit financing with more attractive financing terms (a lower wholesale price), which promotes the manufacturer to collect better product sales and performance. Although the retailer enjoys improved profit from insurance, its default risk increases. In contrast, in one capital‐constrained retailer and one well‐funded retailer scenario, numerically, when the manufacturer's loss aversion level is high or the weak retailer's initial capital is low, insurance is also adopted but is not always preferred by the capital‐constrained retailer due to competition. In addition, as the demand substitution rate increases, the manufacturer is more likely to prefer insurance due to better performance.     

Option contract strategies with risk‐aversion and emergency purchase

This paper considers a one‐period supply chain consisting of a risk‐averse retailer and a risk‐neutral supplier. As a Stackelberg leader, the supplier produces short life‐cycle products to the retailer and determines the option price. The newsvendor‐like retailer orders call option from the supplier with an emergency order opportunity. The analytical model shows that when the emergency purchase price is low, the risk‐averse retailer's optimal order quantity is less than that of a risk‐neutral retailer and independent of the retail price. It is surprising that when it is moderate or high, the risk‐averse retailer may order less than, equal to, or more than a risk‐neutral one. Computational studies are given to investigate the key parameters on optimal decisions and profits. It shows a risk‐averse retailer may get higher profit than a risk‐neutral one. The retailer benefits from a low emergency purchase price, while it harms the supplier.     

需求依赖于产品价格和消费者时间偏好的定价与订货决策

研究产品的市场需求依赖于价格和消费者时间偏好情形下的供应链及其成员的最优定价与订货问题. 利用时间偏好因子刻画消费者的时间偏好, 利用产品市场需求关于零售价格的弹性指数反映消费者的价格敏感程度, 建立存在强势零售商、强势供应商和供需双方势力均衡3 种渠道权力结构下的定价与订货模型. 数值结果表明, 在3 种渠道权力结构下, 消费者的时间偏好和产品市场需求关于零售价格的弹性指数是供应链主导者最优定价、订货量和期望利润的单调减函数, 将其纳入定价与订货决策的影响因素予以考量能够增加供应链主导者的最大期望利润.

     

Co-op advertising and pricing models in manufacturer–retailer supply chains

Cooperative (co-op) advertising plays a significant role in marketing programs in conventional supply chains and makes up the majority of promotional budgets in many product lines for both manufacturers and retailers. Nevertheless, most studies to date on co-op advertising have only assumed that the market demand is only influenced by the advertising level but not in any way by the retail price. That is why our work is concerned with co-op advertising and pricing strategies in distribution channels consisting of a manufacturer and a retailer. Four different models are discussed which are based on three non-cooperative games (i.e., Nash, Stackelberg retailer and Stackelberg manufacturer) and one cooperative game. We identify optimal co-op advertising and pricing strategies for both firms mostly analytically but we have to resort to numerical simulations in one case. Comparisons are then made about various outcomes, especially the profits, for all cases. This leads to consider more specifically the cooperation case in which profits are the highest for both the retailer and the manufacturer, and how they should share the extra joint profit achieved by moving to cooperation. We solve this bargain problem using the Nash bargaining model.     

Optimal production decision for a risk‐averse manufacturer faced with random yield and stochastic demand

Consider a risk‐averse manufacturer who produces a single product with a random yield to satisfy uncertain market demand. The manufacturer maximizes its expected profit subject to a chance constraint that requires the probability of the total profit below a target be less than a predetermined level. We show that due to the profit target constraint in the presence of random yield and stochastic demand, the manufacturer can neither produce too much nor too little irrespective of the predetermined probability level, depending solely on the profit target level. Further, the special case of uniform yield and uniform demand is examined and we obtain the manufacturer's optimal production quantity. In addition, two special cases of random yield rate and deterministic demand or deterministic yield rate and stochastic demand are considered. The opposite impacts of random yield and stochastic demand are revealed: the random yield induces a minimum production quantity that may cause the manufacturer to increase its production quantity, while the stochastic demand induces a maximum production quantity that may cause the manufacturer to decrease its production quantity. By comparing the solutions of the above‐mentioned special cases with the case of both random yield and stochastic demand, it is demonstrated that the existence of both random yield and stochastic demand results in a more constrained production requirement for the manufacturer (a larger minimum production quantity and a smaller maximum production quantity). That is, the opposite impacts of random yield and stochastic demand will not offset, but enhance each other.     

基于提前支付的非瞬时变质产品批量订货定价策略

当供应商处于供应链节点的买方市场时,通常要求零售商提前支付一定比例购置成本作为订金.针对该问题研究零售商促销努力下存在随机需求的非瞬时变质产品批量订货定价策略,考虑零售商提前支付策略,允许部分缺货.在一定条件下可得零售商最优补货周期和局部最优定价策略,随之提出相应的求解算法.数值计算结果表明:若提前支付购置成本占比或利率增大,则零售商利润将显著减少;提前支付期限和期数均对最优利润产生消极影响;零售商采取积极促销策略可有效提升自身利润.     

A cooperative advertising collaboration policy in supply chain management under uncertain conditions

Many industries are facing big challenges to design supply chains in a way to maximize the profit and meet the heightened expectations of the customer. This new era entirely relies on the dynamic advantages of competition and the role played by the collaboration policy. A global economy and increasing demand have put a huge pressure on supply chain partners to build a collaboration policy based on price, order quantity, and advertising. Companies are adopting the idea of ”shaking hands” to obtain more profit instead of taking risks through competition. Cooperative (co-op) advertising is a significant policy of centralized supply chain management (SCM) to boost the revenues generated by the supplier, manufacturer, and retailers. The uncertain costs associated with the supply chain management also create obstacles in economic analysis and feasibility. These uncertainties are associated with the basic costs of all supply chain partners, which are represented using a signed distance formula. This paper develops the concept of co-op advertising among the supplier, manufacturer, and retailers with a variable demand driven by selling price and advertising costs, where all basic costs are considered as fuzzy. The profit is optimized by considering variable cycle time, shipments, pricing and advertising costs for the decision support system of the supply chain management. The optimal results of the co-op advertisement ensured an increase in the revenue of whole supply chain.     

公平关切下具有广告效应的闭环供应链定价决策模型

研究制造商公平关切下具有广告效应的闭环供应链定价决策问题.分别在制造商与零售商广告下,分析广告效应及制造商的公平关切行为对闭环供应链定价策略的影响.研究表明,广告效应对闭环供应链成员及系统整体都是有利的,制造商的公平关切行为有利于自身利润及效用最大化,不利于零售商及系统整体利润最大化.在制造商广告下,当制造商的公平关切程度相对较弱时,零售商的利润不小于制造商的利润;反之,制造商的利润更大.     

Coordinating two-period ordering and advertising policies in a dynamic market with stochastic demand

In this paper, we study the optimal two-stage advertising and ordering policies and the channel coordination issues in a supply chain composed of one manufacturer and one retailer. The manufacturer sells a short-life-cycle product through the retailer facing stochastic demand in dynamic markets characterised by price declines and product obsolescence. Following a two-period newsvendor framework, we develop two members’ optimal ordering and advertising models under both the centralised and decentralised settings, and present the closed-form solutions to the developed models as well. Moreover, we design a two-period revenue-sharing contract, and develop sufficient conditions such that the channel coordination can be achieved and a win–win outcome can be guaranteed. Our analysis suggests that the centralised decision creates an incentive for the retailer to increase the advertising investments in two periods and put the purchase forward, but the decentralised decision mechanism forces the retailer to decrease the advertising investments in two periods and postpone/reduce its purchase in the first period. This phenomenon becomes more evident when demand variability is high.     

风险厌恶因子不确定时的二级供应链定价与订货策略

研究了风险中性的供应商与风险厌恶的零售商所构成的二阶供应链的定价与订货策略,零售商的风险厌恶由条件价值风险来度量.研究结果表明,当供应商不确定零售商的风险厌恶因子时,一定会造成其期望利润的下降,从而也体现了信息的价值.特别地,当风险厌恶因子服从均匀分布时,其期望订货量正是需求的截断随机变量的期望.     

Optimal pricing policies for services with consideration of facility maintenance costs

For survival and success, pricing is an essential issue for service firms. This article deals with the pricing strategies for services with substantial facility maintenance costs. For this purpose, a mathematical framework that incorporates service demand and facility deterioration is proposed to address the problem. The facility and customers constitute a service system driven by Poisson arrivals and exponential service times. A service demand with increasing price elasticity and a facility lifetime with strictly increasing failure rate are also adopted in modelling. By examining the bidirectional relationship between customer demand and facility deterioration in the profit model, the pricing policies of the service are investigated. Then analytical conditions of customer demand and facility lifetime are derived to achieve a unique optimal pricing policy. The comparative statics properties of the optimal policy are also explored. Finally, numerical examples are presented to illustrate the effects of parameter variations on the optimal pricing policy.