A Novel Stackelberg-Game-Based Energy Storage Sharing Scheme Under Demand Charge

Demand response (DR) using shared energy storage systems (ESSs) is an appealing method to save electricity bills for users under demand charge and time-of-use (TOU) price. A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study. In this scheme, the interactions between selfish users and an operator are characterized as a Stackelberg game. Operator holds a large-scale ESS that is shared among users in the form of energy transactions. It sells energy to users and sets the selling price first. It maximizes its profit through optimal pricing and ESS dispatching. Users purchase some energy from operator for the reduction of their demand charges after operator’s selling price is announced. This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model. The upper-level optimization maximizes operator’s profit and the lower-level optimization minimizes users’ costs. The bi-level model is transformed and linearized into a mixed-integer linear programming (MILP) model using the mathematical programming with equilibrium constraints (MPEC) method and model linearizing techniques. Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.      

Coordinating decisions by supply chain partners in a vendor-managed inventory relationship

We look into the linked decision making in the vendor-managed inventory (VMI) relationship. It is a supply chain management model, where the retailer decides the retail price while the vendor determines its capacity commitment. In this model, the retailer and the vendor should coordinate their decisions in order to maximize their individual profit or the total profit combining the two participants together. The vendor has to take into account the demand pattern throughout the product life cycle (PLC) when it decides its capacity commitment, which will affect its inventory management cost during the PLC, while the retailer should change the retail price over the PLC so as to maximize the revenues and minimize the inventory cost at the same time. Employing a system dynamics simulation approach based on differential game theory, which also takes into account the product characteristics such as the demand’s innovation and imitation effects, we analyze and confirm the dynamic coordination of key decision variables by the supply chain partners in the VMI relationship.     

移动边缘计算中基于Stackelberg博弈的算力交易与定价

针对移动边缘计算中轻量级智能设备计算和存储能力有限等问题，提出一种基于Stackelberg博弈的计算卸载解决方案。首先，结合区块链技术构建基于云挖掘机制的算力交易模型——CPTP-BSG，允许移动智能设备（矿工）将密集且复杂的计算任务卸载到边缘服务器；其次，将矿工与边缘计算服务提供商（ESP）之间的算力交易建模为一个两阶段的Stackelberg博弈过程，并构建矿工与ESP的预期利润函数；然后，使用逆向归纳法分别在统一定价和歧视性定价策略下分析纳什均衡解的存在性和唯一性；最后，提出一种低梯度迭代算法来实现矿工和ESP的利润最大化。实验结果证明了所提算法的有效性，并且与统一定价相比，歧视性定价更符合矿工的个性化算力需求，能达到更高的算力需求总量和ESP利润。     

移动边缘计算中基于Stackelberg博弈的算力交易与定价

针对移动边缘计算中轻量级智能设备计算和存储能力有限等问题,提出一种基于Stackelberg博弈的计算卸载解决方案。首先,结合区块链技术构建基于云挖掘机制的算力交易模型——CPTP-BSG,允许移动智能设备（矿工）将密集且复杂的计算任务卸载到边缘服务器;其次,将矿工与边缘计算服务提供商（ESP）之间的算力交易建模为一个两阶段的Stackelberg博弈过程,并构建矿工与ESP的预期利润函数;然后,使用逆向归纳法分别在统一定价和歧视性定价策略下分析纳什均衡解的存在性和唯一性;最后,提出一种低梯度迭代算法来实现矿工和ESP的利润最大化。实验结果证明了所提算法的有效性,并且与统一定价相比,歧视性定价更符合矿工的个性化算力需求,能达到更高的算力需求总量和ESP利润。     

Price-Based Residential Demand Response Management in Smart Grids: A Reinforcement Learning-Based Approach

This paper studies price-based residential demand response management (PB-RDRM) in smart grids, in which non-dispatchable and dispatchable loads (including general loads and plug-in electric vehicles (PEVs)) are both involved. The PB-RDRM is composed of a bi-level optimization problem, in which the upper-level dynamic retail pricing problem aims to maximize the profit of a utility company (UC) by selecting optimal retail prices (RPs), while the lower-level demand response (DR) problem expects to minimize the comprehensive cost of loads by coordinating their energy consumption behavior. The challenges here are mainly two-fold: 1) the uncertainty of energy consumption and RPs; 2) the flexible PEVs’ temporally coupled constraints, which make it impossible to directly develop a model-based optimization algorithm to solve the PB-RDRM. To address these challenges, we first model the dynamic retail pricing problem as a Markovian decision process (MDP), and then employ a model-free reinforcement learning (RL) algorithm to learn the optimal dynamic RPs of UC according to the loads’ responses. Our proposed RL-based DR algorithm is benchmarked against two model-based optimization approaches (i.e., distributed dual decomposition-based (DDB) method and distributed primal-dual interior (PDI)-based method), which require exact load and electricity price models. The comparison results show that, compared with the benchmark solutions, our proposed algorithm can not only adaptively decide the RPs through on-line learning processes, but also achieve larger social welfare within an unknown electricity market environment.      

Pricing games of mixed conventional and e-commerce distribution channels

In this paper, a distribution system is studied, in which a supplier sells a common product through conventional (physical retailer) and e-commerce (e-tailers) channels. We examine two types of Stackelberg pricing games and one type of Nash pricing game in this dual-channel distribution system. We also analyze the effects of several key factors (i.e., the supplier’s pricing mode, game schemes, and efficiency of e-channel in relation to acceptance of channels) on the resulting prices as well as the profits for the supplier and the retailer, respectively. This paper is an effort to examine modeling competition in the multiple-channel environment from a pricing viewpoint. We find that channel acceptance plays a critical role in influencing equilibrium prices and profits in the dual-channel distribution system. When the customer acceptance of one channel exceeds a certain threshold, this channel cannibalizes all retail sales and dominates the distribution system. The supplier can make more profits by adopting a differential pricing strategy; on the contrary, the retailer prefers uniform pricing. Numerical analysis indicates that both the supplier and the retailer are worse off in the Nash game than in the Stackelberg games. The supplier prefers an e-channel with higher efficiency, whereas the physical retailer has to maintain higher channel acceptance to maintain its position in the distribution system.     

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.     

模糊闭环供应链的定价与销售努力决策

从期望利润最大化的角度研究了单周期两级模糊闭环供应链的定价与销售努力最优决策问题。分析了包含一个制造商和一个零售商的闭环供应链中的模糊不确定性及需求依赖于零售价格和零售商销售努力的性质,分别建立了集中式决策模型和零售商主导的Stackelberg 博弈模型并进行了求解。数值算例验证了模型的有效性,结论表明：考虑销售努力时产品的最优零售价格、批发价格分别高于不考虑销售努力情形下的相应价格;考虑销售努力时零售商和系统的最大期望利润分别大于不考虑销售努力情形下的最大期望利润。     

存在强势零售商与直销渠道的供应链内生时机

在由强弱零售商和直销渠道组成的非对称供应链中,探讨定价权转移、消费者忠诚度以及保留价格差异对三种博弈时机下均衡结果的影响,然后研究供应链内生时机,对消费者剩余和社会福利进行分析,最后通过数值仿真验证所得结论。研究表明:在三种博弈时机下,定价权转移使得强势零售商比竞争对手获得更多利润;供应链博弈内生时机为制造商领导和零售商领导;随着产品保留价格差异的增加,消费者剩余降低,但社会福利先降低后升高。     

基于二层规划的供应链定价决策研究

针对一个单一制造商与多个零售商构成的分布控制型供应链,其中制造商作为主导者确定批发价,零售商确定各自的零售价,市场需求量由零售价格决定的问题,利用二层规划模型研究了具有S tacke lberg博弈特征的定价决策,并给出了混沌搜索求解算法,同时给出供应链成员合作的条件.研究结论表明,分布控制型供应链虽然不能保证系统最优,但却能实现成员利益最大化,因而均衡状态下的价格是稳定的.最后通过实例验证了给出的结论.     

Pricing and inventory strategies under quick response with strategic and myopic consumers

We divide consumers in the selling period into two types according to their purchasing behavior: strategic customers and myopic customers. We address the optimal inventory and pricing decision problem of a retailer considering strategic and myopic consumers with and without a quick response. The results indicate that the retailer should establish a higher price to sell only to myopic customers if there is a sufficient presence of myopic customers in the market, and the retailer should set a lower price to sell to myopic and strategic customers if the number of myopic customers in the market is relatively low. A quick response can decrease the initial ordering quantity and increase the retailer's profit when selling only to myopic customers or selling to both myopic and strategic customers. Moreover, a quick response is beneficial for the retailer to improve the product's retail price if the retailer wishes the two types of customers to purchase the product during the selling period. We also find that the pricing strategy considering strategic and myopic consumers under a quick response will increase profits more than the pricing strategy only considering myopic customers. Finally, numerical experiments are conducted to illustrate and validate the proposed models and provide managerial insights.     

Optimal pricing decisions in a fuzzy dual-channel supply chain

This paper analyzes the pricing decisions of a dual-channel supply chain including one retailer and one manufacturer who produces a product and sells it to the end customer through retailer or directly. Both the manufacturing cost and the customer demand are considered as fuzzy variables. Two pricing models, including centralized decision model and manufacturer-leader Stackelberg game, with consideration of different market power structures are adopted. Optimal decisions on wholesale price and retail prices are determined using game theoretical approach and fuzzy set theory for each model. Finally, a numerical example is solved to illustrate the effectiveness of models and provide some managerial insights from analysis.     

Stackelberg game for two-level supply chain with price markdown option

Vendor–retailer collaboration has an important role in supply chain management. Although vendor–retailer collaboration results in better supply chain profit, collaboration is difficult to realize. This is because most vendors and retailers try to optimize their own profit. This paper applies the Stackelberg game with stochastic demand for the vendor–retailer system. The vendor as a leader determines the product price, and the retailer decides order quantity and frequency of price markdown. This study develops example and sensitivity analyses to illustrate the theory. Results show that the price markdown option has a better total supply chain profit than without a price markdown policy, and the vendor receives more benefit. For different demand variances, the retailer profit is more sensitive than the vendor profit.     

一种最小化绿色数据中心电费的负载调度算法

为了减少电费和碳排放,数据中心运营商开始建立就地绿色能源发电厂以进行供电.然而,负载的波动性、电价的时间差异性以及绿色能源的间歇性,给节约数据中心电费带来了挑战.针对以上问题,提出一种在线式负载调度算法,可以在不使用未来的负载、电价和绿色能源可用性信息的前提下,最小化数据中心的电费.首先,建立拥有就地绿色能源发电厂的数据中心的电费模型;然后,将数据中心电费最小化问题形式化为一个随机优化问题;最后,求解该优化问题得到相应的负载调度策略.基于真实数据的实验结果表明：该算法可以在保证负载性能的前提下,有效降低数据中心的电力成本.     

Stackelberg–Nash equilibrium of pricing and inventory decisions in duopoly supply chains using a nested evolutionary algorithm

Pricing and inventory control in a competing environment, as separate entities, have attracted much attention from academics and practitioners. However, integrating these decisions in a competitive setting has not been significantly analyzed by academics, but is of great significance to practitioners. In this study, the joint decision on price and inventory control of a deterioration product is investigated in a duopoly setting. We consider two competing supply chains, each consisting of one manufacturer and one retailer. Each manufacturer, as the leader of their supply chain determines the wholesale price to maximize their profit, while the retailer as the follower should determine the retail price and inventory cycle to maximize his or her profit. Using a game theoretic approach, we formulate in-chain, and chain-to-chain competition as a bi-level programming problem, and analyze Stackelberg–Nash equilibrium of the problem. Furthermore, two versions of a nested algorithm are proposed to obtain the equilibrium. Both versions employ a modified threshold-accepting (TA) algorithm to solve the first level of the problem. However, while the first version utilizes the modified TA algorithm to deal with the second level of the problem, the second version applies a differential evolution (DE) approach. Eventually, a numerical study is carried out not only to compare two developed versions of the algorithm, but also to implement the sensitivity analysis of main parameters. Based on numerical experiments, although the accuracy of both versions of algorithm are alike, using TA is more computationally efficient than using DE. Furthermore, despite the permissibility of partial backlogging, it has never occurred in equilibrium points due to in-chain and chain-to-chain competition.     

Supply chain financing with advance selling under disruption

We study a financing problem in a supply chain (SC) consisting of one supplier and one buyer under supply disruption. The supplier could face a disruption at its end which could effectively reduce its yield in case of disruption, thereby resulting in supply yield uncertainty. The retailer can finance the supplier using advance selling that can help mitigate the impact of disruption. We model this problem as a Stackelberg game, where the supplier as the leader announces the wholesale price and the retailer responds by deciding its optimal order quantity given stochastic demand and an exogenous fixed retail price. The supplier then commences production and a disruption can happen with a known probability. We assume that under disruption the quantity delivered is a fraction of the initial quantity ordered by the retailer. The retailer loses any unmet demand. We analyze three different scenarios of the Stackelberg game, namely no advance selling with disruption, advance selling without disruption, and advance selling with disruption. Our results indicate that advance selling can be used to mitigate the impact of supply disruption and at the same time could lead to an increase in the overall SC profit.     

Research on closed loop supply chain with reference price effect

This paper considers a closed loop supply chain with the manufacturer as the Stackelberg leader. The manufacturer faces three different reverse channels, i.e., (1) manufacturer-managed, (2) retailer-managed, or (3) third party-managed channels. The reference price affects the purchase decision of consumers. Based on game theory, we discuss the reference price effect on the performances across three decentralized reverse channels, and examine the impact of reference price parameter (i.e., reference price coefficient in this paper) on optimal strategies. We conclude that higher reference price coefficient results in lower manufacturer and retailer profits. However, the profit of the third party increases in the reference price coefficient. In addition, some meaningful insights can be derived by comparison without the reference price effect in our models. We found that the scenario without reference price effect is generally superior to that with reference price effect.     

基于零售商创新投入的双渠道供应链协调策略

针对制造商在传统实体渠道的基础上积极开辟网络渠道的双渠道供应链,从消费者效用理论角度构建单一渠道和双渠道供应链Stackelberg博弈模型,在零售商创新投入和消费者渠道偏好扰动因素下,探讨制造商开辟网络渠道形成的渠道竞争效应,寻求供应链系统的组合优化策略,通过一个双重协调机制改善供应链运作效率.研究表明:批发价格、零售价格及创新投入水平的最优组合策略可实现供应链优化;制造商和零售商利润均与创新投入水平呈特定函数关系;网络渠道的引进可降低零售商定价和利润,减少实体渠道市场份额,但总需求增加;双重协调机制可缓解渠道冲突.最后通过数值仿真结果验证了协调机制的可行性.     

Service cooperation and marketing strategies of infomediary and online retailer with eWOM effect

In contemporary electronic commerce, an infomediary displays electronic word-of-mouth (eWOM) information of customers and links shoppers to retail websites, thus acting as an intermediary between buyers and sellers. This paper studies an online supply chain system in which the infomediary presents demand-referral services to online retailers based on eWOM of customer information. It is assumed that online demand is affected by retailer price, referral service effort, and eWOM. The demand function is extended and developed based on Bass’s model. A Stackelberg game model of service cooperation is presented, and then the optimal decisions on retailers’ prices and infomediary service efforts in the decentralized supply chain are analyzed. Moreover, the profits and cumulative sales in supply chain equilibrium are analyzed under several parameters. A computational experiment is implemented to verify the validity and effectiveness of the model. The results show that price sensitivity has a significant negative effect on cumulative retailer sales and the profits of retailers and infomediary, but the effect of service sensitivity and sales periods on profits is absolutely positive. Specifically, eWOM has two different impacts on the profit of the retailer and infomediary respectively. Finally, conclusions and management implications for supply chain parties are presented, along with some possible directions for further research.     

OFDMA认知无线电网络中面向功率控制的频谱定价与分配

针对OFDMA认知无线电网络,提出一种基于Stackelberg博弈的频谱定价和分配模型.对于次基站控制次网络传输功率来保护主网络通信的场景,主基站可通过该模型获得最优的频谱定价方案.从功率控制的角度,重新设计次用户的效用函数,运用Stackelberg博弈对单个主基站和多个次用户在频谱租赁市场中的交易行为进行建模.通过逆向归纳法,求解市场均衡下的最优频谱定价,使得主基站在考虑主网络QoS降级的同时获得最大收益.此外,对于主基站只能获取本地信息的情形,提出了基于动态Stackelberg博弈的分布式频谱定价和分配模型.仿真实验表明,该模型能够在控制次网络传输功率的基础上,提供最优频谱定价和频谱分配方案.