Optimal ordering and pricing policy for an inventory system

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- disruption ，: Global convergence vs nationalSustainable - ，practices and dynamic capabilities in the food industry: A critical analysis of the literature5 Mesoscopic - simulation6 Firm size and sustainable performance in food -s: Insights from Greek SMEs7 An analytical method for cost analysis in multi-stage -s: A stochastic / model approach8 A Roadmap to Green - System through Enterprise Resource Planning (ERP) Implementation9 Unidirectional transshipment policies in a dual-channel -10 Decentralized and centralized model predictive control to reduce the bullwhip effect in - ，11 An agent-based distributed computational experiment framework for virtual - / development12 Biomass-to-bioenergy and biofuel - optimization: Overview, key issues and challenges13 The benefits of - visibility: A value assessment model14 An Institutional Theory perspective on sustainable practices across the dairy -15 Two-stage stochastic programming - model for biodiesel production via wastewater treatment16 Technology scale and -s in a secure, affordable and low carbon energy transition17 Multi-period design and planning of closed-loop -s with uncertain supply and demand18 Quality control in food - ，: An analytical model and case study of the adulterated milk incident in China19 - information capabilities and performance outcomes: An empirical study of Korean steel suppliers20 A game-based approach towards facilitating decision making for perishable products: An example of blood -21 - design under quality disruptions and tainted materials delivery22 A two-level replenishment frequency model for TOC - replenishment systems under capacity constraint23 - dynamics and the ―cross-border effect‖: The U.S.–Mexican border’s case24 Designing a new - for competition against an existing -25 Universal supplier selection via multi-dimensional auction mechanisms for two-way competition in oligopoly market of -26 Using TODIM to evaluate green - practices under uncertainty27 - downsizing under bankruptcy: A robust optimization approach28 Coordination mechanism for a deteriorating item in a two-level - system29 An accelerated Benders decomposition algorithm for sustainable - / design under uncertainty: A case study of medical needle and syringe -30 Bullwhip Effect Study in a Constrained -31 Two-echelon multiple-vehicle location–routing problem with time windows for optimization of sustainable - / of perishable food32 Research on pricing and coordination strategy of green - under hybrid production mode33 Agent-system co-development in - research: Propositions and demonstrative findings34 Tactical ，for coordinated -s35 Photovoltaic - coordination with strategic consumers in China36 Coordinating supplier׳s reorder point: A coordination mechanism for -s with long supplier lead time37 Assessment and optimization of forest biomass -s from economic, social and environmental perspectives – A review of literature38 The effects of a trust mechanism on a dynamic - /39 Economic and environmental assessment of reusable plastic containers: A food catering - case study40 Competitive pricing and ordering decisions in a multiple-channel -41 Pricing in a - for auction bidding under information asymmetry42 Dynamic analysis of feasibility in ethanol - for biofuel production in Mexico43 The impact of partial information sharing in a two-echelon -44 Choice of - governance: Self-managing or outsourcing?45 Joint production and delivery lot sizing for a make-to-order producer–buyer - with transportation cost46 Hybrid algorithm for a vendor managed inventory system in a two-echelon -47 Traceability in a food -: Safety and quality perspectives48 Transferring and sharing exchange-rate risk in a risk-averse - of a multinational firm49 Analyzing the impacts of carbon regulatory mechanisms on supplier and mode selection decisions: An application to a biofuel -50 Product quality and return policy in a - under risk aversion of a supplier51 Mining logistics data to assure the quality in a sustainable food -: A case in the red wine industry52 Biomass - optimisation for Organosolv-based biorefineries53 Exact solutions to the - equations for arbitrary, time-dependent demands54 Designing a sustainable closed-loop - / based on triple bottom line approach: A comparison of metaheuristics hybridization techniques55 A study of the LCA based biofuel - multi-objective optimization model with multi-conversion paths in China56 A hybrid two-stock inventory control model for a reverse -57 Dynamics of judicial service -s58 Optimizing an integrated vendor-managed inventory system for a single-vendor two-buyer - with determining weighting factor for vendor׳s ordering59 Measuring - Resilience Using a Deterministic Modeling Approach60 A LCA Based Biofuel - Analysis Framework61 A neo-institutional perspective of -s and energy security: Bioenergy in the UK62 Modified penalty function method for optimal social welfare of electric power - with transmission constraints63 Optimization of blood - with shortened shelf lives and ABO compatibility64 Diversified firms on dynamical - cope with financial crisis better65 Securitization of energy -s in China66 Optimal design of the auto parts - for JIT operations: Sequential bifurcation factor screening and multi-response surface methodology67 Achieving sustainable -s through energy justice68 - agility: Securing performance for Chinese manufacturers69 Energy price risk and the sustainability of demand side -s70 Strategic and tactical mathematical programming models within the crude oil - context - A review71 An analysis of the structural complexity of - /s72 Business process re-design methodology to support - integration73 Could - technology improve food operators’ innovativeness? A developing country’s perspective74 RFID-enabled process reengineering of closed-loop -s in the healthcare industry of Singapore75 Order-Up-To policies in Information Exchange -s76 Robust design and operations of hydrocarbon biofuel - integrating with existing petroleum refineries considering unit cost objective77 Trade-offs in - transparency: the case of Nudie Jeans78 Healthcare - operations: Why are doctors reluctant to consolidate?79 Impact on the optimal design of bioethanol -s by a new European Commission proposal80 Managerial research on the pharmaceutical - – A critical review and some insights for future directions81 - performance evaluation with data envelopment analysis and balanced scorecard approach82 Integrated - design for commodity chemicals production via woody biomass fast pyrolysis and upgrading83 Governance of sustainable -s in the fast fashion industry84 Temperature ，for the quality assurance of a perishable food -85 Modeling of biomass-to-energy - operations: Applications, challenges and research directions86 Assessing Risk Factors in Collaborative - with the Analytic Hierarchy Process (AHP)87 Random / models and sensitivity algorithms for the analysis of ordering time and inventory state in multi-stage -s88 Information sharing and collaborative behaviors in enabling - performance: A social exchange perspective89 The coordinating contracts for a fuzzy - with effort and price dependent demand90 Criticality analysis and the -: Leveraging representational assurance91 Economic model predictive control for inventory ，in -s92 - ，ontology from an ontology engineering perspective93 Surplus division and investment incentives in -s: A biform-game analysis94 Biofuels for road transport: Analysing evolving -s in Sweden from an energy security perspective95 - ，executives in corporate upper echelons Original Research Article96 Sustainable - ，in the fast fashion industry: An analysis of corporate reports97 An improved method for managing catastrophic - disruptions98 The equilibrium of closed-loop - super/ with time-dependent parameters99 A bi-objective stochastic programming model for a centralized green - with deteriorating products100 Simultaneous control of vehicle routing and inventory for dynamic inbound -101 Environmental impacts of roundwood - options in Michigan: life-cycle assessment of harvest and transport stages102 A recovery mechanism for a two echelon - system under supply disruption103 Challenges and Competitiveness Indicators for the Sustainable Development of the - in Food Industry104 Is doing more doing better? The relationship between responsible - ，and corporate reputation105 Connecting product design, process and - decisions to strengthen global - capabilities106 A computational study for common / design in multi-commodity -s107 Optimal production and procurement decisions in a - with an option contract and partial backordering under uncertainties108 Methods to optimise the design and ，of biomass-for-bioenergy -s: A review109 Reverse - coordination by revenue sharing contract: A case for the personal computers industry110 SCOlog: A logic-based approach to analysing - operation dynamics111 Removing the blinders: A literature review on the potential of nanoscale technologies for the ，of -s112 Transition inertia due to competition in -s with remanufacturing and recycling: A systems dynamics mode113 Optimal design of advanced drop-in hydrocarbon biofuel - integrating with existing petroleum refineries under uncertainty114 Revenue-sharing contracts across an extended -115 An integrated revenue sharing and quantity discounts contract for coordinating a - dealing with short life-cycle products116 Total JIT (T-JIT) and its impact on - competency and organizational performance117 Logistical - design for bioeconomy applications118 A note on ―Quality investment and inspection policy in a supplier-manufacturer -‖119 Developing a Resilient -120 Cyber - risk ，: Revolutionizing the strategic control of critical IT systems121 Defining value chain architectures: Linking strategic value creation to operational - design122 Aligning the sustainable - to green marketing needs: A case study123 Decision support and intelligent systems in the textile and apparel -: An academic review of research articles124 - ，capability of small and medium sized family businesses in India: A multiple case study approach125 - collaboration: Impact of success in long-term partnerships126 Collaboration capacity for sustainable - ，: small and medium-sized enterprises in Mexico127 Advanced traceability system in aquaculture -128 - information systems strategy: Impacts on - performance and firm performance129 Performance of - collaboration – A simulation study130 Coordinating a three-level - with delay in payments and a discounted interest rate131 An integrated framework for agent basedinventory–production–transportation modeling and distributed simulation of -s132 Optimal - design and ，over a multi-period horizon under demand uncertainty. Part I: MINLP and MILP models133 The impact of knowledge transfer and complexity on - flexibility: A knowledge-based view134 An innovative - performance measurement system incorporating Research and Development (R&D) and marketing policy135 Robust decision making for hybrid process - systems via model predictive control136 Combined pricing and - operations under price-dependent stochastic demand137 Balancing - competitiveness and robustness through ―virtual dual sourcing‖: Lessons from the Great East Japan Earthquake138 Solving a tri-objective - problem with modified NSGA-II algorithm 139 Sustaining long-term - partnerships using price-only contracts 140 On the impact of advertising initiatives in -s141 A typology of the situations of cooperation in -s142 A structured analysis of operations and - ，research in healthcare (1982–2011143 - practice and information quality: A - strategy study144 Manufacturer's pricing strategy in a two-level - with competing retailers and advertising cost dependent demand145 Closed-loop - / design under a fuzzy environment146 Timing and eco(nomic) efficiency of climate-friendly investments in -s147 Post-seismic - risk ，: A system dynamics disruption analysis approach for inventory and logistics planning148 The relationship between legitimacy, reputation, sustainability and branding for companies and their -s149 Linking - configuration to - perfrmance: A discrete event simulation model150 An integrated multi-objective model for allocating the limited sources in a multiple multi-stage lean -151 Price and leadtime competition, and coordination for make-to-order -s152 A model of resilient - / design: A two-stage programming with fuzzy shortest path153 Lead time variation control using reliable shipment equipment: An incentive scheme for - coordination154 Interpreting - dynamics: A quasi-chaos perspective155 A production-inventory model for a two-echelon - when demand is dependent on sales teams׳ initiatives156 Coordinating a dual-channel - with risk-averse under a two-way revenue sharing contract157 Energy supply planning and - optimization under uncertainty158 A hierarchical model of the impact of RFID practices on retail - performance159 An optimal solution to a three echelon - / with multi-product and multi-period160 A multi-echelon - model for municipal solid waste ，system 161 A multi-objective approach to - visibility and risk162 An integrated - model with errors in quality inspection and learning in production163 A fuzzy AHP-TOPSIS framework for ranking the solutions of Knowledge ，adoption in - to overcome its barriers164 A relational study of - agility, competitiveness and business performance in the oil and gas industry165 Cyber - security practices DNA – Filling in the puzzle using a diverse set of disciplines166 A three layer - model with multiple suppliers, manufacturers and retailers for multiple items167 Innovations in low input and organic dairy -s—What is acceptable in Europe168 Risk Variables in Wind Power -169 An analysis of - strategies in the regenerative medicine industry—Implications for future development170 A note on - coordination for joint determination of order quantity and reorder point using a credit option171 Implementation of a responsive - strategy in global complexity: The case of manufacturing firms172 - scheduling at the manufacturer to minimize inventory holding and delivery costs173 GBOM-oriented ，of production disruption risk and optimization of - construction175 Alliance or no alliance—Bargaining power in competing reverse -s174 Climate change risks and adaptation options across Australian seafood -s – A preliminary assessment176 Designing contracts for a closed-loop - under information asymmetry 177 Chemical - modeling for analysis of homeland security178 Chain liability in multitier -s? Responsibility attributions for unsustainable supplier behavior179 Quantifying the efficiency of price-only contracts in push -s over demand distributions of known supports180 Closed-loop - / design: A financial approach181 An integrated - / design problem for bidirectional flows182 Integrating multimodal transport into cellulosic biofuel - design under feedstock seasonality with a case study based on California183 - dynamic configuration as a result of new product development184 A genetic algorithm for optimizing defective goods - costs using JIT logistics and each-cycle lengths185 A - / design model for biomass co-firing in coal-fired power plants 186 Finance sourcing in a -187 Data quality for data science, predictive analytics, and big data in - ，: An introduction to the problem and suggestions for research and applications188 Consumer returns in a decentralized -189 Cost-based pricing model with value-added tax and corporate income tax for a - /190 A hard nut to crack! Implementing - sustainability in an emerging economy191 Optimal location of spelling yards for the northern Australian beef -192 Coordination of a socially responsible - using revenue sharing contract193 Multi-criteria decision making based on trust and reputation in -194 Hydrogen - architecture for bottom-up energy systems models. Part 1: Developing pathways195 Financialization across the Pacific: Manufacturing cost ratios, -s and power196 Integrating deterioration and lifetime constraints in production and - planning: A survey197 Joint economic lot sizing problem for a three—Layer - with stochastic demand198 Mean-risk analysis of radio frequency identification technology in - with inventory misplacement: Risk-sharing and coordination199 Dynamic impact on global -s performance of disruptions propagation produced by terrorist acts。

最优定价与订货策略

c
Demand in Period t
per-unit ordering cost Lt (xt+1) holding / shortage cost
R1 (λ1 , λ) R2 (λ, λ2)
21
Optimality Equation
Expected Revenue Profit-to-go from Period in Period t Expected Cost in Period t t + 1 to Period n + 1
Fixed pricing
模型框架
The selles, or multi-units, or both – selling mode
1 2
and 按单价售卖，或 “捆绑”售卖，或两者结合售卖：售卖模式 can change price over time 同时，可以随时改变价格
A
scholarship of HK$14,000 per month Other financial supports are available to students with outstanding performance
1 港元＝ 0。8 人民币。每年招生至少 10 名！
Career Prospects
例如： λ1 (p1, p2) = 200 – 5*p1 + 3*p2 λ2 (p1, p2) = 300 + 2*p1 – 4*p2 p1 = 326/5 – (16/65)* λ1 – (3/26)* λ2 p2 = 550/13 – (1/13)* λ1 – (5/26)* λ2

20
It also makes replenishment decisions 销售

赢在微店英语作文电子版

赢在微店英语作文电子版英文回答：Succeeding in Weidian is a multifaceted endeavor that encompasses a combination of strategic planning, innovative marketing, and exceptional customer service. To establish a thriving Weidian business, consider the following key steps:1. Niche Identification and Targeting:Identify a specific niche market with unmet needs and demand.Conduct thorough research to understand the target audience, their pain points, and preferences.Tailor your products and services to cater to the unique requirements of your niche.2. Product Selection and Sourcing:Offer high-quality products that align with the needs of your target market.Establish partnerships with reliable suppliers to ensure product availability and competitive pricing.Continuously expand and optimize your product range based on customer feedback and market trends.3. Competitive Pricing Strategy:Conduct market research to determine optimal pricing for your products and services.Offer competitive prices while maintaining a reasonable profit margin.Consider offering promotions, discounts, and loyalty programs to attract and retain customers.4. Effective Marketing and Promotion:Utilize Weidian's marketing tools, such as live streaming, flash sales, and social media integration.Run targeted advertising campaigns on platforms frequented by your target audience.Collaborate with influencers and brand ambassadors to promote your products and build credibility.5. Customer-Centric Approach:Provide excellent customer service to build long-term relationships.Respond promptly to inquiries, resolve complaints efficiently, and offer personalized assistance.Gather customer feedback and use it to improve product offerings and overall user experience.6. Data Analysis and Optimization:Track your performance metrics to identify areas for improvement.Use data analysis to optimize your marketing campaigns, product selection, and customer service strategies.Regularly review and update your business plan basedon data-driven insights.中文回答：成功经营微店的方法。

定价即经营员工读后感

定价即经营员工读后感（中英文实用版）English:After reading the book "Pricing is Marketing", I have gained a deeper understanding of the importance of pricing strategy in business.The book highlights that pricing is not just a mathematical calculation, but a strategic decision that reflects the value of a product or service to the customer.It is a crucial element in marketing and can significantly impact the success of a business.中文：阅读了《定价即营销》这本书后，我对定价策略在企业中的重要性有了更深的认识。

书中强调，定价不仅仅是数学计算，更是一种反映产品或服务对客户价值的战略决策。

它是营销的一个关键要素，能够显著影响企业的成功。

English:The book emphasizes that pricing should be aligned with the overall business strategy and should consider factors such as customer perception, competition, and cost.It should be dynamic and adaptable to changes in the market and customer needs.By setting the right price, a company can create value for its customers, differentiate itself from competitors, and achieve its business objectives.中文：书中强调，定价应与整体的商业战略保持一致，并应考虑客户感知、竞争和成本等因素。

谢维-华南理工大学引进人才聘用制教师中期考核表.doc

华南理工大学聘用制教师中期考核表所在单位：华南理工大学
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Distribution center network design under trade credits

Distribution center network design under tradecreditsYu-Chung TsaoDepartment of Industrial Management,National Taiwan University of Science and Technology,Taipei,Taiwana r t i c l ei n f o Keywords:Inventory Trade credit LocationDistribution center Allocationa b s t r a c tThis paper considers a distribution center network design problem under trade credits.An outside supplier provides a credit period to the distribution company.The key decisions of the distribution company are where to locate the distribution centers (DCs),how to assign retail stores to DCs and the joint replenishment cycle time at DCs such that the total net-work cost is minimized.This paper uses a continuous approximation method to formulate the model.One algorithm based on nonlinear optimization is provided to solve the supply chain network design problem.This paper also considers a special case when the distribu-tion company only determines the inventory decision.Numerical studies illustrate the solution procedures and the effects of the parameters on decisions and costs.The results and the modeling approach are useful references for managerial decisions.Ó2013Elsevier Inc.All rights reserved.1.IntroductionTrade credit simply means that a vendor extends a buyer credit terms,giving a buyer extra time to pay or giving a dis-count for early payment.This is an agreement where a customer can purchase goods on account (without paying cash),pay-ing the supplier at a later date.The traditional inventory model tacitly assumes that the payment must be made to the vendor for the items immediately after the buyer receives the products.In practice,the vendor often provides forward ﬁnancing to the buyer.This means that the vendor allows the buyer a certain ﬁxed period (credit period)in which to settle the amount owed,and does not charge any interest on the amount owed during this period.Goyal’s [1]study was the ﬁrst trade credit paper to examine the effect of the credit period on the optimal inventory policy.Over the years,a number of studies have been published that deal with the inventory problems under trade credit.Recently,Huang [2]investigated the optimal retailer’s replenishment decisions under two levels of trade credit policy within the eco-nomic production quantity framework.Huang and Hsu [3]developed an EOQ model under retailer partial trade credit policy in supply chain.Ouyang et al.[4]considered deteriorating items with a partially permissible delay in payments linked to order quantity.De and Goswami [5]considered a probabilistic EOQ model for deteriorating items under trade credit.Tsao [6]determined the optimal ordering and discounting policies under advance booking discount and trade credits.Chen and Kang [7]discussed coordination between vendor and buyer considering trade credit and items of imperfect quality.Tsao [8]determined two-phase pricing and inventory decisions for deteriorating and fashion goods under trade credit conditions.Kreng and Tan [9]determined the optimal replenishment decisions under two levels of trade credit policy if the purchaser’s order quantity is greater than or equal to a predetermined quantity.Tsao [10]considered multi-echelon multi-item channels subject to supplier’s credit period and retailer’s promotional effort.Chang et al.[11]determined optimal manufacturer’s replenishment policies for deteriorating items in a supply chain with up-stream and down-stream trade credits.Balkhi [12]considered an economic ordering policy with deteriorating items under different supplier trade credits for ﬁnite horizon case.Tsao et al.[13]considered a production system under reworking of imperfect items and trade credit.0096-3003/$-see front matter Ó2013Elsevier Inc.All rights reserved./10.1016/j.amc.2013.07.028E-mail addresses:yctsao@.tw ,yctsao@.twFor studies published within one year,Lin et al.[14]determined the optimal ordering and delivery decisions under trade credit and defective items.Tsao and Sheen [15]dealt with the dual problems of determining the ideal supplier credit period,and of the best way for the retailer to make multi-item replenishment and pricing decisions,while still maximizing proﬁts.Cheng et al.[16]considered that the retailer can either pay off all accounts at the end of the credit period or delay incurring interest charges on the unpaid and overdue balance due to the difference between interest earned and interest charged.Zhong and Zhou [17]developed a model for determining ordering/trade-credit policy of a supply chain,where one supplier sells a product to a retailer.Chung et al.[18]addressed some shortcomings in the 2011paper by Kreng and Tan [9].The issue of trade credit is very popular in this ﬁeld of research.The design and management of supply network in today’s competitive business environment is one of the most important and difﬁcult problems that managers face.Based on their great research,this paper incorporates trade credits into the inte-grated facility location and inventory allocation problem,i.e.the supply network design problem.The distribution center (DC)location and inventory policy at the DC are both decision variables in this ﬁeld of research.Teo and Shu [19]proposed a set-covering model to design a two-echelon warehouse-retailer network under deterministic retailers demands.Romeijn et al.[20]extended the problem to consider an additional cost term that may represent costs related to safety stocks or capacity considerations.Pujari et al.[21]utilized a continuous approximation procedure to determine optimal number and size of shipments while considering issues of location,production,inventory,and transportation.Murat et al.[22]pro-vided a continuous approximation framework for solving location–allocation problems with dense demand.Murat et al.[23]formulated the two-facility location–allocation problem as a multi-dimensional boundary value problem and developed a multi-dimensional shooting algorithm to solve it.Shen [24]has made a complete review of the supply chain design literature and of current practices.The goal of this study is to provide logistics network planners with a high-level solution for the integrated facility location and inventory allocation problem under trade credits.Chen [25,26]emphasized the importance of integrated decision-mak-ing.Speciﬁcally,this study intends to determine the following DC network design decisions:(1)which DC locations should be open,(2)which retail store should be served from which DC,and (3)the joint replenishment cycle time at DCs.The contributions of this paper to the literature are as follows.First,this is the ﬁrst study to consider distribution center network design problem under trade credits.Second,the proposed solution deﬁnes the input data in terms of continuous functions and is capable of formulating these functions for a data set of any size.This is very important for dealing with prac-tical problems.Third,this study proposes an efﬁcient algorithm for solving resulting nonlinear programs.We also consider a special case when the DCs only determine the inventory decision.Fourth,numerical study illustrates the solution procedures and effects of the relevant model parameters on distribution center network design decisions and costs.2.Model formulationThe network studied in this paper is a two-echelon supply chain with an outside supplier selling goods to DCs.The DCs are located at level two,and help consolidate shipments arriving from the supplier and deliver them to the retailers.The retailers at the downstream meet the demands from end customers.Goods ﬂow from upper-stream facilities to the down-stream facilities (see Fig.1).The mathematical model in this study is based on the followingassumptions:Y.-C.Tsao /Applied Mathematics and Computation 222(2013)356–3643571.Demand per unit time for retail store in cluster i is an independent and identically distributed Poisson process with rate k i .2.Each DC’s inﬂuence area is close to circular.Service regions have somewhat irregular shapes as opposed to circles,hexa-gons,or squares in the economics literature.This irregular service area is shown to have little effect on the optimal solu-tion [27].Moreover,each DC is located in the center of the inﬂuence area.3.Replenishments occur in very short time,i.e.lead time can be ignored for the DC-Retailer echelon.4.Each retailer is assigned to a particular DC and served only by that DC.5.The unit wholesale price of the products sold during the credit period is deposited in an interest bearing account with rate I e .At the end of this period,the credit is settled and the DCs start paying for the interest charges for the items in stock with rate I p .This study uses the following notations.T:joint replenishment cycle time (decision variable)A i :inﬂuence area for each DC in cluster i ,where i =1,2,...,N (decision variable)F :facility cost of opening each DC d i :store density in cluster ik i :demand rate for retail store in cluster i n :length of the planning horizonc T :transportation cost per unit distance per itemf r :constant that depends on the distance metric and shape of the DC service region R:ordering cost for DCh:inventory holding cost for DC C i :service area in cluster i c :unit purchasing costw:wholesale price per unit I p :interest charged per dollar I e :interest earned per dollar tc :the length of credit periodThis study uses an approximation technique [28]to divide the network into smaller regions over which the discrete var-iable can be modeled using the slow varying ing the method the given service region is covered with clusters i ,i =1,2,...,N .Clusters i ,i =1,2,...,N ,exist within the given service region such that the store density is nearly constant over each cluster.This model calculates the components of the total network cost as follows.(1)The total facility cost is given by multiplying the facility cost of opening each DC with the number of DCs,namely,P N i ¼1ðF C ii Þ.(2)Assuming ‘‘close to circular’’service regions with the facility at the center,the average distance traveled by each itemis f r ﬃﬃﬃﬃﬃA i p [27].The total transportation cost is P N i ¼1ðc T f r ﬃﬃﬃﬃﬃA i p nk i d i C i Þ.(3)The total ordering cost is P N i ¼1ðR C ii Þ.(4)The total inventory holding cost is P N i ¼1ðh nk i d i C i T Þ.(5)There are two cases in which interest is earned.Case 1:when T P tcInterest earned =P N i ¼1ðwI e nk i d i C i tc 2ÞCase 2:when T <tcInterest earned =P N i ¼1½wI e nk i d i C i ðtc ÀT2Þ(6)There are two cases in which interest is paid.Case 1:when T P tcInterest paid =P N i ¼1½cI p nk i d i C i2T ðT Àtc Þ2 Case 2:when T <tc Interest paid =0.Therefore,the total network cost is Case 1.When T P tcTNC 1ðA 1;A 2;...;A N ;T Þ¼X N i ¼1F C i iþX N i ¼1c T f r ﬃﬃﬃﬃﬃA i p nk i d i C i þX N i ¼1R C i i þX N i ¼1hnk i d i C i T þX N i ¼1cI p nk i d i C i 2T ðT Àtc Þ2!ÀX N i ¼1wI e nk i d i C i tc 22T ;ð1Þ358Y.-C.Tsao /Applied Mathematics and Computation 222(2013)356–364Case2.When T<tcTNC2ðA1;A2;...;A N;TÞ¼X Ni¼1FC iA iþX Ni¼1c T f rﬃﬃﬃApink i d i C iþX Ni¼1RTC iA iþX Ni¼1hnk i d i C i T2ÀX Ni¼1wI e nk i d i C i tcÀT2!:ð2Þ3.Optimal DC inﬂuence area and joint replenishment cycle timeThe company wants to determine the optimal DC inﬂuence area AÃi;i¼1;2;...;N and the joint replenishment cycle time TÃto minimize the total network cost TNC jðA1;A2;...;A N;TÞ,where j=1or 2.The problem is to minimizeTNC jðA1;A2;...;A N;TÞ¼TNC1ðA1;A2;...;A N;TÞ;when T P tcTNC2ðA1;A2;...;A N;TÞ;when T<tc&,which is a two-branch function with N+1decision variables.Given T,the second-order derivative of TNC jðA1;A2;...;A N j TÞwith respect to A i is@2TNC jðA1;A2;...;A N j TÞ@Ai ¼2FC iAi!þÀc T f r nk i d i C i4Ai!þ2RC iTAi!;i¼1;2;...;N and j¼1;2:ð3ÞFrom@2TNC jðA1;A2;...;A N j TÞ@A2i ¼ð2FC iA3iÞþðÀc T f r nk i d i C i4A3=2iÞþð2RC iTA3iÞ¼0,we get the threshold of F=fðc T f r nk i d i C i4A3=2iÞÀð2RC iTA3iÞg=ð2C iA3iÞ.This means@2TNC jðA1;A2;...;A N j TÞ@A2i >0when F>fðc T f r nk i d i C i4A3=2iÞÀð2RC iTA3iÞg=ð2C iA3iÞ.Since the facility opening cost F is large,@2TNC jðA1;A2;...;A N j TÞ@A2i>0is satisﬁedin general case.Also,@2TNC jðA i j TÞi k¼0,i=1,2,...,N;k=1,2,...,N,i–k and j=1,2.The Hessian matrix is thenH j¼@2TNC j@A210::::000@2TNC j@A22::0 :::::::::::::::::::::0:0::::0@2TNC j@A2NÀ100::::0@2TNC j@AN2666666666666666666437777777777777777775:Since@2TNC j@A2i>0in general case,we know that j H j j>0and the principal minor determinant j H ji j>0for all i¼1;2;...;N and j¼1;2.From the minimum theorem in Winston[29],we know that TNC jðA1;A2;...;A N j TÞis a convex function ofðA1;A2;...;A NÞ.This means that the optimal A iðTÞ,i=1,2,...,N,can be obtained by solving@TNC jðA1;A2;...;A N j TÞ@A i¼0.To solve this problem,weﬁrst determine the closed form of the retail price A iðTÞthat minimize TNC jðA1;A2;...;A N j TÞ.Solving@TNC jðA1;A2;...;A N;TÞ@A i¼0leads toA iðTÞ¼2ðFþR=TÞT r i i !2=3;i¼1;2;...;N:ð4ÞEq.(4)lead to Property1.Property1.(a)The inﬂuence area for each DC A i increases as the joint replenishment cycle time T or the transportation cost c T decrease.(b)The inﬂuence area for each DC A i increases as the facility cost of opening each DC F increase.Substituting A i(T),i=1,2,...,N,into the corresponding TNC j(A1,A2,...,A N,T)reduces the model to a two-branch function, with T as its single variable:TNC jðTÞ¼TNC1ðA1ðTÞ;A2ðTÞ;...;A NðTÞ;TÞ;when T P tc TNC2ðA1ðTÞ;A2ðTÞ;...;A NðTÞ;TÞ;when T<tc &:Case1.When T P tcY.-C.Tsao/Applied Mathematics and Computation222(2013)356–364359TNC1ðTÞ¼X Ni¼1FC ic T f r nk id i2ðFþR=TÞ!2=3()þX Ni¼1c T f r2ðFþR=TÞc T f r nk id i!1=3nk i d i C i()þX Ni¼1RC iTc T f r nk id i2ðFþR=TÞ!2=3()þX Ni¼1hnk i d i C i T2þX Ni¼1cI p nk i d i C i2TðTÀtcÞ2!ÀX Ni¼1wI e nk i d i C i tc22T;ð5ÞCase2.When T<tcTNC2ðTÞ¼X Ni¼1FC ic T f r nk id i!2=3()þX Ni¼1c T f r2ðFþR=TÞT r i i!1=3nk i d i C i()þX Ni¼1RC i c T f r nk i d i!2=3()þX Ni¼1hnk i d i C i T2ÀX Ni¼1wI e nk i d i C i tcÀT2!:ð6ÞTo obtain the optimal joint replenishment cycle time for each case,the optimal joint replenishment cycle time can be deter-mined by solving dTNC jðTÞdT ¼0,where j=1,2.It is then necessary to check the second-order condition of convexity,i.e.d2TNC jðTÞdT2>0,where j=1,2.Based on the above discussion,the following algorithm determines the optimal values for AÃiand T⁄.AlgorithmStep1:For Case1.If there exists a T0such that T0P tc,and T0satisﬁes dTNC1ðTÞdT ¼0and d2TNC1ðTÞdT2>0,then determine A iðT0Þby(4)andTNC1ðA iðT0Þ;T0Þby(1).Otherwise,set TNC1ðA iðT0Þ;T0Þ¼1. Step2:For Case2.If there exists a T00such that T00<tc,and T00satisﬁes dTNC2ðTÞ¼0and d2TNC2ðTÞdT >0,then determine A iðT00Þby(4)andTNC2ðA iðT00Þ;T00Þby(2).Otherwise,set TNC2ðA iðT00Þ;T00Þ¼1.Step3:Let TNC jðAÃi;TÃÞ¼Min f TNC1ðA iðT0Þ;T0Þ;TNC2ðA iðT00Þ;T00Þg.4.Special case:optimal joint replenishment cycle timeIn this section we consider a special case when the DC inﬂuence area is given This means the company only need to deter-mine the optimal joint replenishment cycle time TÃto minimize the total network cost TNC jðTÞ.TNC jðTÞ¼TNC1ðTÞwhen T P tcTNC2ðTÞwhen T<tc&;where TNC1ðTÞ¼X Ni¼1F C iA iþX Ni¼1c T f rﬃﬃﬃﬃﬃA ipnk i d i C iÀÁþX Ni¼1R C iiþX Ni¼1h nk i d i C i TþX Ni¼1cI p nk i d i C iðTÀtcÞ2h iÀX Ni¼1wI e nk i d i C i tc2;ð7ÞTNC2ðTÞ¼X Ni¼1FC iA iþX Ni¼1c T f rﬃﬃﬃﬃﬃA ipnk i d i C iþX Ni¼1RTC iA iþX Ni¼1hnk i d i C i T2ÀX Ni¼1wI e nk i d i C i tcÀT2!:ð8ÞCase1.When T P tc,theﬁrst and second-order derivatives of TNC1ðTÞwith respect to T aredTNC1ðTÞdT ¼ÀP Ni¼12RC iiþP Ni¼1ðcI PÀwI eÞtc2nk i d i C ih i2TþP Ni¼1ðhþcI PÞnk i d i C i2;ð9Þd2TNC1ðTÞdT2¼P Ni¼12RC iiþP Ni¼1nk i d i C i tc2ðcI pÀwI eÞT3:ð10ÞCase2.When T<tc,theﬁrst and second-order derivatives of TNC2ðTÞwith respect to T aredTNC2ðTÞdT ¼X Ni¼1ÀRC iT2A iþðh iþwI eÞnk i d i C i2!;ð11Þd2TNC2ðTÞdT2¼X Ni¼12RC iT3A i>0:ð12Þ360Y.-C.Tsao/Applied Mathematics and Computation222(2013)356–364Eq.(12)implies that TNC2ðTÞis convex on T>0.Let D¼P Ni¼12RC iA iþP Ni¼1nk i d i C i tc2ðcI pÀwI eÞ,Eq.(10)implies that TNC1ðTÞisconvex on T>0when D>0.Furthermore,Eqs.(7)and(8)imply that TNC jðTÞis convex on T>0when D>0.Since TNC1ðtcÞ¼TNC2ðtcÞ,TNC jðTÞis continuous and well-deﬁned at T¼tc.To minimize TNC2ðTÞ,we set Eq.(11)¼0and obtain the optimal joint replenishment cycle time when T<tc,TÃ2¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃX Ni¼12RðhþI e wÞnk i d i A iv uu t:ð13ÞIf D>0,Eq.(10)implies that TNC1ðTÞis convex on T>0.Let Eq.(9)=0,we obtain the optimal joint replenishment cycle time when T P tc,TÃ1¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃX Ni¼12Rþtc2½nk i d i A iðcI pÀwI eÞP i i iv uu t:ð14ÞFrom above we derive and deduce Theorems1and2to determine the optimal joint replenishment cycle time when D<0 and D P0respectively.Theorem1.If D<0,then TNC iðTÞhas the minimum value TÃ¼TÃ2.Proof.Because TNC2ðTÞis convex on T>0and T<tc.Therefore,TNC2ðTÞis decreasing onð0;TÃ2 and increasing on½TÃ2;tc .SoTNC2ðTÞhas a minimum value at TÃ2onð0;tc .On the other hand,if D<0,Eq.(9)implies that dTNC1ðTÞdT>0and TNC1ðTÞisincreasing on T>0.Therefore,TNC1ðTÞis increasing on½tc;1Þ.So TNC1ðTÞhas a minimum value at tc.FromTNC1ðtcÞ¼TNC2ðtcÞ,we can know that TNC iðTÞhas the minimum value at TÃ2on T>0.Therefore,TÃ¼TÃ2.hTheorem2.If D P0,let!¼P Ni¼1½2RÀtc2ðhþI e wÞnk i d i A i ,then(a)when!>0,the optimal replenishment cycle time is TÃ¼TÃ1 (b)when!<0,the optimal replenishment cycle time is TÃ¼TÃ2(c)when!¼0,the optimal replenishment interval is TÃ¼TÃ1¼TÃ2¼tc.Y.-C.Tsao/Applied Mathematics and Computation222(2013)356–364361Proof.(a)If!>0,Eqs.(14)and(13)imply that TÃ1>tc and TÃ2>tc.According to the convexities and the deﬁnitions ofTNC1ðTÞfor Case1and TNC2ðTÞfor Case2,weﬁnd that TNC1ðTÞis decreasing on½tc;TÃ1and TNC2ðTÞis decreasing onð0;tc .This means TNC1ðTÞhas the minimum value at TÃ1and TNC2ðTÞhas the minimum value at tc.Therefore,fromTNC2ðtcÞ¼TNC1ðtcÞP TNC1ðTÃ1Þ,we know that TNC jðTÞhas the minimum value at TÃ¼TÃ1.The proofs in(b)and(c)are sim-ilar to that in(a).h5.Numerical studyThis section presents a numerical study to illustrate the proposed solution approach and provide quantitative insights. The goals of the numerical study in this study are as follows:1.To illustrate the procedures of the solution approach;2.To discuss the effects of the related parameters on decisions and cost.5.1.Numerical exampleTo illustrate the algorithm described above,consider the parameters of a product in a distribution company:F=100,000; C1=10,000;C2=8000;C3=6000;h=1;c=8;w=20;R=30;c T=10;k1=11;k2=10;k3=9;n=12;d1=0.06;d2=0.05; d3=0.04;f r=0.01,I P=0.15,I e=0.1,tc=0.02.After applying the Algorithm in Section3,the optimal joint replenishment cy-cle time is TÃ=0.0278,the optimal DC inﬂuence area in cluster C1Z is AÃ1=4023.87,the optimal DC inﬂuence area in clusterC2Z is AÃ2=4842.02,the optimal DC inﬂuence area in cluster C3Z is AÃ3=6027.52,and the total network cost isTNCÃ¼1:6382Â106.Fig.2shows the graphic illustrations of TNC vs.different decision variables.For the special case in Section4,the DC inﬂuence area in each cluster is given as follows:AÃ1=4000,AÃ2=5000andAÃ3=6000.Since D¼P3i¼12RC iA iþP3i¼1nk i d i C i tc2ðcI pÀwI eÞ=270.659>0,we use Theorem2to determine the optimal jointreplenishment cycle time TÃ.We then calculate!¼P3i¼1½2RÀtc2ðhþI e wÞnk i d i A i =74.88>0.Therefore,the optimal replen-ishment cycle time is TÃ¼TÃ1=0.0277and the total network cost is TNCÃ¼1:6384Â106.5.2.Numerical analysisSeveral numerical analyses are conducted to gain quantitative insights into the structures of the proposed policies.The following numerical analyses are used to show the effects of F,c T,R,h,I P and I e on the optimal DC inﬂuence area,the joint replenishment cycle time and the total network cost.The results of Table1are as follows:1.When the facility cost F increases,the optimal joint replenishment cycle time TÃdecreases,but the optimal the optimalDC inﬂuence area AÃiand the total network cost TNCÃincrease.This veriﬁes Property1(b).When the facility cost increases,it is reasonable to decrease the DC inﬂuence area to reduce the number of DC opening.Table1The effects from system parameters.Parameter TÃAÃ1AÃ2AÃ3TNCÃF=80,0000.03033471.284177.075199.771:5221Â106 F=100,0000.02784023.874842.026027.521:6382Â106 F=120,0000.02594540.575463.786801.51:7398Â106c T=80.02544672.425622.446999.011:4118Â106c T=100.02784023.874842.026027.521:6382Â106c T=120.02993561.584285.745335.031:8499Â106R=250.02494021.884839.626024.531:6372Â106 R=300.02784023.874842.026027.521:6382Â106 R=350.03044025.774844.36030.361:6391Â106 h=0.80.02924022.534840.416025.511:6378Â106 h=10.02784023.874842.026027.521:6382Â106 h=1.20.02664025.154843.566029.431:6387Â106I P=0.130.02834023.344841.396026.731:63818Â106I P=0.150.02784023.874842.026027.521:63821Â106I P=0.170.02734024.364842.606028.241:63824Â106I e=0.080.02914022.614840.506025.631:6387Â106I e=0.10.02784023.874842.026027.521:6382Â106I e=0.120.02654025.334843.786029.701:6377Â106 362Y.-C.Tsao/Applied Mathematics and Computation222(2013)356–364Y.-C.Tsao/Applied Mathematics and Computation222(2013)356–364363 2.When the transportation cost c T increases,the optimal DC inﬂuence area AÃdecreases,but the optimal joint replenish-iment cycle time TÃand the total network cost TNCÃincrease.When the transportation cost increases,it is reasonable to increase the joint replenishment cycle time to reduce the transportation frequency.3.When the ordering cost R increases,the optimal joint replenishment cycle time TÃ,the optimal DC inﬂuence area AÃandi the total network cost TNCÃall increase.If the ordering cost increases,it is reasonable that the company will increase the replenishment cycle time to reduce replenishment frequency.The company will also likely increase each DC inﬂuence areas to reduce the number of DCs as the ordering cost increases.4.When the inventory holding cost h increases,the joint replenishment cycle time TÃdecreases but the optimal DC inﬂu-and the total network cost TNCÃincreases.It is reasonable that when the inventory holding cost increases, ence area AÃithe company will decrease the replenishment cycle time in an effort to lower inventory costs.They will increase each DC inﬂuence area to reduce the number of DCs as the inventory holding cost increases.5.When the interest charged I P increases,the optimal joint replenishment cycle time TÃdecreases,but the optimal the opti-mal DC inﬂuence area AÃand the total network cost TNCÃincrease.If the interest charged increases,it is reasonable that ithe company decreases the replenishment cycle time to reduce the interest charges for the items in stock.6.When the interest earned I e increases,the optimal DC inﬂuence area AÃincreases,but the optimal joint replenishmenticycle time TÃand the total network cost TNCÃdecrease.6.ConclusionsThis study considers a distribution center network design problem under trade credit.An outside supplier provides a credit period to the distribution company.The proposed method integrates facility costs,inventory costs,transportation costs,and ordering costs.The key decisions of this distribution company are where to locate the distribution centers (DCs),how to assign retail stores to DCs and the joint replenishment cycle time at DCs such that the total network cost is minimized.Numerical studies illustrate the solution procedures and the effects of the facility cost,transportation cost,order-ing cost,inventory holding cost,interest charged and interest earned on decisions and costs.The proposed model provides a powerful analysis tool for studying potential changes in a supply chain system due to changes in the parameters.The results of this study are a useful reference for managerial decision-making and administration.Further research on this topic could consider other situations such as two-level trade credit and multi-item supply chain network.AcknowledgmentsThe author expresses his gratitude to the editor and the anonymous reviewers for their detailed comments and valuable suggestions to improve the exposition of this paper.This paper is supported in part by the National Science Council under Grant NSC102-2410-H-011-029-MY3and Grant NSC102-2221-E-011-159-MY3.References[1]S.K.Goyal,Economics order quantity under conditions of permissible delay in payments,Journal of the Operational Research Society36(1985)335–338.[2]Y.F.Huang,Optimal retailer’s replenishment decisions in the EPQ model under two levels of trade credit policy,European Journal of OperationalResearch176(3)(2007)1577–1591.[3]Y.F.Huang,K.H.Hsu,An EOQ model under retailer partial trade credit policy in supply chain,International Journal of Production Economics112(2)(2008)655–664.[4]L.Y.Ouyang,J.T.Teng,S.K.Goyal,C.T.Yang,An economic order quantity model for deteriorating items with partially permissible delay in paymentslinked to order quantity,European Journal of Operational Research194(2009)418–431.[5]L.N.De,A.Goswami,Probabilistic EOQ model for deteriorating items under trade creditﬁnancing,International Journal of Systems Science40(2009)335–346.[6]Y.C.Tsao,Retailer’s optimal ordering and discounting policies under advance booking discount and trade credits,Computers and Industrial Engineering56(1)(2009)208–215.[7]L.H.Chen,F.S.Kang,Coordination between vendor and buyer considering trade credit and items of imperfect quality,International Journal ofProduction Economics123(1)(2010)52–61.[8]Y.C.Tsao,Two-phase pricing and inventory management for deteriorating and fashion goods under trade credit,Mathematical Methods of OperationsResearch72(1)(2010)107–127.[9]V.B.Kreng,S.J.Tan,The optimal replenishment decisions under two levels of trade credit policy depending on the order quantity,Expert Systems withApplications37(2010)5514–5522.[10]Y.C.Tsao,Managing multi-echelon multi-item channels with trade allowances under credit period,International Journal of Production Economics127(2)(2010)226–237.[11]C.T.Chang,J.T.Teng,M.S.Chern,Optimal manufacturer’s replenishment policies for deteriorating items in a supply chain with up-stream and down-stream trade credits,International Journal of Production 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考虑顾客惰性时的供应链定价与存货决策研究

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假定产品的销售分为正常销售阶段和清仓处理阶段，顾客在确定最优购买时机时会战略性地比较提前购买和延迟购买时获得的期望效用，同时顾客也可能存在延迟购买的消费惰性。

利用理性预期均衡分析，分析了存在顾客惰性时零售商的最优定价与存货数量，并且比较了战略顾客行为下和顾客惰性下的零售商的最优定价和存货数量的关系。

研究表明，顾客惰性的存在减少了零售商的期望利润，降低了零售商的最优销售价格，同时也降低了零售商的最优存货数量。

Abstract: The retailer's optimal pricing and ordering decisions with customer inertia are studied in this paper. It is assumed that thesales period concludes both normal selling period and clearance disposal period. The customers determine the optimal purchase timeaccording to the comparison of the expected utility with spot purchase and delayed purchase. Meanwhile, customers have an inherent inertiato delay purchase. The rational expectation equilibrium analysis is utilized, and the retailer's optimal pricing and stocking quantity withcustomer inertia are analyzed. The optimal pricing and stocking quantity with strategic customer behavior and with customer inertia arecompared. The results indicate that customer inertia reduces the retailer's expected profit, reduce the retailer's optimal selling price, andalso reduces the retailer's optimal stocking quantity.关键词：供应链管理；理性预期均衡；战略顾客；顾客惰性Key words: supply chain management；rational expectation equilibrium；strategic customer；customer inertia中图分类号院F274 文献标识码院A 文章编号院1006-4311（2014）20-0022-040 引言动态定价是提高零售商利润的重要手段。

人工智能大模型优化商品定价策略英文

人工智能大模型优化商品定价策略英文English:Artificial intelligence (AI) has revolutionized many industries, and one area where it can make a significant impact is in optimizing pricing strategies for large retail companies. With the help of AI algorithms, businesses can analyze vast amounts of data to understand customer behavior, market trends, competitor pricing, and pricing elasticity. By leveraging machine learning models, companies can predict optimal pricing points that maximize profit while taking into account various factors such as seasonality, promotion effectiveness, and customer segmentation. These AI-powered pricing strategies can also be continuously updated in real-time to adapt to changing market conditions, ensuring that companies remain competitive and maximize revenue. Additionally, by incorporating dynamic pricing mechanisms into their strategies, companies can offer personalized pricing to individual customers based on their purchasing behavior and preferences, leading to increased customer loyalty and satisfaction. Overall, AI-powered pricing optimization enables companies to make informed pricing decisions that drive revenue growth and enhance customer relationships.中文翻译:人工智能（AI）已经彻底改变了许多行业，其中一个领域可以显著提升的地方是优化零售巨头的定价策略。

提前支付折扣条件下供应链库存与定价策略

提前支付折扣条件下供应链库存与定价策略叶国雨【摘要】延期支付信用时的库存策略得到了较多的关注，然而对提前支付信用条件下的库存策略研究较少。

针对这一不足，研究了需求随机时，在单个供应商和单个零售商组成的供应链中，当供应商的对零售商提前支付给予价格折扣优惠时，零售商的最优采购策略和供应商的最优折扣策略。

零售商在给定价格折扣时，确定最优的提前采购批量和总的采购批量，而供应商则根据零售商对价格折扣的反应设定最优的价格折扣策略。

数值算例验证了论文的结论。

%Inventory policy under delay payment has gained much attention.However, little literature is about inventory policy under advance payment.This paper dealt with the prob-lem of determining the retailer ’ s optimal ordering policy and supplier ’ s optimal cash dis-count under the conditions of stochastic demand and a single-supplier, a single-retailer supply chain.Given the cash discount rate, retailer decides the optimal total order size and advance payment order size.The supplier decided the optimal cash discount rate according t o retailer’ s reflecting.Mathematical models have been derived for obtaining the optimal total and early payment quantity for retailer and optimal cash discount rate for supplier.The nu-merical examples are given to illustrate the results in the paper.【期刊名称】《哈尔滨商业大学学报（自然科学版）》【年(卷),期】2015(000)001【总页数】5页(P120-124)【关键词】提前支付;价格折扣;需求随机;库存策略;定价【作者】叶国雨【作者单位】上海交通大学中美物流研究院，上海200030【正文语种】中文【中图分类】F274在企业运营实践中，为扩大产品的销售量，不少供应商往往会允许下游零售商延期支付货款.与此同时，为及时回笼资金，缓解资金压力和降低坏账风险，供应商也会通过提供折扣的方式鼓励零售商提前支付货款.虽然提前支付和延期支付信用均在实践中得到了广泛的应用，然而学术界仅仅重点研究了延期支付时的库存与供应链协作策略，提前支付对供应链运营管理的影响确研究较少.针对这一不足，本文研究了随机需求条件下，当供应商对零售商提前支付的货款给予现金折扣时，零售商的最优提前支付采购批量和总的采购批量决策，并进而分析供应商最优的现金折扣政策.在供应链商业信用的文献研究中，大部分是延期支付的研究文献，然而对提前支付信用条件下的库存策略研究较少，近些年开始有学者研究提起支付的问题.Goyal[1]最早研究了延期支付条件下的EOQ模型.很多学者在Goyal的模型基础上研究了这一问题.Chand和Ward[2]将延期付款作为一种价格折扣，在考虑平均成本的基础上得出了与Goyal不同的公式.市场需求的波动会对企业的订货策略产生影响，针对各种需求情况下的Goyal模型，许多学者也做了这方面的研究.Kim等[3]研究了当需求依赖于零售价格时Goyal模型的拓展.张钦红和赵泉午[4]研究了存货需求随机波动时，银行的最优质押率决策问题，并分析了不同的风险偏好对质押率的影响，表明风险厌恶及损失规避时的质押率低于风险中性时的质押率.代大钊和张钦红[5]研究了需求随机且库存对需求存在激励作用时，供应商的信用策略决策问题.在运营实践中，供应商为刺激销售，通常给予零售商基于采购数量的延期支付.Huang[6]研究了现金折扣和延期支付条件下零售商的最优订购策略.邱昊等[7]研究了供应商给定延期支付政策下的零售商最优订货决策，得出零售商在供应商给定延期付款、现金折扣政策下最优订货数量和付款时间的判定方法.Sana和Chaudhuri[8]研究了在确定性需求的情况下，零售商面对供应商提供的商业信用和现金折扣时的最优订货策略.Ho等[9]研究了在现金折扣和延期支付条件下的最优定价、订货、运输和支付策略.已有的文献大多研究了供应商给定延期支付信用策略时，零售商依此来做出最优的订货决策.目前，许多文献研究将延期支付作为对于零售商的激励机制.杨树等[10]研究了生产商的延期支付策略的制定.利用斯坦博格博弈模型给出了生产商延期支付策略和销售商的最优订货策略.骆建文[11]从供应商的角度，将信用期限作为一种激励机制，在确定性需求下，研究了信用期限激励机制对单个产品供应链的协调作用，通过与数量折扣合同机制的对比，指出在一定条件下信用期激励机制要优于数量折扣合同.张钦红和骆建文[12]研究了当零售商资金约束与供应商的资金成本存在双边不完全信息时，通过双边拍卖模型给出了均衡的信用期限长度和双边市场势力及信息结构的关系.在提前支付方面，Cachon[13]研究了推式、拉式以及提前支付折扣三种供应链合同契约的有效性，并讨论了三种合同契约下的帕累托最优改进.徐冰，刘蕾[14]考虑了货币的时间价值，研究了供应商在提前支付条件下的批发价折扣策略，供应商和零售商能够同时接受一定范围内的批发价格折扣使双方的利润获得帕累托改进.尽管提前支付信用开始得到学术界的关注，然而相关的研究仍然存在较多的扩展空间[5]，在我国的汽车销售领域，以及钢材贸易等领域，提前支付均有广阔的应用空间.本文考虑由一个供应商和一个零售商构成的二级供应链，市场的需求D为一随机变量，其分布函数及概率密度函数为F(x),f(x). 供应商对提前支付的产品给与k的价格折扣，即对提前支付的部分采购价格为(1-k)w，其中w为非提前支付时的批发价格，p、c、v分别为零售价格，生产成本和产品残值.模型所需主要符号及及其含义见表1.当订货量为q时，零售商的期望销售量：供应商对提前支付的产品批发价为(1-k)w(0<k<1)，延期支付的批发价为w.零售商选择将订货批量q2 提前支付，剩余q-q2延期支付.1.1 零售商的订货策略此时零售商的期望利润为：零售商总利润期望销售收入期末残值产品采购成本提前支付期限的利息支出延期支付期限的利息收入，即由于提前订货量q2小于总订货量q，所以假设即B≤(1-k)qw.则零售商的最优决策问题为：maxΠr(q,q1)s.t.0≤q1(1-k)w≤B由式(4)可得则可得1) 当k(1+r1T1)-r1T1-r2T2>0时，取时，此时零售商利润取得最大值为：零售商利润函数的一阶、二阶导数分别为：由于所以Πr(q)是关于q的凹函数.令可求得零售商最有的订货量q满足式(9)：(v-p)F(q)+p-w+wr2T2=0求解得：由可得：此时，零售商的最大利润为：2) 当k(1+r1T1)-r1T1-r2T2≤0时，取q1w=0时，此时零售商利润取得最大值为：由于令可求得零售商最有的订货量q满足下式：由q1w=0可得：q1=0此时，零售商最大利润为：总结上述结论有如下命题：命题1：零售商的总订货批量q与供应商提供的折扣率k无关，提前订货批量q1与折扣率k有关.当q1≠0时，零售商将所有现有资金全部提前支付时利润取得最大值.当k(1+r1T1)-r1T1-r2T2>0时当k(1+r1T1)-r1T1-r2T2≤0时当供应商提供的价格折扣收益大于利息收益时，零售商的最优订货策略即将全部的现有资金提前支付，从而享有价格折扣带来的利益.反之，零售商不会提前支付. 1.2 供应商的折扣策略供应商在提供价格折扣时，供应商获得零售商提前支付的享有折扣的货款、延期支付货款.对于零售商提前支付的货款，供应商会有一定的无风险利息收入，同时对于延期支付的货款，供应商会有利息支出.因此，供应商的利润函数为：供应商利润零售商支付货款产品成本提前支付额利息收入延期支付额利息支出Πs(k)=q1(1-k)w+(q-q1)w-cq+q1(1-k)wr1T1-(q-q1)wr2T2与零售商的决策依据相同，供应商的决策如下：1) 当k(1+r1T1)-r1T1-r2T2>0时，即零售商提前支付供应商利润函数的一阶、二阶导数分别为：因为当时所以可得最优的k*为临界值，即：将最优的折扣率代入利润函数可得：2) 当k(1+r1T1)-r1T1-r2T2≤0时，零售商提前支付q1=0时，供应商利润函数的一阶导数为：由于供应商利润函数和折扣率不相关，所以这种情况下供应商的最优利润为：Πs(k*,D)2=q(w-c)-qwr2T2由于可知：当k∈(0,k*]，供应商的利润保持不变，所以最优的折扣率即为内的任一k值.总结上述结论可得命题2：命题2：在时供应商利润保持不变，最优的折扣率即为内的任一k值.对于零售商而言，当供应商提供的价格折扣收益大于利息收益时，会将所有的现有资金提前支付.可知，供应商的最优价格折扣率即让零售商提前支付的临界值内的值.当p=1300,w=800,v=300,c=500,r1=0.0285,r2=0.025,T1=0.08,(1个月)，T2=0.08(1个月)时，见图1.1) 当市场需求服从均匀分布，即令b-a=50.此时零售商的总采购批量为：当k∈(0,k*)，零售商和供应商的利润为：Πs(k,D)1=q1(1-k)w+(q-q1)w-cq+q1(1-k)wr1T1-(q-q1)wr2T2当k∈(k*,1)，零售商和供应商的利润为：Πs(k,D)2=q(w-c)-qwr2T22) 当市场需求服从指数分布，即).此时零售商的总采购批量为：当k∈(0,k*)，零售商和供应商的利润为：当k∈(k*,1)，零售商和供应商的利润为：Πs(k,D)=q1(1-k)w+(q-q1)w-cq+q1(1-k)wr1T1-(q-q1)wr2T2Πs(k,D)2=q(w-c)-qwr2T2见图2.由算例结果图可知：当k∈(0,k*)时，零售商和供应商的利润保持不变，当k∈(k*,1)时，零售商的利润不断增加、供应商利润不断减少.本文研究当市场需求不确定时，供应商对零售商提前支付的货款给予价格折扣率的决策问题.本文分析了供应商提供折扣时，存在资金限制的零售商的最有订货量及提前支付比例，结果显示当零售商将所有现有资金提前支付时利润达到最大化.且折扣率对零售商的订货批量没有影响.当折扣率处于时，零售商提前支付批量为零，供应商的利润保持不变，最优折扣为区间内任一值.通过数值算例分析，在不同的提前支付、延期支付期限和利息水平条件下，供应商的最优折扣率的变化情况.本文假设零售商的资金约束对零售商是信息对称的，但是在实践中，供应商通常不知道零售商的资金约束.因而进一步的研究可考虑资金约束不对称时，供应商折扣率决策问题.【相关文献】[1] GOYAL S K. Economic order quantity under conditions of permissible delay in payments [J]. Journal of the Operational Research Society, 1985, 36(4): 335-338.[2] CHAND S, WARD J. A note on economic order quantity under conditions of permissible delay in payments [J]. Journal of the Operational Research Society, 1987, 38(1): 83-84.[3] KIM J, HWANG H S, SHINN S W. An optimal credit policy to increase supplier’s profit with price dependent demand functions [J]. Production Planning and Control: The Management of Operations, 1995, 6(1): 45-50.[4] 张钦红, 赵泉午.需求随机时的存货质押贷款质押率决策分析[J]. 中国管理科学, 2010, 18(5): 21-27.[5] 代大钊, 张钦红.资金约束条件下考虑信用风险的供应链商业信用决策研究[J].上海管理科学, 2013, 35(3): 62-66.[6] HUANG Y F. Buyer's optimal ordering policy and payment policy under supplier credit [J].International Journal of Systems Science, 2005, 36(13): 801-807.[7] 邱昊, 梁樑, 杨树.供应商给定延期付款和现金折扣策略下的零售商最优库存策略 [J]. 系统工程, 2006, 24(9): 18-23.[8] SANA S S, CHAUDHURI K S. A deterministic EOQ model with delays in payments and price-discount offers [J]. European Journal of Operational Research, 2008, 184(2): 509-533.[9] HO C H, OUYANG L Y, SU C H. Optimal pricing, shipment and payment policy for an integrated supplier-buyer inventory model with two-part trade credit [J]. European Journal of Operational Research, 2008, 187(2): 496-510.[10] 杨树, 梁樑, 邱昊.考虑延期支付的斯坦博格库存模型[J].系统工程, 2006, 24(4): 21-24.[11] LUO J W. Buyer vendor inventory coordination with credit period incentives [J]. International Journal of Production Economics, 2007, 108(1): 143-152.[12] 张钦红, 骆建文.双边不完全信息下的供应链信用期激励机制研究[J].系统工程理论与实践, 2009, 29(9): 32-40.[13] CACHON G P. The allocation of inventory risk in a supply chain: push, pull and advanced purchase discount contracts [J]. Management Science, 2004, 50(2): 222-238. [14] 徐冰, 刘蕾.提前支付条件下供应商最优提前支付折扣策略及提前支付实施条件[C]//成都: International Conference on Engineering and Business Management, 2010: 4353-4355. [15] 徐耀群，张松峰.信息不对称下供应链信息共享激励研究[J].哈尔滨商业大学学报：自然科学版，2014，30(2)：229-233.。

易腐商品最优订货批量与定价及其粒子群优化解

2005年3月系统工程理论与实践第3期文章编号：1000-6788(2005)03-0046-06易腐商品最优订货批量与定价及其粒子群优化解田志友，蒋录全，吴瑞明（上海交通大学管理学院，上海 200030）摘要：对易腐商品的订货批量与定价问题进行了研究.基于一种负二项分布的离散需求函数，推导了易腐品利润最大化模型.由于模型中涉及多个随机变量的概率分布，常规函数极值法对此具有极大局限性，故首次将粒子群优化算法引入该领域，并提出两种不同的求解思路：1)枚举法.利用粒子群算法依次计算不同订货批量下的最大化利润，然后根据边际分析法确定最优订货批量及相应定价；2)二维寻优法.将利润视为订货量与定价的二维函数，利用粒子群算法对其进行二维演化寻优.算例分析表明：两种方法均可有效获得问题的满意解，当订货量波动范围较小时，枚举法效果更优.关键词：易腐商品；订货批量；定价；需求分布；粒子群优化算法中图分类号：F830 文献标识码：AOptimal Order Quantity and Pricing for Perishable Commodities and Solutions with Particle Swarm OptimizationTIAN Zhi-you, JIANG Lu-quan, WU Rui-ming(School of Management, Shanghai Jiaotong University, Shanghai 200030, China)Abstract: The problem of ordering policies and optimal pricing for perishable commodities ismainly studied. According to a kind of demand distribution, which can be represented as a negativebinomial distribution, the profit maximization model of those products is deduced. Since themodel involves several different stochastic distributions, which are difficult for the normalfunction optimization methods to solve, the particle swarm optimization (PSO) algorithm isintroduced for the first time to settle it, and two different solving processes are proposed,one can be called enumerative method, which will calculate the optimal price and maximum profitfor each possible orders, and then find the ultimate optimal solution by marginal analysis. Theother is two-dimensional search, which can determine the optimal order quantity and pricesimultaneously with PSO technique. At the end a numerical example is studied and the two methodsare compared, the results indicate that: both can obtain satisfactory solutions effectively,and when the bounds for possible orders are relatively small, the first is preferred.Key words: perishable commodities； order quantity; pricing；demand distribution; particleswarm optimization1 引言易腐商品是指那些必须在有限时间内售出，否则将发生质变，必须清仓处理的商品.狭义的易腐商品主要是指生鲜食品，广义来说，凡是超过正常销售期后市场价值有明显降低的商品均可归属易腐品的类别，如时装服饰，电子消费品，客房,机票等服务.由于这些商品保质期或市场需求周期比较短，或具收稿日期：2004-04-26资助项目：国家自然科学基金（70371075）作者简介：田志友(1974—)，男，河北石家庄人，博士研究生，主要研究方向：指数化评价，系统复杂性, Email: totzy@第3期易腐商品最优订货批量与定价及其粒子群优化解 47 有较高的保存成本，持续时间越长则利润损失越大，因此，销售者需要在销售期初，综合考虑市场需求的波动、顾客的消费偏好，以及此类商品的销售期长短，制定合理的采购批量和售价，以确保实现其利润最大化目的.关于随机需求条件下易腐商品的订货量与定价问题，文献[1-4]给出了较为详尽的评述和一些共性结论，如：不同时段内顾客的到达服从不同质的随机分布，一般设为泊松分布；在同一时段内，顾客的感知价值是相互独立的，并服从某种同质概率分布；这种感知价值将随时间延续而不断降低，并且不同时段内的需求分布有可能发生质变.在满足上述假设条件下，通过经验数据可以获得销售期内的期望需求，进而可以在利润最大化原则下制定出相应的最优定价和最优订货批量.由于在订货与定价过程中，顾客的到达、对商品价值的感知等均具有不同形式的概率分布，往往导致有效需求的分布形式比较复杂，常规函数极值算法不易获得问题的解析解.本文将在文献[4]研究基础上，重点针对单一时段条件下最优订货批量与定价问题，推导易腐商品的利润最大化模型，并首次将粒子群优化算法引入该模型的求解过程，提出了两种不同的求解思路，以便互相印证，有效地获得单阶段最优订货批量与最优定价.2 建模2.1变量定义在对易腐商品最优订货批量与定价问题研究中，所涉及的若干变量及其含义如下：s ——易腐商品的订货量；t——正常销售期；ω——正常销售期内单位商品的定价；φ——超过正常销售期后的单位商品处理价；c——单位商品的综合成本(包括存储、运输、采购、处理等费用)；πs (ω)——订货量为s ，定价为ω时销售者的期望收入；R s (ω)——订货量为s ，定价为ω时销售者的期望利润，R s (ω)= πs (ω)-sc ；n——正常销售期内到访顾客的总人次，∞=,,2,1,0"n ;m——正常销售期内，定价为ω时的商品需求；P ω(m )——正常销售期内，定价为ω时，商品需求为m 的概率分布.2.2 需求分布与常见商品的需求分布相似，易腐商品的需求函数也应该满足如下两个条件.1) 需求与价格呈反方向变动，即00()(), 0,1,...,; 0k km m P m P m k ωω+∆==≤=∞∆>∑∑.2) 当价格趋向于无穷时，期望需求趋向于0，即lim (|)0E m ωωω→∞=，其中，(|)E m ω表示定价为ω时的期望需求.此外，影响易腐商品需求量的主要因素还包括：销售期t 内的到访顾客人数n ，以及所有到访顾客中可能会发生购买行为的人数m 等.关于顾客的到达，常见研究中均假设销售期t 内到访顾客的总人次n 属于系统外生变量，与定价无关，并服从参数为λ的泊松分布[3]，即：()(|), 0,1,2,...,!n tt e P n n n λλλ−==∞ (1) 考虑到不同时段内顾客到达率λ具有较大波动性，可假设λ服从参数为(α, β)的gamma 分布，即：(1)/1(), 0()g e αλβαλλλαβ−−=≤<∞Γ (2) 之所以选择gamma 分布，是因为到达率λ是一个非负取值的随机变量，并且，当参数α或β取某固定值时，原来的gamma 分布将相应地转化为2χ分布或指数分布.因此，选择gamma 分布可以涵盖较多的λ的变动情况[4].在所有到访顾客中，只有那些对商品的感知价值超过定价的顾客才会发生购买行为.设第i 位到访顾48 系统工程理论与实践 2005年3月客的感知价值为X i ，0≤X i <∞，根据Gallego 等人的研究[3]，可以认为所有到访顾客的感知价值(X 1, X 2, …, X n )均为独立同分布的连续随机变量，概率密度设为f (x ).当定价为ω时，顾客感知价值的累积分布函数为F (ω)，并且满足：0()1 ; lim ()1F F ωωω→∞≤≤=.我们可以把销售期t 内的商品需求m 定义为：到达并愿意以当前定价购买一单位商品的潜在人次，即所有感知价值X i ≥ω的顾客人数.则潜在需求m 可以表示为一个服从二项分布的随机变量，分布概率为：()(|)[1()][()] , 0,1,2,...,.n m n m m P m n C F F m n ωωω−=×−×= (3)根据公式(1)-(3)，销售期t 内潜在需求m 的最终概率分布可以表示如下：001()(|)(|)()[1()]1 , 0,1,...,; 0,1,,;1[1()]1[1()]n m m m P m P m n P n g d t F C n m t F t F ωωλααλλλβωβωβω∞∞==+−=⎡⎤⎡⎤−=××=∞=∞⎢⎥⎢⎥+−+−⎣⎦⎣⎦∑∫" (4)可以看出，最终所得销售期内的需求m 服从一种负二项分布，其期望值为：()(1())E m t F w αβ=−.2.3 利润最大化模型当期初订货量为s 时，如果销售期t 内的潜在需求m ≥s ，则销售收入πs (ω)=s ω；如果m <s ，意味着部分商品将在销售期过后按处理价φ进行低价清仓，则此时的销售收入为：πs (ω)=m ω+(s -m )φ.综合两种情况，可得s 单位易腐商品在定价为ω时的期望收入为：10110010()()[()]() ()[()()()] ()()()s s m s m s s m m s m s P m m s m P m s s P m m P m s P m m P m s s m P m ωωωωωωωπωωωϕωωωϕϕωωϕ∞−==−−==−==++−=−++−=−−−∑∑∑∑∑ (5) 对应的销售利润为：1(1)0[1()]1()()()()()1[1()]1[1()]m s m s s m m t F R sc s c s m C t F t F ααβωωπωωωϕβωβω−+−=⎧⎫⎡⎤⎡⎤−⎪⎪=−=−−−−×⎨⎬⎢⎥⎢⎥+−+−⎣⎦⎣⎦⎪⎪⎩⎭∑ (6) 则最优订货量s *和最优定价ω*就是如下最大化模型的解：10max ()()()()().. >; 0;s s m R s c s m P m s t s ωωωωϕωϕ−==−−−−>∑ (7)由于潜在需求m 和顾客达到人次n 均为离散取值随机变量，顾客对商品的感知价值则为连续分布随机变量，如采用求偏导数等常规函数极值法，将很难获得问题的解析解.下面我们选用粒子群优化算法，对模型(7)进行演化求解.3 粒子群优化求解粒子群优化算法(Particle Swarm Optimization, PSO )是一种较新的全局优化方法，最早由Eberhart和Kennedy 博士于1995年提出[5].与遗传算法相比，粒子群算法没有交叉、变异等遗传操作，可调参数少，具有结构简单、运行速度快等特点，尤其适用于实数编码问题的求解.将其引入易腐商品最优订货批量与定价的求解过程，有利于快速有效地获得满意解.3.1 算法描述在粒子群算法中，待优化问题的每个潜在解均称为搜索空间中的一个粒子，每个粒子都用位置向量和速度向量来表示.其中，位置代表参数取值，速度表示各参数改进的方向和步长.算法首先通过随机初第3期易腐商品最优订货批量与定价及其粒子群优化解 49 始化产生一群粒子，然后进行叠代寻优.在每一演化代中，粒子通过跟踪两个极值来不断更新自己：一个是粒子本身所找到的最优解，称为个体极值pBest ，另一个是整个种群目前为止所找到的最优解，称为全局极值gBest .然后根据下列公式来不断更新速度与位置：1()(Pr )2()(Pr )V w V c rand pBest esent c rand gBest esent =×+××−+××− (8) Pr Pr esent esent V =+ (9) 其中，V 是粒子速度，Present 是粒子当前位置，rand ()表示是(0, 1) 之间的随机数，c 1和c 2 被称作学习因子，通常，c 1 = c 2 = 2. w 表示加权系数，一般取值在0.1到0.9之间.叠代过程中，算法将根据粒子的适应度值不断更新pBest 与gBest 的取值，粒子在不断向全局最优转移的同时也不断向个体最优靠拢.当满足既定的终止规则，如达到预定演化代数、出现满足要求的满意解，或全局极值的改进步长小于指定阈值时，搜索过程结束，最后得到的gBest 就是最终的满意解[6].3.2 求解在利用粒子群算法求解模型(7)时，可以有两种不同的解题思路, 分别命名为枚举法和二维寻优法.3.2.1枚举法根据边际分析法，当边际收益不小于边际成本时，即：**11()()s s s s c πωπω−−−≥时，多订购一单位商品将增加销售商的净利润.因此，可以把利润视为价格ω的一元连续函数，利用粒子群算法依次计算不同订货量情况下所对应的最优定价与最大化利润，并将满足上述不等式的最大订货批量s *及其对应的定价*s ω作为最终解.设订货量的波动范围是：[s l , s u ]，求解流程描述如下.1) 令s =s l ;2) 利用粒子群算法求解一元连续函数10()()()()s s m R s s m P m ωωωωϕ−==−−−∑的最优订价*s ω与最大化利润*()s sR ω; 3) 判断：如果s<s u ，令s =s +1，转入步骤2)，否则继续;4) 令**()()s s s s R sc πωω=+，**11()()s s s s πωπω−−∆=−，然后确定满足c ∆≥的最大订货量s *及对应的*s ω; 5) 输出最终结果：[s *, *sω, *()s s πω, *()s s R ω]. 二维寻优法将利润R s (ω)视为订货量s 和定价ω的二元函数，利用粒子群算法在二维解空间进行演化寻优，从而同时确定最优订货量s *及最优定价ω*.求解过程如下：1) 个体解编码.每个粒子编码方式如下：p=[s, ω, v s , v ω, f ].其中，v s 和v ω,分别为s 和ω的运动速度，f 为该粒子的适应度值，即当订货量为s 、价格为ω时的销售利润;2) 粒子群初始化.设种群规模为popsize ，在订货量s 和价格ω的波动范围内随机取值popsize 组，作为初始种群，并随机初始化粒子的速度;3) 根据公式(6)，计算粒子的目标函数值;4) 根据公式(8)和(9)，更新粒子运动速度和所在位置;5) 更新当前演化代中的个体极值和全局极值;6) 检验终止规则.当满足指定规则时输出最终结果.否则，转入步骤3);7) 输出最优结果.最后一代种群中的gBest 即为满足利润最大化条件的最优解.4 算例分析设某种易腐商品的销售期t =1，单位成本c =6，超过正常销售期后的处理价φ=5.根据以往销售数据，销售期内顾客的到达率λ服从gamma 分布，参数为：α=3，β=2；顾客的感知价值X i 服从正态分布，分布参数为：µ=10，σ=1.则当订货量为s 、价格为ω时，利润函数为：10()(6)(5)()()s s m R s s m P m ωωωω−==−−−−∑ (10)50 系统工程理论与实践 2005年3月首先利用枚举法求解最优订货量与定价.算法参数设定如下：种群规模popsize=100；学习因子c1=c2=2；加权系数取固定值w=0.2.根据销售经验，设订货量s取值范围为[1，20]，售价ω取值范围为[c, 2c]，即[6, 12]；s和ω的速度取值范围分别为[0, 0.3]和[0，0.1]；算法终止规则为：当全局最优解改善程度小于0.01时终止运行.枚举法所得结果见表1.表 1 不同订货量情况下所对应的最优定价及最大化利润订货量s 1 2 3 4 5 6 7 8 9 10最优定价ω10.08 9.803 9.6039.4529.3359.2449.1719.114 9.069 9.033最大化利润R 3.38 5.877 7.6938.9449.72310.10910.1759.986 9.595 9.048订货量s11 12 13 14 15 16 17 18 19 20最优定价ω9.005 8.982 8.9658.9528.9418.9338.9278.923 8.92 8.917最大化利润R8.382 7.625 6.801 5.927 5.017 4.08 3.125 2.156 1.178 0.193从表1可以看出，当需求分布已知时，最大化利润将随订货量s增加而呈现先增后减趋势，而边际收益则持续下降.当边际收益等于边际成本时，所对应的最优订货量为7，最优定价为9.171，最大化利润为10.175.从图1中也可看出各变量的变动趋势.在二维寻优过程中，随着种群规模的增加，算法将逐渐收敛于全局最优，即订货批量为7，定价为9.17，这与枚举法所得结论是一致的.通过对算例的求解可以看出：枚举法的实质是在订货量s既定情况下，将利润视为价格ω的一元连续函数，利用粒子群算法进行一维优化，从而得到不同订货量下的最大利润与最优定价，然后根据边际分析，确定最优订货批量与定价.其特点是：准确度高，但效率较低，主要适用于订货量s波动范围较小的情况.二维寻优法的实质是将利润视为订货量和定价的二维函数，利用粒子群算法同时在s和ω所构成的二维解空间内寻找全局最优解,这种方法的特点是运行速度快，但容易停留在局部最优.因此，在实际操作中，建议同时采用两种方法，分别计算最优解，并互相印证，以便帮助销售者制定更为合理的采购与定价决策.5 结论1)在易腐商品订货量与定价研究中，最为关键的是准确估计销售期内的需求分布，而影响需求的主要因素包括：商品定价，顾客的到达情况，以及顾客对商品的感知价值.2)当其他参数不变时，对粒子群算法演化结果影响最大的参数就是种群规模.这是因为：粒子群算法是一种有导向的概率寻优方法，其探索未知空间的主要方式是通过跟踪全局极值和个体极值来实现的，增加种群规模有利于尽快发现全局最优.3)本文将整个销售期t视为一个完整阶段，并重点解决了最优订货批量与最优定价问题.由于顾客对易腐商品的感知价值将随时间的延续而不断缩减，不同时段内的需求分布有可能发生质变，而销售者也可以根据需求的波动、剩余库存量的多少等动态调整定价，以实现利润最大化目的.因此，对不同时段内、不同质需求条件下的最优定价与最优订货批量等问题，都还需要进一步的详细研究.第3期易腐商品最优订货批量与定价及其粒子群优化解 51[1] Weatherford L R, Bodily S E. 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(In Chinese)﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡﹡ (上接第6页)[7] Engle R F, Manganelli S. CAViaR: Conditional autoregressive value at risk by regression quantiles[R]. NBER,Working Paper 7341, 1999.[8] Hamilton J D. Time Series Analysis[M].Princeton University Press, New Jersey,1994.[9] Hans F and Alexander S. Stochastic Finance, An Introduction in Discrete Time[M].Walter de Gruyter,2002.[10]Hansen B E.Testing for parameter instability in linear models[J]. Journal of PolicyModeling,1992,14(4):517-533.[11] Inclan C and Tiao G C. Use of cumulative sums of squares for retrospective detection of changes ofvariances[J]. J. Amer. Statist. Assoc,1994, 89(3):913-923.[12] Jorion P. Value at Risk: The New Benchmark for Controlling Market Risk[M].Chicago: Irwin ProfessionalPublishing,1997.[13] Morgan J P. Risk Metrics Monitor[M]. 2nd Quarter,1996.[14] Koenker R, Bassett J. Regression quantiles[J]. Econometrica,1978,46(1):33-50.[15] Manganelli S, Engle R F. Value at risk models in finance[R]. working paper(75), European Central Bank,2001.[16] Schwert G W. Why does stock market volatility change over time?[J]. Journal of Finance,1988,XLIV(5):1115-1153.[17] Taylor S. Modeling Financial Time Series[M]. John Wiley and Sons, London, 1986.。

维京救生筏技术信息救生筏和容器说明书

EDITION 2 / 2015 VIKING LiferaftsT echnical InformationVIKING LIFE-SAVING EQUIPMENT- Protecting people and businessLiferafts and containers VIKING liferafts are found all over the globe - from the arctic to the tropicsA full range of throw-overboard and davit-launched liferaftsVIKING’s liferafts are available in a standard version and a top of the line automatically self-righting version. The proven self-righting liferafts ensure that no matter how the liferaft lands in the water it will always inflate rightside up,ready for boarding.Liferafts can be equipped with a hydrostatic release unit to ensure that it inflates automatically if it has not been released manually.Liferafts are subjected to rough sea trials, wind velocity tests at forces of 30 metres per second and deployment at extremely low temperatures. Self-righting liferafts are also tested for automatic self-righting capabilities.Ready for installationLiferafts can be delivered with optional galvanized deck cradles and lashings. A full set can be delivered with the liferaft mounted in the cradle including the hydrostatic release unit ready to be installed on the vessel. We also offer assistance with installation tests for davit-launched liferafts. Contact your local VIKING office for more information.Standard features- Equipped with emergency packs and liferaft equipment according to SOLAS and flagrequirements.- Provided with two individual buoyancycompartments. Even if one compartment is damaged, the other still has sufficient buoyancy to carry thespecified number of passengers.- Stored in a rigid fibre glass container for durability.- Installed onboard either on cradles, racks, or stacked column racksby VIKINGContainers by VIKINGDurable and easy to handle VIKING containers aredesigned with several unique features. The specialVIKING shell overlap design gives a secure watertightfit to protect against the elements.Unlike many other containers, our rim makes a solideasy grip for faster and easier handling - even in wetand slippery conditions. The overlap design is easier toopen and re-seal during servicing.We manufacture our own containers and build them tolast. Ongoing reseach and development for 50 yearsensures that the containers that we use today areamong the best on the market. The ribbed designadds extra stability to the sturdy fibre glass, makingour containers approved to withstand a drop of up to36 metres, some are even approved for heights of 55metres.Quality makes a difference.Throw-overboard liferafts, self-rightingThrow-overboard liferafts are stored incontainers on deck and inflate in thewater when the painter line is pulled.25 DKS, Self-righting liferaft25 & 39 DKS, A & B Pack, Self-righting liferaft50 DKS, Self-righting liferaft50 DKS, A & B Pack, Self-righting liferaftLiferaftContainer40804057340T O W N G L N E258040551 PERSONS51 PERSONS51P E R S O N SCApprox. size of container in mmApprox. weight kgA PACK ABCD A Pack B Pack 50 DKS 1865860910-393-B PACK A B C D A Pack B Pack50 DKS1550890929--285BA25 & 39 DKS, A & B Pack, Self-righting liferaft BA CApprox. size of container in mmApprox. weight kgAB C D A Pack B Pack 25 DKS 1420760795-215155*39 DKS1550890920290* Can be mounted on a standard deck cradle as the weight is below 185 kg.9100 DKR, Open reversible liferaft (IBA)100 DKR, Open reversible liferaft (IBA)50 DKR, Open reversible liferaft (IBA)50 DKR, Open reversible liferaft (IBA)ABC66404256640+/386425 DKR, Open reversible liferaft (IBA)25 DKR, Open reversible liferaft (IBA)LiferaftContainerApprox. size of container in mmApprox. weight kgAB C D Pack type HSC100 DKR1550890920-330Approx. size of container in mmApprox. weight kgAB C D Pack type HSC50 DKR1385735790-179*Approx. size of container in mmApprox. weight kgAB C D Pack type HSC25 DKR1355565650-93*CBA CA B* Can be mounted on a standard deck cradle as the weight is below 185 kg.11Storage racksFlexible storage and easy handling Array witha minimal crewVIKING has developed a range of liferaft racks as aflexible storage alternative to traditional cradles.Our racks are constructed for flexible integration withmodern ship design, increasing the number of possibleinstallation locations. Optional remote release systemsalso allow liferaft containers to be stored in otherwiseinaccessible locations. Racks can be operated by a singlecrew member for a faster and more effective launch,as liferafts in racks do not need to be lifted.Racks are available in galvanised stainless steel oraluminium. Custom-made racks can also be suppliedupon request.Column rack for liferaft containersApprox. size of rack systemAB C D Pack type 16 DK 13559251970800 A + B 20 DK 13559251970800 A + B 25 DK13859251970800A + BGRP RackApprox. size of rack systemAB C D Pack type25 DKFS 14648401888690A 25 DKFS 14208401774690B 35 DKF 15509402000720A 35 DKF 14648401888690B 39 DKFS 15509402000720A 39 DKFS14648401888690BLiferaft serviceThe unique VIKING global servicing network of liferaft specialists perform customer convenient liferaft servicing according to strict guidelines.Documentationn Liferaft is received and registeredn Logbook in the liferaft is completed (proof that the liferaft has been opened and tested)n Inspection is performed using VIKING approved inspection checklistn Certificate of re-inspection is issuedn Full documentation for service is archived according to regulations n Detailed invoice is issuedServicen Container is opened and the inflation system dismountedn Liferaft is removed from the container n Container shell is cleaned and fibreglass is repaired if needed n Container is relabelledn Liferaft is inspected inside and outn Emergency pack is checked and items replaced if expired according to regulationsn Liferaft equipment is inspected and replaced if neededn Cylinder operating head, valve, knife and release wire is inspectedn Inflation systems and high pressure hoses are inspectedn CO 2 cylinder is checked for correct content level n Liferaft is deflated, repacked in the container and prepared for despatchTestingn Liferaft is inflated with compressed air and pressure tested including a 60 min. working pressure test of the lower buoyancy chamber, upper buoyancy chamber and arch chamber n If the liferaft is equipped with an inflatable floor, this is pressure tested for 60 min.Liferaft is subjected to specific tests at various intervals according to international regulations.n Gas inflation stress test (GI) is conducted every 5 years using the liferaft’s own CO2 cylinder to inflate the liferaftn Necessary additional pressure test (NAP) at double the working pressure rate is conducted at 11 years end then annually thereaftern Floor seam test (FS) is performed to check the seams of the internal floor and is conducted at 10 years and then annuallyADCB See our full range of liferafts on 13Dedicated global productionVIKING products are manufactured using a combination of modern technology and skilled manual labour.VIKING has an award winning workplace. Our commitment to quality and safety and our loyal and experienced employees mean that our working atmosphere is quite exceptional.VIKING practices integrated production with joint global planning. Special competences are concentrated at individual production units.All our production facilities follow uniform guidelines and have identical systems and procedures. VIKING Life-Saving Equipment is certified according to ISO 9001 standards and is regularly evaluated by the Norwegian Veritas for compliance. All of our products and components are subject to prototype testing and quality control procedures. VIKING is registered in the Achilles Joint Supplier Qualification System.Global serviceAn important considerationwhen investing in marine safety equipment is servicing in the long term.VIKING is a global all-in-one service provider offering consolidated servicing of safety equipment on board.n Liferafts and evacuation systemsn Boats, davits and release hooksn Marine fire safety equipmentn Immersion suits and lifejacketsWe offer total concept service packages including competitive global pricing, handling specifications and service certificates.Our unique network of 270 certified servicing stations follows strict guidelines for servicing VIKING’s products.The network is supported by certified educational programmes, spare parts supplies and continually updated online information and manuals.Certified servicing stations have the appropriate tools and spare parts available as turnaround time is important to our customers. Service can be booked by contacting any of our offices in our global network.Contact your local office for the nearest VIKING servicing station or visit .Global logisticsOur logistics network acts as one global unit with specialised systems for handling and tracking stock and delivery.VIKING’s logistics specialists have the necessary certifications for optimising handling of products covered by the Dangerous Goods Act, such as lifejackets and liferafts. We are experienced in customising logistics for customers with centralised stock or several delivery points.VIKING has worldwide stock facilities for selected products that are geared to carry the appropriate stock for each market to ensure that our customers benefit from optimaldelivery and pricing at appropriate locations.15VIKING LIFE-SAVING EQUIPMENT Brasil LTDA Av. Rio Branco 45 – 19th floor 20090-003 Centro Rio de Janeiro BrazilTel: +5521 2516 5005e-mail: viking-br@VIKING LIFE-SAVING EQUIPMENT China Building 3, 1456 Xin Tanwa Highway Pudong District 201321 Shanghai PR ChinaTel: +86 21 6289 9922Fax: +86 21 5815 6010e-mail: viking-ch@VIKING LIFE-SAVING EQUIPMENT Estonia AS Helgi tee 3,Peetri alevik, Rae vald, 75312 Harjumaa.EstoniaTel: +372 606 93 93Fax: +372 606 93 99e-mail: viking-ee@VIKING LIFE-SAVING EQUIPMENT Oy, Finland Pääskykalliontie 13F-21420 Lieto FinlandTel: +358-(0)2-489 500Fax:: +358-(0)2 489 5011e-mail: viking-fi@VIKING LIFE-SAVING EQUIPMENT France S.a.r.l.41, Rue Michel Ange 91026 Evry Cedex FranceTel: +33 (0) 160 87 09 00 Fax: +33 (0) 160 87 09 01e-mail: viking-f@ VIKING LIFE-SAVING EQUIPMENT A/S Moorfleeter Strasse 27D-22113 Hamburg GermanyTel: +49-(0) 40 670 10 25 Fax: +49-(0) 40 670 10 67e-mail: viking-d@VIKING LIFE-SAVING EQUIPMENT Hong Kong Ltd.G/F , Chiap Luen Industrial Building,30-32, Kung Yip StreetKwai Chung, New Territories Hong KongTel: +852 2429 7878Fax: +852 2423 6228e-mail: viking-hk@VIKING LIFE-SAVING EQUIPMENT Ltd. Aberdeen Unit 19, Ocean Trade Centre Minto Avenue, Altens AB12 3JZ, Aberdeen Great BritainTel: +44 (0) 1224 898969Fax: +44 (0) 1224 894565e-mail: vikingabz@ VIKING LIFE-SAVING EQUIPMENT Ltd . Gt YarmouthSouth Denes RoadGt Yarmouth, Norfolk – NR30 3 PJ Great BritainTel: +44 (0) 1493 850250Fax: +44 (0) 1493 851222e-mail: vikingldn@VIKING LIFE-SAVING EQUIPMENT Ltd. Liverpool Unit 31, Wellington Employment Park Dunes WayL5 9RJ Liverpool Great BritainTel: +44 (0) 151 207 3030Fax: +44 (0) 151 207 3807e-mail: vikingliv@VIKING LIFE-SAVING EQUIPMENT Ltd. Southampton Hamble Court, Hamble LaneSO31 4QL Southampton, Hampshire Great BritainTel: +44 (0) 2380 454184Fax: +44 (0) 2380 454284e-mail: vikingsth@VIKING LIFE-SAVING EQUIPMENT Iceland ehf.Ishella 7IS-221 Hafnarfjörður IcelandTel.: +354-544-2270Fax: +354-544-2271e-mail: viking-is@VIKING LIFE-SAVING EQUIPMENT Pte LTD 67, Krishna Bhuvan, No. 4, 1st Floor,Nehru Road, Near Shiv Sagar Hotel,Vileparle (E), Mumbai - 400 057Maharashtra, India Mobile: +91-22-2618 6233VIKING LIFE-SAVING EQUIPMENT Italia s.r.l.Via Delle Pianazze, 17019136 – La Spezia ItalyTel: +39 () 187-981322Fax: +39 0 187-982499e-mail: pedrotti@ VIKING LIFE-SAVING EQUIPMENT B.V .P .O. Box 2663330 AG Zwijndrecht The NetherlandsTel: +31 (0) 88 008 05 00 Fax: +31 (0) 88 008 05 95e-mail: viking-nl@VIKING LIFE-SAVING EQUIPMENT Norway AS IdrettsveienStraume NæringsparkNO-5353 Straume (Bergen)NorwayTel: +47-815-00- 325Fax: +47-56-32 61 10e-mail: bergen@VIKING LIFE-SAVING EQUIPMENT Norway AS Oluf Onsumsvei 11N-0680 Oslo NorwayTel: +47-815-00- 325Fax: +47-22-68 84 80e-mail: viking-n@VIKING LIFE-SAVING EQUIPMENT ISTANBUL DENIZCILIK TICARET ASAydinli mah., Istanbul Anadolu Yakasi OSB.4. Sokak. No 12TR 34953 Tuzla-Istanbul TurkeyTel: +90 216 593 31 79 Fax: +90 216 593 31 78e-mail: vikingistanbul@VIKING LIFE-SAVING EQUIPMENT Russia Promzona Gorelovo, Quarter 2Volkhonskoe Shosse, Bldg. 2B, korp. 15Lomonosovskiy Rajon188508 Leningrad oblast, RussiaTel.: +7 812 493 59 24 Fax: +7 812 493 59 22e-mail: viking-ru@VIKING LIFE-SAVING EQUIPMENT Pte LTDPlot no. W-9, T.T.C. Industrial Area, Thane-Belapur Road, Pawane Village , MIDC, District: Thane-400613507601 Singapore SingaporeTel: +65 64249200Fax: +65 64249210e-mail: viking-sg@VIKING LIFE-SAVING EQUIPMENT (SA) (Pty) Ltd C/o Neptune & Carlisle Street Paarden Eiland 7420, P .O. Box 2577420 Parden Eiland, Cape Town South AfricaTel: +27 21 514 5160 / +27 21 514 5178Fax: +27 (0)86 403 4211e-mail: viking-sa@VIKING LIFE-SAVING EQUIPMENT (SA) (Pty) Ltd Units No.2 Seebrook Park 210 Chamberlain Road 4026 Jacobs, Durban South AfricaTel: +27 31 4681261 Fax: +27 31 4681251e-mail: vikingdbn@VIKING LIFE-SAVING EQUIPMENT Iberica S.A.Camino Rasposeira, 34 – Nave 236214 Vigo SpainTel: +34-98-6421445Fax: +34-98-6419286e-mail: viking-e@VIKING LIFE-SAVING EQUIPMENT Sweden AB Strömfallsvägen 53135 49 Tyresö, Stockholm SwedenTel: +46 (0)8 7700170Fax: +46 (0)8 7700183e-mail: viking-se@VIKING LIFE-SAVING EQUIPMENT (Middle East)Al Jadaf Shipdocking Yard P .O. Box 13448DubaiUAE (United Arab Emirates)Tel: +971-4-324 3555Fax: +971-4-324 3444e-mail: viking-uae@VIKING LIFE-SAVING EQUIPMENT (America), Inc.1400 NW 159St., Suite 10133169 Florida, Miami U.S.A.Tel: +1 (305) 614-5800Fax: +1 (305) 614-5810e-mail: usasales@VIKING LIFE-SAVING EQUIPMENT PRODUCTION BG LTD .BG4202195-198 Vtora Str., Radinovo BulgariaVIKING global networkTel: +45 76 11 81 00Fax: +45 76 11 81 01e-mail: VIKING@ (Headquarters)Saedding Ringvej 136710 Esbjerg V DenmarkVIKING LIFE-SAVING EQUIPMENT A/S1022544 - 08.15 - P r i n t e d i n D e n m a r kVIKING (Headquarters): Saedding Ringvej 13 . DK-6710 Esbjerg V . Denmark Tel +45 76 11 81 00 .Email:*********************. VIKING LIFE-SAVING EQUIPMENTDeciding on marine safety equipment and servicing plans is no easy task. That’s why it’s best to talk to someone who has every piece of the puzzle.Today, VIKING offers the widest choice of fixed price safety solutions and product packages on the market.We already manage 1000 flexible safety servicing agreements for shipowners with some of the largest fleets in the world.To find out more, contact your local VIKING branch office or Corporate Sales Manager Helene Andersen attel.+*******************************.Put our know-how to work for your businessVIKING solves the global safety servicing puzzle。

旅游包车企业准入条件

旅游包车企业准入条件英文回答：Licensing Requirements for Private Hire Vehicle Companies.1. Legal Entity and Financial Stability.Be a legally registered company in the jurisdiction of operation.Have a sound financial standing, with sufficient capital and insurance coverage to meet operating expenses and potential liabilities.2. Vehicles and Drivers.Maintain a fleet of vehicles that meet safety and regulatory standards.Implement a comprehensive driver screening process to ensure the safety and reliability of drivers.Conduct regular vehicle inspections and maintenance to ensure optimal performance.3. Technology and Dispatch.Utilize a robust technology platform for seamless trip booking, tracking, and communication.Establish a reliable dispatch system to manage bookings and dispatch drivers efficiently.Ensure data security and compliance with relevant regulations.4. Customer Service and Support.Provide excellent customer service through multiple channels (e.g., phone, email, mobile app).Establish a clear process for handling complaints and resolving disputes.Seek and respond to customer feedback to improve service quality.5. Pricing and Payment.Set transparent and competitive pricing for services.Offer various payment options to cater to customer preferences.Maintain clear policies for cancellations, refunds, and disputes.6. Compliance and Regulations.Comply with all applicable laws and regulations, including traffic regulations, licensing requirements, and data protection.Obtain necessary permits and licenses from relevant authorities.Regularly review and update policies and procedures to ensure compliance.7. Sustainability and Social Responsibility.Embrace sustainability practices, such as using eco-friendly vehicles and promoting energy-efficient operations.Promote ethical and responsible business practices, including driver safety, fair wages, and community engagement.8. Quality Assurance and Improvement.Establish a quality assurance program to monitorservice delivery and identify areas for improvement.Seek industry certifications and accreditations to demonstrate commitment to excellence.Regularly evaluate and enhance processes and procedures to maintain high standards.中文回答：旅游包车企业准入条件。

英语版营销策划方案怎么写

英语版营销策划方案怎么写Executive Summary:Our marketing plan proposal aims to outline a comprehensive strategy to promote and grow our brand in the market. With careful analysis and research, we have identified key target segments and developed creative initiatives to engage customers and drive sales. This proposal covers various aspects of marketing, including product positioning, target market analysis, competitive analysis, pricing strategies, promotion tactics, and distribution channels. Our goal is to increase brand awareness, customer loyalty, and market share while achieving a sustainable competitive advantage.1. Introduction:Provide an overview of the company, its products/services, mission, and vision. Explain the purpose of the marketing plan proposal and outline its structure.2. Situation Analysis:a. Internal Analysis:Analyze the company's strengths, weaknesses, and resources. Identify competitive advantages, such as unique products, strong brand reputation, or advanced technology. b. External Analysis:Analyze the external environment, including market size, trends, and customer behavior. Study competitors, their strengths and weaknesses, and the overall competitive landscape.3. SWOT Analysis:Present a comprehensive analysis of the strengths, weaknesses, opportunities, and threats facing the company. Use this analysis to identify strategic areas for growth and improvement.4. Objectives:Set clear marketing objectives that are specific, measurable, achievable, realistic, and time-bound. For example, increase sales by 20% in the next fiscal year or gain 10% market share within six months.5. Target Market Analysis:Identify and understand the target market segments that offer the greatest potential for growth. Consider demographics, psychographics, purchasing behavior, and preferences. This analysis will help tailor marketing efforts to effectively reach and engage these segments.6. Positioning Strategy:Develop a unique value proposition and positioning strategy that highlights the company's competitive advantage and differentiation. This strategy should resonate with the target market and communicate the brand's core values and benefits.7. Competitive Analysis:Analyze key competitors, their products, pricing strategies, distribution channels, and promotional efforts. Identify gaps in the market and areas where the company can gain a competitive edge.8. Pricing Strategy:Determine an optimal pricing strategy based on consumer insights, production costs, and competitor pricing. Consider factors such as perceived value, market demand, and price elasticity.9. Promotion Tactics:Develop a comprehensive promotional plan to build brand awareness, generate leads, and drive sales. Consider a mix of traditional and digital channels, such as advertising, public relations, social media, influencer partnerships, events, and content marketing.10. Distribution Channels:Evaluate existing distribution channels and identify opportunities to expand or optimize them. Consider direct sales, retail partnerships, e-commerce, or other channel options based on market dynamics and target audience preferences.11. Budget and Metrics:Allocate a budget for each marketing activity and establish key performance indicators (KPIs) to measure success. Monitor and track performance regularly, making adjustments as needed to achieve objectives.12. Implementation Timeline:Create a detailed timeline that outlines the execution of marketing activities, including deadlines, responsibilities, and dependencies. Ensure alignment with other departments, such as sales and product development.13. Evaluation and Control:Establish a framework for evaluating marketing performance and controlling expenses. Regularly review and analyze results against objectives, metrics, and competitors. Use this insight to refine strategies and tactics for continuous improvement.14. Conclusion:Summarize the key points of the marketing plan proposal, emphasizing its potential impact on brand growth, market share, and customer satisfaction. Reiterate the importance of a comprehensive marketing strategy in achieving the company's overall objectives.Appendix:Include relevant supporting documents, such as market research reports, competitor analysis, financial statements, and marketing materials.Note: The word count provided exceeds 6000 words. Please review, refine, or adjust the content as needed to fit your requirements.。

Risk, Financing and the Optimal Number of Suppliers

According to the data presented by Rajan and Zingales (1995), in 1991 Accounts payable and creditors constituted 15% ,while Debt in current liabilities only 7.4%, of the total book value for an average non-ﬁnanecent empirical studies emphasize the importance of trade credit as a ﬁnancing source in developing economies. Fisman and Love (2003) observe that the industries with higher dependence on trade credit ﬁnancing exhibit higher rates of growth, relative to other industries, in countries with weaker ﬁnancial institutions. Fisman (2001) discovers a correlation between the availability of trade credit ﬁnancing and ﬁrm’s operational performance. Using a sample of African ﬁrms, he ﬁnds that ﬁrms with access to trade credit ﬁnancing are less likely to experience stock-outs, and are more likely to have higher production-capacity utilization. In addition to being capital constrained, ﬁrms operating in developing economies may have to pay greater costs of working with suppliers and cope with greater uncertainty about supplier reliability due to underdeveloped production, transportation, information, and ﬁnancial infrastructures, and due to insuﬃcient legal protection. In this paper we analyze how ﬁnancial constraints, the dual role played by the suppliers as the providers of parts and the ﬁnanciers of the manufacturer, supplier risk, ﬁxed costs of working with suppliers, and limited liability of the ﬁrm’s shareholders aﬀect the relationship among ﬁrms in a supply chain, supplier selection, and supply chain performance. Using a one-period model with homogeneous suppliers, we consider joint procurement and ﬁnancing decisions of a ﬁrm with access to limited loans from the bank and the suppliers, facing either an uncertain demand or an uncertain supply (random yield). As one would expect, our analysis suggests that the alternative ﬁnancing sources (bank loans and trade credit) are complementary and, ceteris paribus, the ﬁrm uses more suppliers if bank ﬁnancing is not available. Surprisingly, we also ﬁnd that, because of limited liability of the shareholders, the optimal production quantity could be increasing in ﬁxed costs. Furthermore, the optimal number of suppliers could be increasing in the ﬁxed costs as well, because of the limit on the supplier loans. In addition, we observe that the limits on the loans and the wholesale price aﬀect the optimal number of suppliers in a non-monotone way. Interestingly, we ﬁnd that the value of the shareholders and the optimal number of suppliers of the ﬁrm could be increasing or decreasing in the standard deviation of the supplier random yield. This is a consequence of the tradeoﬀs between the expected proﬁt and the value of the option to default that shareholders hold. Finally, we address the question whether the ﬁrms operating in the developing economies must contract with more suppliers than the ﬁrms operating in the developed economies. The answer is “no”, if the ﬁxed cost of an extra supplier is high. However, in this case, ﬁnancial constraints will force ﬁrms in the developing economies to the suboptimal level of production and cause higher stockout rates. This conclusion is consistent with the results of the earlier empirical studies.

讲义二定价的策略和战术管理经济学长江商学院-陶志刚

•Wing On Group, 1993 永安集团, 1993
Revenue 收入 Expenses 成本 Profit 利润
HK$2,236 million HK$2,210 million HK$ 26 million
Opportunity cost HK$ 53 million 机会成本
8•管理经济学
• implementation: must know entire marginal benefit curves 实施: 必须知道每个消费者的支付意愿情况
7•管理经济学
•Hysterectomy in Hong Kong 香港的子宫切除术
• price ranging from HK$20,000 to HK$200,000 even for same operation and treatment• 伦敦“疯人源自饭店• 可口可乐的新型贩卖机
Coca-Cola’s New Vending Machine
4•管理经济学
•Key Factors For an Effective Pricing Strategy
有效订价策略的决定因素
• customers’ willingness to pay for the good or service 消费者的购买意愿
9•管理经济学
•Opportunity Cost 机会成本
• definition -- net revenue from best alternative course of action
• 定义: 所有被放弃的可能方案中能带来的最大净收益。
0•管理经济学
•Debt to Equity 债转股
• In 1964, Ford introduced Mustang, at a base price of $2,368, and made a net profit of $1.1 billion in just the first two years

管理经济学第四章ppt课件

没有明确的价值取向和人生目标，实现自我人生价值就无从谈起。人生价值就是人生目标，就是人生责任。每承担一次责任
OVERVIEW
Measuring Market Demand Demand Sensitivity Analysis: Elasticity Price Elasticity of Demand Price Elasticity and Marginal Revenue Price Elasticity and Optimal Pricing Policy Cross-price Elasticity of Demand Income Elasticity
The price elasticity of demand will be greater the longer the time period allowed consumers to adjust their spending habits e.g. petrol.
没有明确的价值取向和人生目标，实现自我人生价值就无从谈起。人生价值就是人生目标，就是人生责任。每承担一次责任
没有明确的价值取向和人生目标，实现自我人生价值就无从谈起。人生价值就是人生目标，就是人生责任。每承担一次责任
Relationship between income and product demand
Inferior goods (countercyclical) Noncyclical normal goods
A price reduction for personal computers will increase both the number of units demanded and the total revenue of sellers.

Optimization and Coordination of Fresh Product Supply Chains with Freshness-Keeping Effort

we study the following problem: A distributor procures a quantity of a fresh product from a producer and transports it to a target market for sale. ‘‘Obsolescence’’ and ‘‘deterioration’’ may occur during transportation, which cause ‘‘quantity loss’’ and ‘‘quality drop’’ (quality refers to the freshness of the product), respectively. The market demand for the product depends on the freshness of the product and the selling price. The distributor has to decide: (i) the quantity he should order from the producer, (ii) the freshnesskeeping effort he should invest during the transportation process, and (iii) the selling price in the market. The producer, on the other hand, has to determine the wholesale price. We consider decision making under both the decentralized and centralized settings and design an incentive scheme that coordinates the supplier–distributor channel.

关于短生命周期产品的供应链协调

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52.Georoge Q Huang.Jason S K Lau.K L Mak The impacts of sharing production information on supply chain:a review of the literature 2003(07)
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16.Diks E B.Kok A godimos A G Multi-echelon systems:a service measure perspective 1996(02)
24.Metters R Quantifying the bullwhip effect in supply chain 1997(02)
25.Genues J P.Ramasesh R V.Hayya J C Adapting the Newsvendor Model for Infinite-horizon Inventory system 2001(03)
21.Kaplan R A A dynamic inventory model with stochastic lead times 1970(07)
22.Decroix G A.Risa A A Optimal production and inventory policy for multiple products under resource constrains 1998(07)