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1、A game theory-based model for product portfolio management in a competitive marketA.Sadeghi,M.ZandiehExpert Systems with Applications,2010StructurelIntroductionlLiterature reviewlDescription of the PPM problemlProblem formulationlExamplelConclusions and future work1.IntroductionlConsumers,industrial
2、 managers,and sales and marketing people,all demand products that improve their lifestyles or to gain an edge over the competition.So,product portfolios are interesting for many people.But unlimited product variety is not a way to be successful;there has to be an optimum.It is true for most companie
3、s that the Pareto rule applies:80%of the sales and/or profits come from 20%of the products.It is evident that a single product cannot fulfill the manufacturer needs and on the other hand,for diversity there exists limitation.lIn todays highly competitive environment,determining an optimal product po
4、rtfolio is very important for the survival of a firm.Optimal product portfolio has received considerable attention,because the rates of failure of new product portfolio and their associated losses are very high.The whole product component information（产品构建信息品构建信息）,engineering portfolio decision（工程工程组
5、合决策合决策）is very crucial for the progress of a firm,because it is very costly and difficult to change.The key questions are,what the best product portfolio is,and how manufacturer can find it.lProduct portfolio management(PPM)is a general business concept that analyze the production ability（生（生产能力）能力）
6、and market potential,simultaneously,and then determine the best set of products to offer.lPPM is developed to direct a product and its diversity including not only attributes（属性属性）,levels,and prices,but also analysis results,environmental requirements（环保需求）保需求）,manufacturing procedures（生（生产流程）流程）,pr
7、oduct performance information（产品性能信息）品性能信息）,and etc.Therefore PPM has been classified as a combinatorial optimization problem.Each company strives for the optimality of its product offerings through various combinations of products.The PPM problem may develop from two perspectives:(I)For attract the
8、 opinion of customers in target markets.(II)For reduce the manufacture engineering costs.First is the problem of marketing managers,and second is the problem of producer.When both of them compose with each other as reflect to utility of costumers and engineering costs,this problem becomes to miss li
9、nk between sale and production chain.Jiao and Zhang(2005)consider the customerengineering interaction in product portfolio planning,which aims to create product family specifications(产品族品族/系列系列规格格)for a target market segment,and proposed a maximizing surplus share model（最大剩余份最大剩余份额模型模型）.lIn competit
10、ive environment,we determine our product portfolio with regard to products that offer by competitors,while the competitors manage their product portfolios in regard to our products.Game theory can be used to model this problem.lThe proposed model constructs product portfolio based on customerenginee
11、ring interaction model in product portfolio planning which is developed by Jiao and Zhang.Present paper extends previous works in PPM with regard to customerengineering concerns and competitive environment.It is not for any specific product,and it can be applied to a diversity of products or service
12、s.lobjective:develop a game theory-based model as a procedure of finding optimal product portfolio.2.Literature reviewlA PPM is defined as a decision making that optimizes some criteria,such as market share.The main contribution of the most researches in PPM is summarized in following issues:1)Gener
13、ating design alternatives via multi-objective optimization（通过多目标优化生成设计方案通过多目标优化生成设计方案）.2)Accounting for uncertainty and competition when estimating the achievement of business goals.3)Applying meta-heuristic algorithms（元启元启发式算法式算法）to solve a combinatorial problem during the product line design.lThe
14、development of algorithms Heuristic(identify product profile product line design)algorithms improved heuristic algorithms genetic algorithms.lThe development of models 1)Jiao and Zhang proposed a model to address the product portfolio planning problem,it considers customer preferences,choice probabi
15、lities and platform based product costing.Also,a genetic algorithm procedure is applied.2)Aiyoshi and Maki proposed a game problem under the constraints of allocation of product and market share simultaneously.Their research is considered several manufacturers in oligopoly market（寡头垄断市寡头垄断市场场）.This
16、proposed model,on the one hand had the competitive circumstance,but on the other hand,did not has details such as large variety of customers preferences,customerengineering concerns,etc.3)model in this paper considers both details and competitive circumstance.3.Description of the PPM problemlConside
17、ring the firm capabilities to produce products,a set of product portfolios have been identified.Each product has certain desirability between customers.More specifically,we consider a scenario in which a set of products,have been identified,given that the manufacturer(m)has the capabilities(both des
18、ign and production)to produce all these products,.A product portfolio,is a set consisting of some selected product.Combined with the products,a set of product portfolios are created,.相关参数相关参数lFor example,if manufacturer m can produce 3 product,7 product portfolio are available:（=7）l Every product,is
19、 associated with certain engineering costs,denoted as .There are multiple market segments,S=s1,.,sg,.,sG,each containing homogeneous customers,with a definite size,Qg.The customerengineering interaction is embodied in the decisions associated with customers choices of different products.Various cust
20、omer preferences on diverse products are represented by respective utilities,(utility of the gth segment for the nth product of mth manufacturer).Product demands or market shares,(market share of the gth segment for the nth product of mth manufacturer),are described by the probabilities of customers
21、 choosing products.Customers choose a product based on the surplus buyer rule.They have the option of not buying any products or buying competitors products.lWe assume that competitors respond to the manufacturers moves,meaning that,the competition react by introducing new products.4.Problem formula
22、tionlThe present paper considers a market with G segments,S=s1,.,sg,.,sG,and 2 manufacturers that each of them can offer Nm products,and Jm product portfolios,.This gives the bimatrix-game（双矩阵对策双矩阵对策）problem with 2 players and Jm strategy for each,(m=1 or 2).lThe payoff for each player will of cours
23、e depend on the combined actions of both players.A payoff matrix shows what payoff each player will receive at the outcome of the game.For player m(m=1 or 2),the payoff matrix,Fm,is as follows:lIn summary,a J1 J2 bimatrix game is played by two players,player 1 and player 2.Player 1 has a finite set
24、and player 2 has a finite set of pure strategies.The payoff matrixes f1(),of player 1 and of player 2 are denoted by F1 and F2 respectively.This game is denoted by(F1,F2).lNow the game(F1,F2)is played as follows.Players 1 and 2 choose,independent of each other,a strategy and respectively.Here can be
25、 seen as the probability that player 1(2)chooses his th row(th column).The(expected)payoff for player 1 is x1F1x2 and the expected payoff to player 2 is x1F2x2.lA strategy pair()is an equilibrium for the game(F1,F2)iflThe set of all equilibria for the game(F1,F2)is denoted by E(F1,F2).By a theorem o
26、f Nash this set is non-empty for all bimatrix-games(Nash,1950).lSome methods for calculating payoff matrix arrays,are there(see Section 2).We used the function that proposed by Jiao and Zhang(2005).This function is based on customer-engineering interaction model in PPM.This is as follows:lEq.(3)is t
27、he expected shared surplus by offering a product portfolio,consisting of products ,to customer segments,sg,each with size Qg.The market potentials,Qg,can be given exogenously at the outset or estimated through a variety of techniques based on historical data or test markets.The utility of the gth se
28、gment for the nth product of mth manufacturer is denoted as .lThis model assumes that customers only choose a product with a positive surplus.The choice probability,that a customer or a segment,sg,chooses a product,with Ncom competing products,is defined as follows:lwhere u is a scaling parameter（尺度
29、参数尺度参数）.lAccording to matrix(1)and Eq.(3),let thel function be defined by5.ExamplelIn this section,a simple example to use the proposed model is presented.For simplicity,we consider a market with two competitor(M=2),and four different products(Nm=4)for each.Feasible strategies,is defined as follows:
30、产品组合数=24-1=15?lThree segments are identified,i.e.,s1,s2,and s3.Q1,Q2,and Q3 are assumed 0.2,0.3 and 0.5,respectively.Table 1 shows the utilities of three segments to every product()and cost of each().Also,scaling parameter(u)is supposed 0.8.Therefore,2 payoff matrixes F1 and F2 formed for manufactur
31、er 1 and 2,separately.This game and obtained data from expected shared surplus values(Eq.(5)are summarized in Fig.1.返回lThe optimal result for each manufacturer is derived from the Nash equilibrium point of the game.A strategy pair is an alone equilibrium for the game.The related payoff pair is(0.74,
32、0.83).6.Conclusions and future worklThis paper proposed a game theory-based model that is used to maximize the expected shared surplus for a product portfolio managed.The product portfolio management(PPM)is an important optimization problem that includes the large set of constraints and characterist
33、ics.Therefore,it is very helpful for a manager to use a marketing decision support system which provides him the acceptable solutions with considering more terms.According to this goal,a game theory-based model is proposed and applied to solve the problems involved in PPM.There are potentially unlim
34、ited opportunities for research in PPM.Future studies can focus on other characteristics to achieve more ideal results.Other notable directions for future researches include allowing for sequential entry strategies,time varying utilities and changing customer behaviors.返回相关概念纳什定理纳什定理：在一个有在一个有n n个博弈方
35、的博弈个博弈方的博弈G=S1,SnG=S1,Sn：u1,unu1,un中，如果中，如果n n是有限的，且是有限的，且Si Si 都是有限集（对都是有限集（对i=1i=1，n n），则该博弈至少存在一个纳什均衡，但可能包含），则该博弈至少存在一个纳什均衡，但可能包含混合策略混合策略。产品组合：产品组合：由不同的产品线构成，而产品线又是由不同的由不同的产品线构成，而产品线又是由不同的产品项目构成。产品项目构成。产品组合策略产品组合策略：在产品组合的深度、广度和相关性方面做在产品组合的深度、广度和相关性方面做的筹划和安排。的筹划和安排。产品组合的广度：产品线的数量。产品组合的广度：产品线的数量。产品
36、组合的广度：产品项目（规格或品种）的数量产品组合的广度：产品项目（规格或品种）的数量l遗传算法遗传算法（Genetic AlgorithmGenetic Algorithm）是一类借鉴生物界的进化）是一类借鉴生物界的进化规律（适者生存，优胜劣汰遗传机制）演化而来的随机化规律（适者生存，优胜劣汰遗传机制）演化而来的随机化搜索方法。其主要特点是直接对结构对象进行操作，不存搜索方法。其主要特点是直接对结构对象进行操作，不存在求导和函数连续性的限定；具有内在的隐并行性和更好在求导和函数连续性的限定；具有内在的隐并行性和更好的全局寻优能力；采用概率化的寻优方法，能自动获取和的全局寻优能力；采用概率化的寻优方法，能自动获取和指导优化的搜索空间，自适应地调整搜索方向，不需要确指导优化的搜索空间，自适应地调整搜索方向，不需要确定的规则。定的规则。单一产品策划单一产品策划程序策划目标环境分析市场细分目标市场市场定位概念产品营销组合返回