ijcrb.webs.com INTERDISCIPLINARY JOURNAL OF CONTEMPORARY RESEARCH IN BUSINESS MAY 2013 VOL 5, NO 1 Abstract

Transcription

1 INTERDISCILINARY JOURNAL OF CONTEMORARY RESEARCH IN BUSINESS MAY 03 Alication of Markov Chain in Forecasting Demand of Trading Comany HamedAlioorTalemi,KiyoumarsJahanbani,ArashHeidarkhani, Afshin Azad Khomami,AminTorabiGolSefidi,Seyed Abbas Abolghasemi,,3,4,5,6 M.A. Student of Business Management, Rasht Branch, Islamic Azad University, Rasht, Iran Abstract Markov chain is one of the techniques used in oerations research with ossibilities view that managers in organizational decision making (industrial and commercial) use it. Markov rocesses arise in robability and statistics in one of two ways. Markov rocess is a tool to redict that it can be make logical and accurate decisions about various asects of management in the future. A stochastic rocess, defined via a searate argument, may be shown mathematically to have the Markov roerty, and as a consequence to have the roerties that can be deduced from this for all Markov rocesses. Keywords: Markov Chain,Forecasting Demand,Trading Comany. Introduction Managementis defined decisionsina simle form and the most imortant factor for decision making is forecasting future. Atresent erathose organizations have highcomlexity and much information is available, so their arrangement and refine can hel to managementina logicaland accuratedecisions.the use of various asects of oerations research is easier to deal with comlex issues for managers. Markov chain isone of the techniques used in oerations research with ossibilities view that managers in organizational decision making (industrial and commercial) use it.successful decision is a icture of the future that this will not be achieved only from the rediction, based on scientific rinciles. Markov rocess is a chain of random events that by having information about the current location can be redicted next eriod and in fact Markov chain is a tool that used for forecasting of situation organization in future eriods.. Definition ofstochastic rocessesandmarkov Chains Arandomrocessis definedasaset ofrandom variables [x t ] that defects of T is often referred to time, there is around a secific set of { x( t), t T} be such that withidentify the value of x (s) values of x (t) for t> s deends T (hakimiour,998).if random rocess on the values x (u) make for u <s, then its rocess is called Markov rocess that such a rocess is defined by the following exression: t t... t t n { a x( t) b x( t ) x,..., x( t ) x r n n { a x( t) b x( t ) x } r n n If for } { x( t), t T} is Markov rocess (soldo, 0). It is result that rocess Markovanalysisbegan withtheresearch. A.Markov, Russian theoristin years( )in the field of robabilityscience. However, a comrehensive theory rocesses and analysis of Markov by. A.n.gorov- w.dublin- loe-j.l.dub& others were comleted it in 930 (Hakimiour, 998). Markovchain is certainmodelsfrommore generalotential model that these models are famous random rocesses and in them current state of a system deends on all revious states. Markov rocess is a random rocess. With this feature that current state of system is deendent just rior final state of the system. In other words in rediction of state of a system at the future times according to the information related to current state of system will be analyzed (Wang, 004). In fact Markov analysis, it will establish a way to the current analyze for certain variables because is ossible to redict the future movement same as variables because Markov rocess is chain of a random events that by having the current success can be redicted the next hase (Lee, Tong, 0). The field of Markov chains has been widely used in management science that these can include:. Human resources lanning model. yramid Maslow's model on human needs 3. Model to redict rice changes. 4. Changes in brand by customer roduct 5. Behavior of customer receivables COY RIGHT 03 Institute of Interdiscilinary Business Research 070

2 INTERDISCILINARY JOURNAL OF CONTEMORARY RESEARCH IN BUSINESS MAY Maintenance model 7. Inventory control 8. Describing a articular tye of storage issues 9. Analysis and relacement human resources 0. rediction of system reliability Basic Concets of Markov rocesses For analysis of system from Markov model should determine the two basic elements of the system and the ossibilities of movement between them. System state is the status of the system at a moment in time like a car works or does not work at a moment in time. robability of movement among the states call transition robabilities that reresenting the system moves from ( i j) one state to another state during a secified eriod robability of some change from one state to another state in the next eriod is called transition robabilities of the Markov model {Xt+=jXt=i} If thenumber ofossible statesin Markov chain isalimited,transition robabilities can show to form a matrix that this matrix in Markov rocess will be always square (m * m). In thismatrixijshowtransition robabilities fromstateto stateinnext time eriod (Deng, 990). i il i m m m Also transition robabilities can show in form of grah. j j ij mj j m m im mm m X X Every issue to resolve by a Markov rocess should be having the following three characteristics: - Transition robabilities are deendent on only the current state of the system. - Transition robabilities are always fixed. 3- Sum of transition robabilities move to other states in the next time eriod should be equal one. 4. rediction offuturestates redictions of future states require that initial states of the system are identified and transition robabilities fixed. There are severalmethodsfor redictingfuturestates that in this aerrefers to as case to the matrix multilication (Yamaguchi, Nagai, 006). Matrix multilication is a simle method for redicting the state of a Markov system for future eriods. By havingthe initial state of matrix multilication can be used for rediction system at timen. A) Thestateof the system: COY RIGHT 03 Institute of Interdiscilinary Business Research 07

3 INTERDISCILINARY JOURNAL OF CONTEMORARY RESEARCH IN BUSINESS MAY 03 Firstsystem stateat timenis showed by aone-dimensionalmatrix to name of vector (n)={ (n), (n)} That in this relation (n)= value vector (n). (n)= the robability that system at time n be in state (n)= the robability that system at time n be in state If we suose that system at time n be in state Then (n)=[,0] If we suose that system at time n be in state Then (n)=[,0] It is necessary to note here that if there is a system of more than two states, not necessary that the system in the initial state is only one of the states and may be more than one state but in any state vector sum must always be equal to one. For examle, the state vector for a system of three cases may be [0/ and 0/7 and 0/] b) Matrix of transition robabilities (): Transition robabilitiesmatrixis shownas following In this matrix: = Transition robabilities matrix ij= Transition robabilities of system from statei to state j C) rediction ofthe futurestate: To calculate therobability thatsystem at time(n +) bestatej, we use as follows relationshi (n+)=(n). That this relationshi: (n+)= Staterobability vectorat timen + (one time eriodlater) (n)= State robability vector at time (n) (current time eriod) = Transition robabilities matrix According toabove relationshicanbe calculatedtransition robabilities inseveral eriods later in form of simle. (n+)=(n+). (n+3)=(n+). A general relationshi is obtained from these relationshis that as follow: (n)=(0). n That this equation: (n) = State robability vector in time eriod n th (0)= robability vector in time eriod zero (starting oint of time that robability of each state is certain) n = ower of n th in transition robabilities matrix n= Number of time eriods for which it is redicted. Therefore it can be done necessary rojectionsofthis relationshiforany eriod of time and used for decision making in lanning (Zhang, 00). 5. Stable State Conditions In Markovrocess often by more n (in long term) value vector tends tofixing state (Stable state). As to achieve its eriod multilying the state vector in transition robabilities matrix is equal to transition robabilities matrix in eriods later that this state is called Stable state. If stable value show by π symbol, instable state, the state vectorwill beinterms ofdecimal values as follow:, ] [ Inthis relationshi: Π=State robability vector (as relative amounts) =amount of state =amount of state Since in stable state conditions isn t imortant time eriod and values are indeendent of time, multilicationof state vector in transition matrix avectorin stable statewill be same as state vector. Therefore stable state values can be determined in the following manner algebra: COY RIGHT 03 Institute of Interdiscilinary Business Research 07

4 INTERDISCILINARY JOURNAL OF CONTEMORARY RESEARCH IN BUSINESS MAY 03.,.... And on the other hand sumof robability states must be equal to one: Thereforewe havethree equationsandtwo assive that solving it will obtainedvalue of thestate vectorineriodn th that it isbeginning ofstable state.a Markov rocess may not reach always stable state. However, it can be stated thatif there is a value of n that all elements of n be greater than zero,in this conditions there will be a Stable state.to calculate the Stable state can be used MicroManager Software that is alicable to in the analysis of Stable state (Ujjwal Kumar, Jain, 00). 6. Conclusion: Markov rocessisatool toredict that it can be make logical and accurate decisions about various asects of management in the future. Also Markov is random rocess. With these differencesinmarkovrocessto redictthefuturestateis used information related to the lasteriodthat this is one of the analyzable fundamental rinciles through Markov chains. In transition robability matrix that rows and columns should always be equal (it be square shae)sum of rows is equal to one. In rediction offuturestates based on amarkovchainifredictionare calculatedfor several eriod consecutive of a system.finally, after some time the results will be the same that is called stable state and thiscaused by interference only data ofone eriod (zero eriod) in calculation. COY RIGHT 03 Institute of Interdiscilinary Business Research 073

5 INTERDISCILINARY JOURNAL OF CONTEMORARY RESEARCH IN BUSINESS MAY 03 References Hakimiour,A.(998). decision making in Management, Astan Quds Razavi - Second Edition Soldo,Bozidar(0). Forecasting natural gas consumtion, Alied Energy,6-37. Wang,Chao-Hung (004). redicting tourism demand using fuzzy time series and hybrid grey theory,tourism Management, Deng JL (990).Control roblems of Grey s\system,wuhang: Huazhong University of Science and Technology ress. Yamaguchi,G.D.L i, D.Nagai,M. (006). A grey- Based Aroach to sulers selection roblem,roc.int.conf.onarallel,distributed rocessing Techniques and Alications. UjjwalKumar,V.K.Jain (00).Time series models(grey-markov,grey Model with rolling mechanism and singular sectrum analysis) to forecast energy consumtion in India,Energy,35: Yi-ShianLee,Lee-Ing Tong (0). Forecasting energy consumtion using a grey model imroved by incororating genetic rogramming,energy Conversion and Management,5:47-5 Zhang SJ,He Y (00). A Grey Markov forecasting model for forecasting the total ower requirement of agricultural machinery in Shangxi rovince. J Shanxi AgricUniv(Nat Sci Edi ),(3): COY RIGHT 03 Institute of Interdiscilinary Business Research 074