Linear Programming- Lecture 1

Linear Programming- Lecture 1

• 1.
  LECTURE-1 LINEAR PROGRAMMING-508 Decision theory Stateof decision •Certainty •Risk •Uncertainty •Conflict
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   Making decisionsis an integral and continuous aspect of human life  Decision is an essential part of planning.  Decision theory represents a generalized approach to decision making.  It enables a decision maker to 1) Analyze a set of complex situations with many alternatives and many different possible consequences. 2) Identify a course of action consistent with basic economic and psychological decision of the decision maker.
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  DECISION MAKING ENVIRONMENTS Certainty  Uncertainty  Risk  Conflict The domain of decision analysis models falls between two extreme cases i.e Deterministic and Uncertainty between these two lies the problem of risk.
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  DIFFERENT TYPES OFDECISIONS  Strategic –external environment of organization  Administrative-optimal allocation of resources . structuring and acquisition of resources so as to optimize.  Operating cost –day to day decisions.
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  DEFINITIONS  Courses ofaction- decision making problems deals with selection of a single act from a set of alternative acts . if two or more alternative courses of action occur then decision making is necessary to select only one course of action.  States of nature- when there are many possible outcomes of an event .one cannot predict what will happen. It is only in terms of probability one can forecast. Decision maker has no direct control on occurrence of particular future event.
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   Preference orvolume system- the criteria used by decision maker to choose best alternative.  Pay off- the effectiveness associated with specified combination of courses of action and states of nature. A1 A2 A3 A4 ……Ai  S1 A1S1 A2S2 ……………………  S2 …………….……………………..  S3 …………………..……………….  . ……………………………........  . .………………………………….  Sj ………………………………..AiSj
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   Opportunity losstable- loss incurred due to failure of not adopting most favorable course of action or strategy .this is found separately for each state of nature.
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  DECISION MAKING UNDERCERTAINTY  Decision maker have all the information of consequence of every alternative or decision choice with certainty . One can predict the outcome of each alternative course of action exactly. here optimal payoff is available. Linear programming technique is commonly used.
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  DECISION UNDER RISK Decision maker does not know which state of nature will occur but can say probability of the occurrence of each state .i.e expected value criteria and expected opportunity loss criteria.  One assumes that there exists no. of possible future states of nature Nj and each Nj has probability Pj occurring and there may not be one future state that results in the best outcome for all alternatives Aj  Outcomes = Nj * Aj = Oij  Expected value = Oij*Pj
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   The highestvalue Pj is defined as some of the products of each outcome Oij times the Pj associated states of nature Nj occurs. It is the best alternative.  Expected opportunity loss criteria- also known as regret criteria this utilizes opportunity loss to minimize the regret. Expected opportunity loss criteria = Oij*Pj → regrets
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  DECISION MAKING UNDERUNCERTAINTY  Maximax criteria  Maximin criteria  Salvage regret criteria  Hurwicz criteria  Laplace criteria
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   Maximax criteria-based on the assumption of optimistic choosing alternative maximum of maximum pay offs.  Maximin criteria – based on assumption of pessimistic choosing maximum out of min pay offs  Salvage regret criteria-also known as minmax.this criteria examines the regret or the opportunity loss resulting when the particular situation occurs and the pay offs of selected alternatives is the smaller than the pay off that could have been attained with that particular situation .here pay off matrix is converted into regret matrix. The decision maker finds the maximum regret for each strategy and selects the one with smallest regret .
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   Hurwicz criteria-its compromise between maximax and maximin criteria. No equal weightage is given here because of the co-efficients. α = co-efficient of optimism 1-α= co-efficient of pessimism The maximum payoff will be multiplied by co-efficient of optimism and vice versa.  Laplace criteria - also known as equally likelyhood criteria. Here equal weightage is given. the possibility of occurrence of each states of nature has one third chance of occurrence .Also known as Principle of insufficient criteria. Each decision alternative will be assigned an average payoffs value.