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Multi-criteria and Non-linear programming

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McMaster University
Manish Verma

Ch07 Multicriteria and Nonlinear Programming Models Not responsible for Section 72 The Analytic Hierarchy Process GOAL PROGRAMMING MODELSProfit maximization or cost minimization is not always a firms only objectives Often it is combined with one or more objectives in the real business environmentLP and IP can measure objective function in only one dimension For example LP models cannot combine multiple objectives unless they are measured in the same units such as dollarsGoal Programming can overcome the above shortcoming by o First setting a goal for each objective In most business settings some of the goals may be achieved at the expense of the otherso Second establishing a hierarchy or rank of importance among these goals so that lowerranked goals are given less prominence than higherranked goals o Based on the hierarchy GP attempts to reach a satisfactory level for each goal HOW o GP tries to minimize deviations between the specified goals and what can be actually achieved for the multiple objective functions within the given constraintso Deviations can be positive or negative depending on whether the goal has to be overachieved or underachieved o Only these deviational variables appear in the objective function though there could be other variables in the model EXAMPLE WILSON DOORS COMPANY Enumber of exterior doors to make Inumber of interior doors to make and Cnumber of commercial doors to make 70110110subject to 4379000steel usage 2436000forming time 2345200assembly time0Optimal LP Solution E1400 I800 and C0 for total sales of 186 000 Manish VERMA Winter 2014 Course 4QC3
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