GOAL PROGRAMMING

GOAL PROGRAMMINGPAWAN KUMAR 2K12/ME/121PAWAN KUMAR MEENA 2K12/ME/122PRANAY MOHADIKAR 2K12/ME/123PRASHANT MATHUR 2K12/ME/124PRATEEK 2K12/ME/125INTRODUCTIONGOAL PROGRAMMING VERSUS LINEAR PROGRAMMINGTERMINOLOGYTYPES OF GOAL PROGRAMMINGGOAL FORMULATIONSOLVING GOAL PROGRAMMING PROBLEMS GRAPHICALLYMODIFIED SIMPLEX METHOD FOR GOAL PROGRAMMING

CONTENTSIntroduced by Charnes and Cooper in 1960s Provides a method of dealing with a collection of goals, rather than an explicit objective function. Objective is to minimize the deviation from each of the goals that have been established. Constraints are soft in that you may violate one (i.e. not meet one goal) if it means you can make better progress toward one of the other goals. INTRODUCTIONDIFFERENCESMultiple Goals (instead of one OBJECTIVE) Deviational Variables Minimized (instead of maximizing profit or minimizing cost of LP) Satisficing (instead of optimizing) SIMILARITIESGP models are similar to LP models in that both are formulated under the same requirements and assumptions (e.g., linearity, non-negativity, certainty).GP uses, like LP, graphical methods to illustrate linear programming concepts.

GOAL PROGRAMMING VERSUS LINEAR PROGRAMMINGASPIRATION LEVELSpecific value associated with the desired or acceptable level of the objectiveUsed to measure achievement of the objectiveGOALAn objective in conjunction with an aspiration levelGOAL DEVIATIONDifference between what we aspire to and what we accomplish w.r.t. objectiveCan be high or lowTERMINOLOGYWeights methodthe single objective function is the weighted sum of the of the functions representing the goals of the problem. MIN Z= w1d1+w2d2++wndn

Preemptive methodprioritizes the goals in order of importance, then optimizes one goal at a time. MIN Z= P1d1+P2d2++Pndn TYPES OF GOAL PROGRAMMINGLet fi(x) be the mathematical representation of the objective Can be linear or nonlinear (usually linear)

Let bi be the aspiration level

Three possible goals(1) fi(x) >bi fi(x)+di--di+=bi Min di+(2) fi(x)