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# opti - Goal programming The LPP models discussed so far are...

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Goal programming The LPP models discussed so far are based on the optimization of a single objective function. There are situations where multiple objectives are to be met. We now present the goal programming technique for solving multi objective models. The principle idea is to convert the original multiple objectives into a single goal. The resulting model usually gives an efficient solution because it may not meet all the objectives.

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Formulation of Goal Programming problems (problem 2 problem set 8.1A page 349) The NW shipping model conducts special events to attract potential patrons. The two most popular events that seem to attract teenagers, the young/middle-aged group, and senior citizens are band concerts and art and craft shows. The costs per presentation of the band and art show are \$1500 and \$3000 respectively. The total (strict) annual budget allocated to the two events is \$15000. The mall manager estimates the attendance of the events as follows:
Number attending per presentation Event Teenagers Young/middle age Seniors Band concert 200 100 0 Art show 0 400 250 The manager has set the minimum annual goals of 1000,1200 and 800 for the attendance of teenagers, the young/middle-aged group, and seniors, respectively. Formulate the problem as a goal-programming model.

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Solution 1 x Let = number of band concerts to be held per year 2 x = number of art shows to be held per year Thus the goals are 1000 200 1 x 1200 400 100 2 1 + x x 800 250 2 x (attendance of teenagers) (attendance of young/middle-aged group) (attendance of seniors)
Subject to 15000 x 3000 x 1500 2 1 + 0 2 , 1 x x + + + 2 1 1 400 100 200 x x x We now convert the goals into equalities by adding slack/ surplus variables- G1: G2: + 2 250 x G3: 1000 = 1200 = 800 = - + - 1 1 s s - + - 2 2 s s - + - 3 3 s s

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- + i i s s , + i s are called deviational variables . They measure the amount by which a goal is underachieved or over achieved. For example - i s is positive(& so will be 0) means the attendance of teenagers fall short of the desired goal of 1000 by + i s persons. Similarly - 3 s
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