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(a, b) (an, bz) L1 Distance (x, y) LA (az, 6) (a, b) Distance GRAPH OF MINIMAX LOCATION PROBLEM EXAMPLE In a foundry there are seven shops whose coordinates are summarized in the following table. The company is interested in locating a new costly fire fighting equipment in the foundry determine the minimax location of the new equipment SL NO EXISTING FACILITIES OF 1 2 3 4 5 Sand plant Molding shop Pattern shop Melting shop Felting shop Fabrication shop Annealing shop CO-ORDINATE CENTROID 10,20 30,40 10,120 10,60 30,100 30,140 20,190 6 7 SOLUTION The movement of new equipment is constrained within in the foundry the assumption of rectilinear distance more appropriate The co ordinate of the centroid of the existing shops are (a4,64)=(10,60) (a5,55)=(30,100) (a1,b1)=(10,20) (a2,b2)=(30,40) (a3,b3)=(10,120) (a6,b6)=(30,140) (a7,67)=(20,140) Objective- To locate the new emergency facility (X,Y) such that the maximum distance from the new emergency facility to any of the existing facilities is minimized Fi(X,Y)= Distance between the new facilities and the existing facilities Fi(X,Y)=X-ai|+|Y-bi| Fmax (X,Y)=maximum of the distance between the new facility and various existing facilities Fmax(X,Y)= max {]X-a;+Y-bil} 1sism The distance between new facility and existing facility may be rectilinear or Euclidean m=different shops in an industry in the event of fire in any one of these shops a costly firefighting equipment showed reach the spot as soon as possible from its base location. Movements within any industry are rectilinear in nature. Our objective is to locate the new fire fighting equipment within the industry such that maximum distance it has to travel from its base location to any of the existing shops is minimized. Step 1 Find C1, C2, C3, C4 and C5,using following formula C4 = max (-ai + bi) S 1 sism C3 = min (-a; +b;) 1 sism C = min (a + b) Ca = max (a + b) 1sism C5=max (C2-C1,C4 - C3) 1sism 1 sism Step 2 Find the points P, and P2 using the following formula P1=[1/2(C1 C3), 72(c1 + c3 +C5)] P2=[1/2(c2 C4), 12(C2 + C4 - C5)] Step 3 Any pt(X*,Y*) on the line segment joining points P1 and P2 is a minimax location that minimize fmax(X,Y) 11. How do the logos and certification on cover help the consumers to buy standardised products