 PROFESSOR GOODCHILD CEE 587 APRIL 15, 2009 Basic Optimization.

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PROFESSOR GOODCHILD CEE 587 APRIL 15, 2009 Basic Optimization

f(x) x objective function constraints

Optimization Problem Elements Objective function  The thing you want to minimize or maximize  Typically total cost Constraints  The complexities of the problem  E.g. capacities, demands, supply  An unconstrained optimization leads to 0 or infinity

f(x) x objective function (nonlinear) minimum Constraints can’t improve the solution

Route choice Objective function  Minimize  k c k y k Subject to:   k y k =1  y k =0 or 1 where, c k = cost of travel on link k y k =1 if link k is used, 0 otherwise

c1c1 c2c2 c3c3 y1y1 y2y2 y3y3

c 1 =4 y1y1 y2y2 y3y3 c 2 =2 c 3 =3 y1y1 y2y2 y3y3 Objective function 1004 1106 1119 0102 0013

Assigning Customers to Vehicles Minimize  i  k c ik y ik Subject to:   k y ik =1   i a i y ik ≤b k  y ik =0 or 1 where,  c ik = cost of serving customer i with vehicle k  a i =order size from customer i  b k =capacity of vehicle k  y ik =1 if customer i is assigned to vehicle k, 0 otherwise

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