73-220-Lecture13 - IntrotoIntegerProgramming 73-220 Lecture...

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1 Intro to Integer Programming 73-220 Lecture 13
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2 Agenda Review Last Class Network models Integer Programming Pure integer problems Mixed integer problems Binary variables Solution Methods LP relaxation Excel solver Next Class
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3 Types of Integer Programming  Problems All integer   (all variables are restricted to be  Mixed integer   (some variables are restricted  to be integer) Binary  (all variables are restricted to be  Open new world of modeling options!
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4 Pure Integer Programming  Problem A tailor makes wool tweed sport coats and wool slacks. He is  able to get a shipment of 150 square yards of wool cloth from  Scotland each month to make coats and slacks, and he has 200  hours of his own labour to make them each month. A coat  requires 3 square yards of wool and 10 hours to make, and a pair  of pants requires 5 square yards of wool and 4 hours to make. He  earns $50 in profit from each coat he makes and $40 from each  pair of slacks. He wants to know how many coats and slacks to  produce to maximize profit.
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5 Formulation: Pure Integer  Problem Decision Variables: C= number of coats to make S=number of slacks to make Objective function: Maximize z = 50C + 40S Constraints: Cloth availability: 3C + 5S  <   150 Labour Availability: 10C + 4S <  200 C, S >  0 and integer
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6 Mixed Integer Problem A company has five plants (pant 1, 2, 3, 4, and 5) that manufacture a lightweight vehicle and four regional distribution centers (warehouse A, B, C, and D). With the recent declining demand for the product, the firm is considering reducing its fixed operating costs by closing one or more plants, even though it would incur an increase in transportation costs. The relevant costs for the problem are provided in the following table. The transportation costs are $ per vehicle shipped. A B C D Capacity Fixed cost 1 56 21 32 65 12,000 2,100,000 2 18 46 7 35 18,000 850,000 3 12 71 41 52 14,000 1,800,000 4 30 24 61 28 10,000 1,100,000 5 45 50 26 31 16,000 900,000 Demand 6,000 14,000 8,000 10,000
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7 Formulation: Mixed Integer  Problem Decision Variables: y(i) = 1 if plant i is open i=1,2,3,4,5 = 0 if plant i is not open x(i,j) = # of vehicles to ship from plant i to warehouse j; j=A,B,C,D Objective Function: Minimize z = 2,100,000y(1) + 850,000y(2) + 1,800,000y(3) + 1,100,000y(4) + 900,000y(5) + 56x(1,A) + 21x(1,B) + 32x(1,C) + 65x(1,D) + 18x(2,A) + 46x(2,B) + 7x(2,C) + 35x(2,D) + 12x(3,A) + 71x(3,B) + 41x(3,C) + 52x(3,D) + 30x(4,A) + 24x(4,B) + 61x(4,C) + 28x(4,D) + 45x(5,A) + 50x(5,B) + 26x(5,C) + 31x(5,D)
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8 Formulation contd. Constraints:
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This note was uploaded on 11/28/2011 for the course FINANCE 101 taught by Professor Chan during the Spring '11 term at Aarhus Universitet.

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73-220-Lecture13 - IntrotoIntegerProgramming 73-220 Lecture...

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