Srita

Problema 1 (extraído del libro de texto, problema 17, página 504)
A product can be produced on four different machines. Each machine has a fixed setup cost, variable production costs per-unit-processed, and a production capacity given in Table 15. A total of 2,000 units of the product must be produced. Formulate an IP whose solution will tell us how to minimize total costs.

Solución
CostoTotal = Costo Fijo – Costo Variable
Sea Yi Total de unidades en máquina i (i=1, 2, 3, 4)
Sea Xi Máquina i a utilizar (i=1, 2, 3, 4)

Min z = 20Y1+24Y2+16Y3+28Y4+1000X1+920X2+800X3+700X4
ST
Y1 <= 900X1
Y2 <= 1000X2
Y3 <= 1200X3
Y4 <= 1600X4

Y1+Y2+Y3+Y4 =2000
Y1,Y2,Y3,Y4 >= 0 (Enteros)
X1,X2,X3,X4 = 0 ó 1
END
GIN Y1
GIN Y2
GIN Y3
GIN Y4
INT X1
INT X2
INT X3INT X4

Problema 2 (extraído del libro de texto, problema 23, página 505)
At a machine tool plant, five jobs must be completed each day. The time it takes to do each job depends on the machine used to do the job. If a machine is used at all, there is a setup time required. The relevant times are given in Table 20. The company’s goal is to minimize the sum of the setup and machine operation timesneeded to complete all jobs. Formulate and solve (with LINDO, LINGO, or Excel Solver) an IP whose solution will do this.

Solución
Sea Xij máquina i para realizar el trabajo j donde Xij = 1 ó 0
Sea Yi si la máquina es usada

MIN Z = 42 X11 + 70 X12 + 85 X22 + 45 X23 + 58 X31 + 37 X34 + 58 X41 + 55 X43 + 38 X45 + 60 X52 + 54 X54 + 30 Y1 + 40 Y2 + 50 Y3 + 60 Y4 + 20 Y5 + 93 X13
ST
X11+ X31 + X41 = 1
X12 + X22 + X52 = 1
X23 + X43 + X13 = 1
X34 + X54 = 1
X45 = 1
X11 + X12 - 3 Y1 + X13 <= 0
X22 + X23 - 2 Y2 <= 0
X31 + X34 - 2 Y3 <= 0
X41 + X43 + X45 - 3 Y4 <= 0
X52 + X54 - 2 Y5 <= 0
END
INT 17

Problema 3 (extraído del libro de texto, problema 27, página 506)
The Father Domino Company sells copying machines. A major factor in making a saleis Domino’s quick service. Domino sells copiers in six cities: Boston, New York, Philadelphia, Washington, Providence, and Atlantic City. The annual sales of copiers projected depend on whether a service representative is within 150 miles of a city (see Table 24).
Each copier costs $500 to produce and sells for $1,000. The annual cost per service representative is $80,000. Domino must determinein which of its markets to base a service representative. Only Boston, New York, Philadelphia, and Washington are under consideration as bases for service representative. The distance (in miles) between the cities is shown in Table 25. Formulate an IP that will help Domino maximize annual profits.

Solución

Sea Xi si el representante se encuentra en la ciudad i, donde i=1, Bos, i=2, NY, i=3Phil, i=4, Wash. (Xi = 0 ó 1)
Sea Yi si hay un representante en 150 millas de radio (i= 1, 2, 3, 4, 5, 6) Yi = (0 ó 1)

Maximizar la utilidad = utilidad por copiadora vendida – gastos de representación
Max u = precio de venta - costo de produccion – gastos de representación

Max Z = 350Y1 + 250(1–Y1) + 500Y2 + 375(1–Y2) + 450Y3 + 350(1-Y3) + 400Y4 + 225(1–Y4) +200Y5 + 100(1-Y5) + 225Y6 +150(1-Y6) - 80(X1+X2+X3+X4)

ST
1–X1–Z1<=0
Y1-1+Z1<=0
1-X2-X3-Z2<=0
Y2-1+Z2<=0
1-X2-X3-X4-Z3<=0
Y3-1+Z3<=0
1-X3-X4-Z4<=0
Y4-1+Z4<=0
1-X1+Z5<=0
Y5-1+Z5<=0
1-X2-X3-Z6<=0
Y6-1+Z6<=0
END
INT 16

Todas las variables son 0 ó 1.

Problema 4 (extraído del libro de texto, problema 30, página 557)
New York City has 10 trash districts and is trying todetermine which of the districts should be a site for dumping trash. It costs $1,000 to haul one ton of trash one mile. The location of each district, the number of tons of trash produced per year by the district, the annual fixed cost (in millions of dollars) of running a dumping site, and the variable cost (per ton) of processing a ton of trash at a site are shown in Table 112.

For example,...