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
Costo Total = 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 …ver más…

Each ton of trash processed at site 3 incurs $51 in variable costs. Each dump site can handle at most 1,500 tons of trash. Each district must send all its trash to a single site. Determine how to locate the dump sites in order to minimize total cost per year.

MIN 15190X11 + 153782.93X12 + 397892.23X13 + 279063.08X14 + 64190X15 + 113190X16 + 325093.21X17 + 124757.33X18 + 265041.96X19 + 260190X10 + 2507005.31X21 + 34960X22 + 7502419.27X23 + 2656960X24 + 3186211.81X25 + 1782960X26 + 7026960X27 + 4404960X28 + 3743027.96X29 + 1989283.41X20 + 4362993.57X31 + 4770227.08X32 + 28305X33 + 4468305X34 + 3952747.64X35 + 3751358.18X36 + 1693305X37 + 4802595.52X38 + 2803305X39 + 5054043.75X30 + 2015610.01X41 + 1176032X42 + 2936032X43 + 120032X44 + 2172527.07X45 + 1389186.05X46 + 3127521.32X47 + 2800784.13X48 + 1176032X49 + 617835.17X40 + 430911X51 + 1423626.04X52 + 2743987.84X53 + 2271503.67X54 + 49911X55 + 901852.9X56 + 2101658.79X57 + 811911X58 + 1954911X59 + 2205172.47X50 + 933896X61 + 933896X62 + 2949007.28X63 + 1621071.95X64 + 1034933.09X65 + 77896X66 + 2645896X67 + 1842585.21X68 + 1431350.84X69 + 1621071.95X60 + 6249386.99X71 + 7899700X72 + 2974700X73 + 8435543.69X74 + 5324087.34X75 + 5929700X76 + 19700X77 + 6326777.37X78 + 5763187.62X79 + 9100951.29X70 + 238987.14X81 + 529200X82 + 907444.15X83 + 803856.18X84 + 214200X85 + 437126.09X86 + 676528.04X87 + 4200X88 + 739200X89 + 761365.77X80 + 1361213.03X91 +