研究生课内实验报告-高级运筹学-第二次

NanjingUniversityofPostsandTelecommunications

LabReport

Title:AdvancedOperationalResearch

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SchoolofManagement

FirstSemester2015-2016SchoolYear

4.MetropolitanMicrowaves,Inc.isplanningtoexpanditssalesoperationbyofferingotherelectronicappliances.Thecompanyhasidentifiedsevennewproductlinesitcancarry.Relevantinformationabouteachlinefollowsonthenextslide.

MetropolitanhasdecidedthattheyshouldnotstockprojectionTVsunlesstheystockeitherTV/VCRsorTVs.Also,theywillnotstockbothVCRsandDVDplayers,andtheywillstockvideogamesiftheystockTVs.Finally,thecompanywishestointroduceatleastthreenewproductlines.Ifthecompanyhas$45,000toinvestand420sq.ft.offloorspaceavailable,formulateanintegerlinearprogramforMetropolitantomaximizeitsoverallexpectedreturn.

Definethedecisionvariables:

ifprodrctline1isproduced,x1=1;ifnot,x1=0;

ifprodrctline2isproduced,x1=1;ifnot,x2=0;

ifprodrctline3isproduced,x1=1;ifnot,x3=0;

ifprodrctline4isproduced,x1=1;ifnot,x4=0;

ifprodrctline5isproduced,x1=1;ifnot,x5=0;

ifprodrctline6isproduced,x1=1;ifnot,x6=0;

ifprodrctline7isproduced,x1=1;ifnot,x7=0;

definetheobjectivefunction:

definetheconstraints:

thetotalamountofmoneyinvstedis$45,000:

thetotalfloorsquaravailableis420sq.ft.:

VCRsandDVDplayerscannotbebothstocked：

theyshouldnotstockprojectionTVsunlesstheystockeitherTV/VCRsorTVs：

theywillstockvideogamesiftheystockTVs：

thecompanywishestointroduceatleastthreenewproductlines：

Maximize[{0.081*6000x1+0.09*12000x2+0.11*20000x3+0.102*14000x4+0.101*15000x5+0.141*2000x6+0.132*32000x7,

6000x1+12000x2+20000x3+14000x4+15000x5+2000x6+32000x745000,

125x1+150x2+200x3+40x4+40x5+20x6+100x7420,

x4+x51,

x1+x2x3,

x2-x60,x1+x2+x3+x4+x5+x6+x73

x11||x10,

x21||x20,

x31||x30,

x41||x40,

x51||x50,

x61||x60,

x71||x70},

{x1,x2,x3,x4,x5,x6,x7}]

结果：{5304.,{x10.,x21.,x30.,x40.,x50.,x60.,x71.}}

5.HartManufacturingmakesthreeproducts.Eachproductgoesthroughthreemanufacturingdepartments,A,B,andC.Therequiredproductiondataaregiveninthetablebelow.(Alldataareforamonthlyproductionschedule.)

ProductionDepartment

Product1

Product2

Product3

Hoursavailable

A(hours/unit)

1.5

3

2

450

B(hours/unit)

2

1

2.5

350

C(hours/unit)

0.25

0.25

0.25

50

ProfitContributionsperUnit

$25

$28

$30

SetupCostsperproductionrun

$400

$550

$600

MaxProductionperproductionrun(Units)

175

150

140

FormulateanintegerlinearprogramforHartManufacturingtomaximizeitsoverallprofit.

Definethedecisionvariables:

x1:theamountofproduct1;

x2:theamountofproduct2;

x3:theamountofproduct3;

ifproduct1isproduced,y1=1;ifnot,y1=0;

ifproduct2isproduced,y1=1;ifnot,y1=0;

ifproduct3isproduced,y1=1;ifnot,y1=0;

Definetheobjectivefunction:

(1)HoursavailableinmanufacturingAis450:

1.5x1+3x2+2x3<=450;

(2)HoursavailableinmanufacturingBis350:

2x1+x2+2.5x3<=350;

(3)HoursavailableinmanufacturingCis50:

0.25x1+0.25x2+0.25x3<=50;

(4)themaxproductionofproduct1is175,sonomatterwhetherproduct1isproducedornot,itsproductionmustnotgetover175:

x1<=175y1;

(5)themaxproductionofproduct2is150,sonomatterwhetherproduct1isproducedornot,itsproductionmustnotgetover175:

x2<=150y2;

(6)themaxproductionofproduct3is140,sonomatterwhetherproduct1isproducedornot,itsproductionmustnotgetover175:

x2<=140y3;

(7)thevalueofx1,x2,x3shouldnotbenegative:

x1>=0,x2>=0,x3>=0;

Maximize[{25x1+28x2+30x3-400y1-550y2-600y3,

1.5x1+3x2+2x3450,

2x1+x2+2.5x3360,

0.25x1+0.25x2+0.25x350,

x1-175y10,

x2-150y20,

x3-140y30,

x10,x20,x30,

y11||y10,

y21||y20,

y31||y30},

{x1,x2,x3,y1,y2,y3}]

结果：{4350.,{x1100.,x2100.,x30.,y11.,y21.,y30.}}

6.AdistributioncompanywantstominimizethecostoftransportinggoodsfromitswarehousesA,B,andCtotheretailoutlets1,2,and3.Thecosts(in$’s)fortransportingoneunitfromwarehousetoretaileraregiveninthefollowingtable.

Thefixedcostofoperatingawarehouseis$500forA,$750forB,and$600forC,andatleasttwoofthemhavetobeopen.Thewarehousescanbeassumedtohaveadequatestoragecapacitytostoreallunitsdemanded,ie.,assumeeachwarehousecanstore525units.

Retailer

Warehouse

1

2

3

A

$15

$32

$21

B

$9

$7

$6

C

$11

$18

$5

Demand

200

150

175

Formulateanintegerlinearprogramforthedistributioncompanytominimizeitsoverallcost.

Definethedecisionvariables:

x11:theamountofproductstramiitedfromwarehouseAtoretailer1;

x12:theamountofproductstramiitedfromwarehouseAtoretailer2;

x13:theamountofproductstramiitedfromwarehouseAtoretailer3;

x21:theamountofproductstramiitedfromwarehouseAtoretailer1;

x22:theamountofproductstramiitedfromwarehouseAtoretailer2;

x23:theamountofproductstramiitedfromwarehouseAtoretailer3;

x31:theamountofproductstramiitedfromwarehouseAtoretailer1;

x32:theamountofproductstramiitedfromwarehouseAtoretailer2;

x33:theamountofproductstramiitedfromwarehouseAtoretailer3;

ifproductsistransmittedfromwarehouseA,y1=1;ifnot,y=0;

ifproductsistransmittedfromwarehouseB,y1=1;ifnot,y=0;

ifproductsistransmittedfromwarehouseC,y1=1;ifnot,y=0;

definetheobjectivefunction:

(1)thedemandofretailer1is200:

x11+x21+x31=200;

(2)thedemandofretailer2is150:

x12+x22+x32=150;

(3)thedemandofretailer3is175:

x31+x32+x33=175;

(4)themaxvolumeofwarehouseAis525,sothetotalamounttransmiitedfromwarehouseAshouldnotgetover525:

x11+x12+x13<=525y1;

(5)themaxvolumeofwarehouseBis525,sothetotalamounttransmiitedfromwarehouseAshouldnotgetover