运筹学模型与软件实践

Models and Software Practice of the Operations Research

199645507970

()Dijkstra

2321341s2=27s3=19d1=22d2=13d3=12d4=13s1=146753842759106

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mna1, a2, , am b1, b2, , bnai=bj xij i j wijmnm+n m+n1m+n1

()

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813131466

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6350-232=118

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1:2

_1183210819.unknown

_1183211008.unknown

-5xijzij-cij(1)z12-c12=(c11-c21+c22)-c12=6-8+4-7=-5

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-5(2)z13-c13=(c11-c21+c23)-c13=6-8+2-5=-5-5

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-5(3)z14-c14=(c11-c21+ c21 - c23 + c33 -c14)-c13=(6-8+2-10+6)-3=-7-7-5

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-5(4)z24-c24=(c23-c33+ c34)-c24=(2-10+6)-7=-9-9-5-7

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-5(5)z31-c31=(c21-c23+ c33)-c31=(8-2+10)-5=+11+11-5-7-9

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-5(6)z32-c32=(c22-c23+ c33)-c32=(4-2+10)-9=+3+3-5-7-9+11

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Lingo

Lingo

_1183396226.unknown

_1183396593.unknown

Wireless Widget68 Lingo

WH1

WH2

WH3

WH4

WH4

WH5

V1

V2

V3

V4

V5

V6

V7

V8

Lingo

V1V2V3V4V5V6V7V8WH16267425960WH24953858255WH35219743351WH47673927143WH52395726541WH655228143523537223241324338

!68;sets: warehouses/wh1..wh6/: capacity; vendors/v1..v8/: demand; links(warehouses,vendors): cost, volume;endsets

!; min=@sum(links: cost*volume);!; @for(vendors(J): @sum(warehouses(I): volume(I,J))=demand(J));!; @for(warehouses(I): @sum(vendors(J): volume(I,J))

AB 34Time=Rate*Flow/(1-Flow/Limit)

Rate()Flow()Limit()

[]

[]123(Limit)

!;sets: ORIG/CHIC CINC ERIE/: supply; DEST/HAM AKR COL DAY/: demand; OXD(ORIG,DEST): rate, limit, traf;endsets!;data: supply=1200 800 1400; demand=1000 1200 700 500; rate=39 14 11 14 27 9 12 9 24 14 17 13; limit= 500 1000 1000 1000 500 800 800 800 800 600 600 600;enddata

!; [TOTAL_COST] min = @sum(OXD:rate*traf/(1-traf/limit));!; @for(ORIG(I): @sum(OXD(I,J): traf(I,J)) = supply(I));!; @for(DEST(J): @sum(OXD(I,J): traf(I,J)) = demand(J));!(Limit); @for(OXD:@BND(0,traf,Limit););

Wal-Mart3

1995 95%200015 (Carrefour)GIS

51015,

60%3470%28%45%

5.2.1 Bid-Rent Curves

5.2.2

5.2.3

Bid-Rent Curves 12

Johann von Thnen1875 Johann von Thnen1.2=--

Johann von Thnen =-

WeberWeber1909 1

2

3

Single Facility Location 5.4.1 / 123

1 1 2 (2)(3)(4),(5)345

2 6 7 7 0

8 689 2 9

6

89a,b

a,b

N

Y

2 --

Y

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P2

P1

M3

M2

M1

?X= 4.996,Y= 5.026 VC

,.

,(crossdock),,,.

CustomerDCWhere inventory needs to be for a one week order response time - typical results --> 1 DC

CustomerDCWhere inventory needs to be for a 5 day order response time - typical results --> 2 DCs

CustomerDCWhere inventory needs to be for a 3 day order response time - typical results --> 5 DCs

CustomerDCWhere inventory needs to be for a next day order response time - typical results --> 13 DCs

CustomerDCWhere inventory needs to be for a same day / next day order response time - typical results --> 26 DCs

Percent Service Level Within Promised TimeTransportationCost Build-up as a function of facilitiesCost of OperationsNumber of FacilitiesInventoryFacilitiesTotal CostsLabor

_1183464316.unknown

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()

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91,70,2439,35,314

,

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,15,17,22,12

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---

---

---

!;SETS: PLANTS/P1,P2,P3/:FCOST,CAP,OPEN; CUSTOMERS/C1,C2,C3,C4/:DEM; ARCS(PLANTS,CUSTOMERS):COST,VOL; ENDSETS

!;

MIN=@SUM(ARCS:COST*VOL)+@SUM(PLANTS:FCOST*OPEN);

_1190210666.unknown

!;@FOR(CUSTOMERS(J):[DEMAND] @SUM(PLANTS(I):VOL(I,J))>=DEM(J));!;@FOR(PLANTS(I):[SUPPLY] @SUM(CUSTOMERS(J):VOL(I,J))

!;SETS: PLANTS/P1,P2,P3/:FCOST,CAP,OPEN; CUSTOMERS/C1,C2,C3,C4/:DEM; ARCS(PLANTS,CUSTOMERS):COST,VOL;ENDSETS

DATA: !; FCOST=91,70,24; !; CAP=39,35,31; !; DEM=15,17,22,12; !; COST=6,2,6,7, 4,9,5,3, 8,8,1,5;ENDDATA!;[TTL_COST] MIN=@SUM(ARCS:COST*VOL)+@SUM(PLANTS:FCOST*OPEN);!;@FOR(CUSTOMERS(J):[DEMAND] @SUM(PLANTS(I):VOL(I,J))>=DEM(J));!;@FOR(PLANTS(I):[SUPPLY] @SUM(CUSTOMERS(J):VOL(I,J))

DC1,DC2,DC3,DC4C1,C2,C3,C4,C5

_1183469292.unknown

_1183469304.unknown

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C2

C3

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C5

P1

P1

P1

DC1

DC2

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C1

0-1

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Lingo Lingo2345

-------------------

SETS: PRODUCT/A,B/; !; PLANT/P1,P2,P4/; !; DISTCTR/DC1,DC2,DC3,DC4/:F,Z;! F""Z; CUSTOMER/C1,C2,C3,C4,C5/;!; DEMLINK(PRODUCT,CUSTOMER):D;!D; SUPLINK(PRODUCT,PLANT):S;!S; YLINK(DISTCTR,CUSTOMER):Y;!,Y; CLINK(PRODUCT,PLANT,DISTCTR):C,X;!; GLINK(PRODUCT,DISTCTR,CUSTOMER):G;!;ENDSETS

!--; [OBJ] MIN = SHIPDC + SHIPCUST + FXCOST; SHIPDC = @SUM(CLINK: C*X); SHIPCUST = @SUM(GLINK(I,K,L):G(I,K,L)*D(I,L)*Y(K,L)); FXCOST = @SUM(DISTCTR:F*Z);

_1190213506.unknown

!; @FOR(PRODUCT(I): @FOR(PLANT(J):@SUM(DISTCTR(K):X(I,J,K))

!; @FOR(PRODUCT(I):@FOR(DISTCTR(K):@SUM(PLANT(J):X(I,J,K))=@SUM(CUSTOMER(L):D(I,L)*Y(K,L))));

_1183535718.unknown

!; @FOR(CUSTOMER(L):@SUM(DISTCTR(K):Y(K,L))=1);

_1190226456.unknown

@FOR(CUSTOMER(L):@FOR(DISTCTR(K):Y(K,L)

!Y; @FOR(DISTCTR(K):@FOR(CUSTOMER(L):@BIN(Y(K,L))));

WinQSB

8

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----

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80

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20

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WinQSB

Network ModelingTransportation Problem

Solve and AnalyzeSelect Initial Solution Method ()1:234567Vogel8RussellRM

(MM)Solve the Display StepsTableau,

Pual

Pual

B210

_1184180943.unknown

_1184181043.unknown

_1184180909.unknown

ResultsGraphic Solution

Matlab

AB

AB()

_1190370087.unknown

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A

B

X2

X1

X4

X3

X6

X5

Z1

Z2

ABx

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,

,

,

EMBED Equation.3

_1190371242.unknown

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()

()

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1.25

8.75

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5.75

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7.25

1.25

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4.75

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7.75

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11

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myfun3

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Documents

运筹学模型与软件 实践

运筹学模型与软件实践