Qualitative and Quantitative Analysis of Population Models ...
Quantitative Models(Chp10)
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Transcript of Quantitative Models(Chp10)
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
QUANTITATIVEFACILITIES PLANNING
MODELS
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
• FACILITY LOCATION MODELS– RECTILINEAR FACILITY LOCATION PROBLEM– n-FACILITY LOCATION PROBLEM– LOCATION-ALLOCATION MODELS– WAREHOUSE/PLANT LOCATION MODEL
• SPECIAL FACILITY LAYOUT MODELS– QUADRATIC ASSIGNMENT PROBLEM – WAREHOUSE LAYOUT MODELS– MACHINE LAYOUT MODELS
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Distances
• Rectilinear Distance• Euclidean Distance• Flow Path Distance (Actual path traversed between
two points)
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Rectilinear Facility Location
•X=(x,y): Location of the new facility•Pi =(ai, bi): Location of existing facility i i=1,2,..m•wi : “Weight” associated between the new facility and existing facility i• d(X, Pi) = Distance between the new facility and the existing facility i• Optimization opportunities
m
iii PXdwxf
1
),()(min
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Rectilinear Facility Location
•SINGLE-FACILITY MINISUM LOCATION PROBLEM
m
ii
m
iiii bYwaXwxf
1 1
)(min
•SINGLE-FACILITY with EUCLIDEAN??
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Rectilinear Facility Location
•SINGLE-FACILITY MINISUM LOCATION PROBLEM
•What if we have only a few of alternative locations?
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Iso-cost contour lines
•SINGLE-FACILITY MINISUM LOCATION PROBLEM
•What if we have only a few of alternative locations?
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Iso-cost contour lines
•SINGLE-FACILITY MINISUM LOCATION PROBLEM
•What if we have only a few of alternative locations?
![Page 9: Quantitative Models(Chp10)](https://reader036.fdocuments.us/reader036/viewer/2022081508/55cf9c06550346d033a8495e/html5/thumbnails/9.jpg)
Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Iso-cost contour lines
•SINGLE-FACILITY MINISUM LOCATION PROBLEM
•What if we have only a few of alternative locations?
![Page 10: Quantitative Models(Chp10)](https://reader036.fdocuments.us/reader036/viewer/2022081508/55cf9c06550346d033a8495e/html5/thumbnails/10.jpg)
Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Iso-cost contour lines
•SINGLE-FACILITY MINISUM LOCATION PROBLEM
•What if we have only a few of alternative locations?
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Iso-cost contour lines
•SINGLE-FACILITY MINISUM LOCATION PROBLEM
•What if we have only a few of alternative locations?
![Page 12: Quantitative Models(Chp10)](https://reader036.fdocuments.us/reader036/viewer/2022081508/55cf9c06550346d033a8495e/html5/thumbnails/12.jpg)
Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Rectilinear Facility Location
•SINGLE-FACILITY MINISUM LOCATION PROBLEM•Problem 10.1
–Location of existing facilities: P1(0,10), P2(5,10), P3(5,15), P4(10, 5).–Weights: w1: 15, w2: 20, w3: 5, w4: 30.–Determine the optimum location for a single new facility when cost is proportional to rectilinear distance.–Construct a contour line passing through the point (10, 10).
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Rectilinear Facility Location
•SINGLE-FACILITY MINIMAX LOCATION PROBLEM
mibYaXxf ii ,..2,1),(max)(min
•Linearize?? Optimization??•C1=minimum(ai + bi)•C2=maximum(ai + bi)•C3=minimum(- ai + bi)•C4=maximum( - ai + bi)•C5=max(c2 - c1, c4 - c3)•(x1,y1)=0.5(c1-c3, c1+c3+c5)•(x2,y2)=0.5(c2-c4, c2+c4-c5)
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
n-Facility Location
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Location-Allocation Models
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Location-Allocation Models
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Warehouse Location Problem
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Quadratic Assignment Problem
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Quadratic Assignment Problem
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Warehouse Layout Models
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Warehouse Layout Models
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Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004
Warehouse Layout Models