quantitative models(chp10)

Dr. Muzaffer Kapanoğlu – Production Systems and Facilities Planning © 2004

QUANTITATIVEFACILITIES PLANNING

MODELS


• 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


Distances

• Rectilinear Distance• Euclidean Distance• Flow Path Distance (Actual path traversed between

two points)


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



•SINGLE-FACILITY MINISUM LOCATION PROBLEM

m

ii

m

iiii bYwaXwxf

1 1

)(min

•SINGLE-FACILITY with EUCLIDEAN??




•What if we have only a few of alternative locations?


Iso-cost contour lines


•What if we have only a few of alternative locations?



•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).



•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)


n-Facility Location


Location-Allocation Models


Warehouse Location Problem


Quadratic Assignment Problem


Warehouse Layout Models

quantitative models(chp10)

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