02 pf#02 basic location problem.ppt

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TI091314 /Perancangan Fasilitas/2012/#2 1

Facilities LocationLecture Notes #2

Stefanus Eko Wiratno ©2012

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Location Problems and Models A classification scheme for location models can used to

help identify those problems Location problems and models may be classified in a

number of ways (Daskin, 1995) :1. Demands and candidate facility locations2. Type of network location models3. Number of Facilities to Locate4. Distance Metrics5. Nature of inputs about time6. Nature of inputs about uncertainty7. Homogenous product and demand 8. Sector problems9. Objective10. Elasticity demand11. Capacity of facilities 12. The allocation of demand to facilities13. Level of facilities14. Locating desirable facilities

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Taxonomy of Location Problems and Models Demands and candidate facility locations

Planar location models; demands occur anywhere on a plane

Network location models; demands and travel between demand sites and facilities are assumed to occur only on a network or graph composed of nodes and links

Discrete location models; allow for the use of arbitrary distance between nodes. As such, the structure of the underlying network is lost

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Type of network location models Tree problems; a network in which there is at

most one path from any node to any other node General graph problem; consists of a connected

general network and a complete graph

Number of Facilities to Locate Single facility location problem Multiple facilities location problem

(exogenous: number of facilities is parameter, endogenous: number of facilities is decision variable)

Taxonomy of Location Problems and Models

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Distance Metrics Manhattan or right–angle distance metric

Euclidean or straight–line distance metric

Ip distance metric

jijijjii yyxxyxyxd ,;,

22,;, jijijjii yyxxyxyxd

Taxonomy of Location Problems and Models

pp

ji

p

jijjii yyxxyxyxd1

,;,

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Taxonomy of Daskin (1995)

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Taxonomy of Brandeau and Chiu (1989)

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Taxonomy of Nagy and Salhi (2007)

1. Hierarchical structure, 2. Type of input data (deterministic/stochastic), 3. Planning period (single/multi-period), 4. Solution method (exact/heuristic), 5. Objective function, 6. Solution space, 7. Number ofdepots (single/multiple), 8. Number and types of vehicles (homogeneous/

heterogeneous),9. Route structure.

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Taxonomy of ReVelle et al. (2008)

1. Analytic models are based on large simplifying assumptions (fixed cost of locating a facility dependent of where it will locate, demand uniformly distributed, etc).

2. Continuous models assume that facilities can be located anywhere in service area, while demands are often taken as being at discrete locations

3. Network models assume that topological structure of the location model is a network composed of lines and nodes. Much of the literature in this area is concerned with finding special structures that can be exploited to derive low-order polynomial time algorithms

4. Discrete models assume that the set of demands and candidate location for facilities are discrete. These problems often formulate in integer or mix-integer programming that most of them are NP-hard on general network

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Classification of Location Problem[Logistics Management]

1. Location Problems2. Allocation Problems3. Location – Allocation Problems

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Determine the location of one or more new facilities in one or more of several potential sites

The number of sites must at least equal the number of new facilities being located

The cost of locating each new facility at the potential sites (fixed cost and operating & transportation cost) is assumed to be know.

Location Problems

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Location problems can be classified as:Single-facility problemsMultifacility problems

Classification of location problems is based on whether the set of possible locations for a facility is finite or infinite :Discrete space location problemContinuous space location problem

Location Problems

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Assume that the number and location of facilities are known a priori and attempt to determine how each customer is to be served (problem determines how much each facility is to supply to each customer center)

Allocation Problems

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Problems determine not only how much each customer is to receive from each facility but also the number of facility along with their locations and capacities

Location-Allocation Problems

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Can be classified as (Hax and Candea, 1984) : Single-facility location problem; deal with the

optimal determination of the location of a single facility Location Problem

Multi-facility location problem; deal with the simultaneous location determintaion for more than one facility Location-Allocation Problem

Facility Location Problems

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Another classification it is based on whether the set of possible locations for a facility is finite or infinite :

1. Discrete space location problem It have a finite feasible set of sites in which to

locate a facility For most real-world problem, this models are

more appropriate The solutions may be near optimal but

feasible


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2. Continuous space location problem; A facility can be located anywhere within the

confines of a geographic area, then the number of possible locations is infinite

Assuming that the transportation costs are proportional to distance

The solutios may be infeasible but optimal


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Proximity to source of raw materials Cost and availability of energy and utilities Cost, availability, skill, and productivity of labor Government regulations Taxes Insurance Construction costs and land price Government and political stability Exchange rate fluctuation Export and import regulations, duties, and tariffs

Important Factors in Location Decisions (1)

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Transportation system Technical expertise Environmental regulations Support service Community services Weather Proximity to customer Business climate Competition-related factors

Important Factors in Location Decisions (2)

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1. Qualitative Analysis

2. Quantitative Analysis

3. Hybrid Analysis

Techniques forDiscrete Space Location Problems

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It usually using scoring method (subjective decision making tools), consists of these steps:

Qualitative Analysis (1)(Technique for Discrete Space Location Problems)

Step 1 : List all the factors that are important – that have impact on the location decision

Step 2 : Assign an appropriate weight (typically between 0 and 1) to each factor based on the relative importance of each

Step 3 : Assign a score (typically between 0 and 100) to each location with respect to each factor identified in step 1

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Step 4 : Compute the weighted score for each factor for each location by multiplying its weight by the corresponding score

Step 5 : Compute the sum of the weighted scores for each a location based on these scores

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A payroll processing company has recently won several major contracts in the midwest region of the U.S. and central Canada and wants to open a new, large facility to serve these areas. Because customer service is so importance, the company wants to be as near its “customers” as possible. Preliminary investigation has shown that Minneapolis, Winnipeg, and Springfield, Illinois, would be the three most desirable locations and the payroll company has to select one of these three. A subsequent thorough investigation of each location with respect to eighnt important factors has generated the raw scores and weights listed in table 2. Using the location scoring method, determine the best location for the new payroll processing facility.


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Steps 1, 2, and 3 have already been completed for us. We now need to compute the weighted score for each location-factor pair (Step 4), and these weighted scores and determine the location based on these scores (Step 5).

Solution

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Wt. Factors LocationMinn. Winn. Spring.

.25 Proximity to customers 95 9065

.15 Land/construction prices 60 6090

.15 Wage rates 70 45 60

.10 Property taxes 70 90 70

.10 Business taxes 80 90 85

.10 Commercial travel 80 65 75

.08 Insurance costs 70 95 60

.07 Office services 90 90 80

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From the analysis in above Table, it is clear that Minneapolis would be the best location based on the subjective information.

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Wt. Factors LocationMinn. Winn. Spring.

.25 Proximity to customers 23.75 22.5 16.25

.15 Land/construction prices 9 9 13.5.15 Wage rates 10.5 6.75 9.10 Property taxes 7 9 8.5.10 Business taxes 8 9 8.5.10 Commercial travel 8 6.5 7.5.08 Insurance costs 5.6 7.6 4.8.07 Office services 6.3 6.3 5.6

Sum of weighted scores 78.15 76.65 72.15


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Of course, as mentioned before, objective measures must be brought into consideration especially because the weighted scores for Minneapolis and Winnipeg are close.

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It is appropriate for a specific set of objectives and constraints : Minimax location model is approriate for

determining the location of an emergency service facility, where the objective is to minimize the maximum distance traveled between the facility and any customer

Transportation model is approriate for determining the location of facility, where the objective is to minimize total distance traveled between the facility and any customer

Quantitative Analysis(Technique for Discrete Space Location Problems)

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Minimax Location Model (1)

The minimax location problem is given by:

mibyaxXfMin ii ,,2,1,max

In order to obtain the minimax solution, let

c1 = minimum (ai+bi)c2 = maximum (ai+bi)c3 = minimum (-ai+bi)c4 = maximum (-ai+bi)c5 = maximum (c2–c1, c4–c3)

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Optimum solutions to the minimax location problem can be shown to be all points on the line segment connecting the point

The maximum distance will be equal to c5/2

5313111 ,5.0, cccccyx

and the point

5424222 ,5.0, cccccyx

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Minimax Location Model (3) Example :Consider the problem of locating a maintenance department in a production area. It is desirable to locate the maintenance facility as close to each machine as possible, in order to minimize machine downtime.Eight machines are to be maintained by crews from the central maintenance facility. The coordinate locations of the machine are (0,0), (4,6), (8,2), (10,4), (4,8), (2,4), (6,4), and (8,8).

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Minimax Location Model (4) i ai bi ai + bi -ai + bi

1 0 0 0 02 4 6 10 23 8 2 10 -64 10 4 14 -65 4 8 12 46 2 4 6 27 6 4 10 -28 8 8 16 0

c1=0 c2=16 c3=-6 c4=4 c5=16

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The optimum solutions lie on the line segment connecting the point

)5 ,3(10 ,65.0, 11 yx

)2 ,6(4 ,125.0, 22 yx

and the point


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2 4 6 8 10 12

2

4

6

8

10

P5

P2

P6 P7

P8

P4

P3

x*


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Transportation Model (1)

It is mathematical model (linear programming) that can be solved using:

1. Optimization methods• Manual: Simplex Algorithm• Software: QSB, LINDO, LINGO, GAMS

2. Heuristic methods• Least cost assignment routine method• Northwest corner rule method• Vogel approximation method

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m

i

n

jijij xcZ

1 1

Costtion Transporta Total Minimize

) seat warehoun restrictio(supply 21 ,

Subject to

1

i,...,m ,iaxn

jiij

)market at t requiremen (demand 21 ,1

j,...,n,jbxm

ijij

ns)restrictio negativity-(non21 ,0 ,...,n , i,jxij


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number of units transported from warehouse i to customer j

Parametercost of transporting one unit from warehouse i to customer jsupply capacity at warehouse idemand at customer j

cij :

ai : bi :

Decision Variablesxij :


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Seers Inc. has two manufacturing plants at Albany and Little Rock supplying Canmore brand refrigerators to four distribution centers in Boston, Philadelphia, Galveston and Raleigh. Due to an increase in demand of this brand of refrigerators that is expected to last for several years into the future, Seers Inc., has decided to build another plant in Atlanta or Pittsburgh. The expected demand at the three distribution centers and the maximum capacity at the Albany and Little Rock plants are given in Table 4. Determine which of the two locations, Atlanta or Pittsburgh, is suitable for the new plant. Seers Inc., wishes to utilize all of the capacity available at it’s Albany and Little Rock Locations


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Bost. Phil. Galv. Rale. SupplyCapacity

Albany 10 15 22 20 250Little Rock 19 15 10 9 300Atlanta 21 11 13 6 No limitPittsburgh 17 8 18 12 No limitDemand 200 100 300 280


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Albany 10 15 22 20 250Little Rock 19 15 10 9 300Atlanta 21 11 13 6 330Demand 200 100 300 280 880


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Albany 10 15 22 20 250Little Rock 19 15 10 9 300Pittsburgh 17 8 18 12 330Demand 200 100 300 280 880


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Hybrid Analysis(Technique for Discrete Space Location Problems)

It is a method that incorporates subjective (qualitative) as well as quantitative cost and other factors

1. Brown – Gibson Model (1972)2. Buffa – Sarin Model (1987)

This model classifies the objective and subjective factors important to the specific location being addressed as:

1. Critical, 2. Objective,3. Subjective

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Buffa – Sarin Model (1)

After the factors are classified, they are assigned numerical values:

CFij

OFij

SFij

wj

1 if location i satisfies critical factor j

0 otherwise

cost of objective factor j at location i

numeric value assigned (on a scale of 0-1) to subjective factor j for location i

weight assigned to subjective factor j (0wj

1)

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Determine the overal critical factor measure (CFMi), objective factor measure (OFMi), and subjective factor measure (SFMi) for each location i with these equations:

, ... ,m,iCFCFCFCFCFMp

jijipiii 21 ...

121

, ... ,m, i

OFOF

OFOF

OFMq

jiji

q

jiji

q

jij

q

jiji

i 21 minmax

max

11

11


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r

jijji miSFwSFM

1, ... ,2,1

The location measure LMi for each location is then calculated as:

iii SFMOFMCFMLM 1

where is the weight assigned to the objective factor measure


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Mole-Sun Brewing company is evaluating six candidate locations-Montreal, Plattsburgh, Ottawa, Albany, Rochester and Kingston, for constructing a new brewery. There are two critical, three objective and four subjective factors that management wishes to incorporate in its decision-making. These factors are summarized in Table following. The weights of the subjective factors are also provided in the table. Determine the best location if the subjective factors are to be weighted 50 percent more than the objective factors.

Example


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Location

FactorsCritical

Water Supply

Tax Incentives

Albany 0 1Kingston 1 1Montreal 1 1Ottawa 1 0Plattsburgh 1 1Rochester 1 1


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Location

FactorsCritical Objective

Revenue Labor Cost

Energy Cost

Albany 185 80 10Kingston 150 100 15Montreal 170 90 13Ottawa 200 100 15Plattsburgh 140 75 8Rochester 150 75 11


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Location

FactorsObjective Subjective

Community Attitude

0.3

Ease of Transportation

0.4Albany 0.5 0.9Kingston 0.6 0.7Montreal 0.4 0.8Ottawa 0.5 0.4Plattsburgh 0.9 0.9Rochester 0.7 0.65


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Location

FactorsSubjective

Labor Unionization

0.25

SupportServices

0.05Albany 0.6 0.7Kingston 0.7 0.75Montreal 0.2 0.8Ottawa 0.4 0.8Plattsburgh 0.9 0.55Rochester 0.4 0.8


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Location

FactorsCritical Objective Subjective

Sum of Objective Factors

OFMi SFMi LMi

Albany -95 0.7 0.7 0Kingston -35 0.67 0.67 0.4Montreal -67 0.53 0.53 0.53Ottawa -85 0.45 0.45 0Plattsburgh -57 0.88 0.88 0.68Rochester -64 0.61 0.61 0.56


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Brown – Gibson Model

See “Tata Letak Pabrik dan Pemindahan Bahan”,

Wignjosoebroto, S

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1. Median Method

2. Contour Line Method

3. Gravity Method

4. Weiszfeld Method

Techniques for Continuous Space Location Problems

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Median Method (1)(Technique for Continuous Space Location Problems)

The median method finds the median location (defined later) and assign the new facility to it.

Interaction between the new facility and existing ones is known

Problem is to minimize the total interaction cost between each existing facility and the new one.

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Notation :ci

fi

xi , yj

traffic flow between existing facility i and new facilitycoordinates of existing facility i

cost of transportation between existing facility i and new facility, per unit

Model :

m

iiiii yyxxfcTCMinimize

1


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Model can be solved using :

1. Algorithm

2. Equivalent linear-constrained model


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AlgorithmStep 1 : List the existing facilities in nondecreasing

order of the x coordinates

Step 2 : Find the jth x coordinate in the list (created in step 1) at which the cummulative weight equals or exceeds half the total weight for the first time

m

i

ij

ii

m

i

ij

ii

wwandww111

1

1 2

2


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Step 3 : List the existing facilities in nondecreasing order of the y coordinates

Step 4 : Find the kth y coordinate in the list (created in step 3) at which the cummulative weight equals or exceeds half the total weight for the first time

m

i

ik

ii

m

i

ik

ii

wwandww111

1

1 2

2The optimal location of the new facility is given by the jth x coordinate and the kth y coordinate in step 2 and 4, respectively


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Example :Two high-speed copiers are to be located on the fifth floor of an office complex that houses four departments of the Social Security Administration. The coordinates of the centroid of each department as well as the average number of trips made per day between each department and the copiers yet-to-be-determined location are known and given in Table. Assume the travel originates and ends at the centroid of each department. Determine the optimal location – the x,y coordinates – for the copiers


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Department Number

x Coordinate y Coordinate Average Number of Daily Trips to Copiers

1 10 2 62 10 10 103 8 6 84 12 5 4


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Department Number

x Coordinatesin Nondecreasing

OrderWeights Cumulative

Weights

3 8 8 81 10 6 142 10 10 244 12 4 28

Cumulative Weights = half of the total weights (28/2=14)

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Department Number

y Coordinatesin Nondecreasing

OrderWeights Cumulative

Weights

1 2 6 64 5 4 103 6 8 182 10 10 28

Cumulative Weights half of the total weights (28/2=14)

Thus the optimal coordinates of the new facility are (10 , 6)

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Transforming the nonlinear-unconstrained model into an equivalent linear-constrained model

otherwise00 if

otherwise00 if

xxxxx

xxxxx

iii

iii

Consider the following notation:


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We can observe that

iii

iii

xxxx

xxxx

A similar definition,

iii

iii

yyyy

yyyy


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Thus the transformed linear model is:

n

iiiiii yyxxwMin

1

Subject to

signin edunrestrict ,,,2,1 0,,,

,,2,1

,,2,1

yxniyyxx

niyyyy

nixxxx

iiii

iii

iii


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Solve the problem using LINDO


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Contour Line Method (1)(Technique for Continuous Space Location Problems)

Draw a vertical line through the x coordinate and a horizontal line through the y coordinate of each facility

Step 1 :

Label each vertical line Vi, i=1, 2, ..., p and horizontal line Hj, j=1, 2, ..., q where Vi= the sum of weights of facilities whose x coordinates fall on vertical line i and where Hj= sum of weights of facilities whose y coordinates fall on horizontal line j

Step 2 :

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Step 3 : Set i = j = 1; N0 = D0 = - wii=1

m

Step 4 : Set Ni = Ni-1 + 2Vi and Dj = Dj-1 + 2Hj. Increment i = i + 1 and j = j + 1

Step 5 : If i < p or j < q, go to Step 4. Otherwise, set i = j = 0 and determine Sij, the slope of contour lines through the region bounded by vertical lines i and i + 1 and horizontal line j and j + 1 using the equation Sij = – Ni/Dj. Increment i = i + 1 and j = j + 1


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Step 6 :

Step 7 :

If i < p or j < q, go to Step 5. Otherwise select any point (x, y) and draw a contour line with slope Sij in the region [i, j] in which (x, y) appears so that the line touches the boundary of this line. From one of the end points of this line, draw another contour line through the adjacent region with the corresponding slopeRepeat this until you get a contour line ending at point (x, y). We now have a region bounded by contour lines with (x, y) on the boundary of the region


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The number of vertical and horizontal lines need not be equal

The Ni and Dj as computed in Steps 3 and 4 correspond to the numerator and denominator, respectively of the slope equation of any contour line through the region bounded by the vertical lines i and i + 1 and horizontal lines j and j + 1


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Consider Example 4. Suppose that the weight of facility 2 is not 10, but 20. Applying the median method, it can be verified that the optimal location is (10, 10) - the centroid of department 2, where immovable structures exist. It is now desired to find a feasible and “near-optimal” location using the contour line method.

Example


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SolutionThe contour line method is illustrated using Figure 1Step 1: The vertical and horizontal lines V1, V2, V3 and

H1, H2, H3, H4 are drawn as shown. In addition to these lines, we also draw line V0, V4 and H0, H5 so that the “exterior regions” can be identified

Step 2: The weights V1, V2, V2, H1, H2, H2, H4 are calculated by adding the weights of the points that fall on the respective lines. Note that for this example, p=3, and q=4


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Step 3 : Since

Set N0 = D0 = –38Step 4 : Set

384

1

i

iw

N1 = -38 + 2(8) = -22; D1 = -38 + 2(6) = -26;N2 = -22 + 2(26) = 30; D2 = -26 + 2(4) = -18;N3 = 30 + 2(4) = 38; D3 = -18 + 2(8) = -2;

D4 = -2 + 2(20) = 38;(These values are entered at the bottom of each column and left of each row in figure 1)


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Step 5 : Compute the slope of region

S00 = -(-38/-38) = -1; S14 = -(-22/38) = 0.58;S01 = -(-38/-26) = -1.46; S20 = -(30/-38) = 0.79;S02 = -(-38/-18) = -2.11; S21 = -(30/-26) = 1.15;S03 = -(-38/-2) = -19; S22 = -(30/-18) = 1.67;S04 = -(-38/38) = 1; S23 = -(30/-2) = 15;S10 = -(-22/-38) = -0.58; S24 = -(30/38) = -0.79;S11 = -(-22/-26) = -0.85; S30 = -(38/-38) = 1;S12 = -(-22/-18) = -1.22; S31 = -(38/-26) = 1.46;S13 = -(-22/-2) = -11; S32 = -(38/-18) = 2.11;


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Step 5 : Compute the slope of region (con’t)

Step 6 : When we draw contour lines through point (9, 10), we get the region shown in figure 1.

S33 = -(38/-2) = 19;S34 = -(38/38) = -1;

(The above slope values are shown inside each region.)


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Example:Since the copiers cannot be placed at the (10, 10) location, we drew contour lines through another nearby point (9, 10). Locating anywhere possible within this region give us a feasible, near-optimal solution.


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As before, we substitute wi = ci fi, i = 1, 2, ..., m and rewrite the objective function as

m

iiiii yyxxfc

1

22 )()( TC Minimize

2

11

2 )()( TC Minimize yywxxw i

m

ii

m

iii

The cost function is

Gravity Method (1)

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Since the objective function can be shown to be convex, partially differentiating TC with respect to x and y, setting the resulting two equations to 0 and solving for x, y provides the optimal location of the new facility

m

1i

m

1i

m

1i

m

1i

022 x

TC

iii

iii

wxwx

xwxw

Gravity Method (2)

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Similarly,

m

1i

m

1i

m

1i

m

1i

022 y

TC

iii

iii

wywy

ywyw

Thus, the optimal locations x and y are simply the weighted averages of the x and y coordinates of the existing facilities

Gravity Method (3)

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Example:Consider Example 4. Suppose the distance metric to be used is squared Euclidean. Determine the optimal location of the new facility using the gravity method.

Gravity Method (4)

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We conclude that :

4.628180 and 7.928

272 yx

1 10 2 6 60 122 10 10 10 100 1003 8 6 8 64 484 12 5 4 48 20

Department i xi yi wi wixi wiyi

Total 28 272 180

Gravity Method (5)

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If this location is not feasible, we only need to find another point which has the nearest Euclidean distance to (9.7, 6.4) and is a feasible location for the new facility and locate the copiers there.

Another way, we can again draw contour lines from neighboring points to find a feasible, near-optimal location

Gravity Method (6)

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Weiszfeld Method (1)

As before, substituting wi=ci fi and taking the derivative of TC with respect to x and y yields

yyxxfcTCm

iiiii

1

22 )()( Minimize

The objective function for the single facility location problem with Euclidean distance can be written as:

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Although the Weiszfeld method is theoritically suboptimal, it provides x, y values that are very close to optimal

For practical purposes the algorithm works very well and can be readily implemented on a spreadsheet

If the optimal location is not feasible, use the contour line method to draw contour lines and then choose a suitable, feasible, near-optimal location for the new facility


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m

i ii

im

i ii

ii

m

i ii

ii

yyxx

xw

yyxx

xw

yyxx

xxw x

TC

11

1

0)()(

)()(

)()(

)2(21

2222

22

)()(

)()(

1

1

22

22

m

i ii

i

m

i ii

ii

yyxxw

yyxxxw

x


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m

i ii

im

i ii

ii

m

i ii

ii

yyxx

yw

yyxx

yw

yyxx

yyw y

TC

11

1

0)()()()(

)()(

)(221

2222

22

m

i ii

i

m

i ii

ii

yyxxw

yyxxyw

y

1

1

22

22

)()(

)()(


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m

ii

m

iii

km

ii

m

iii

k

w

ywy;

w

xwx

1

1

1

1

Step 0 : Set iteration counter k=1

Step 1 : Set

m

ik

ik

i

i

m

ik

ik

i

ii

k

yyxxw

yyxxxw

x

1

11

22

22

)()(

)()(


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Step 2 : If xk+1 ≈ xk and yk+1 ≈ yk, Stop. Otherwise, set k = k + 1 and go to Step 1

)()(

)()(

1

11

22

22

m

ik

ik

i

i

m

ik

ik

i

ii

k

yyxxw

yyxxxw

x


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Example:Consider Example 5. Assuming the distance metric to be used is Euclidean, determine the optimal location of the new facility using the Weiszfeld method. Data for this problem is shown in Table below


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Departements # xi yi wi

1 10 20 62 10 10 203 8 6 84 12 5 4

Using the gravity method, the initial seed can be shown to be (9.8, 7.4). With this as the starting solution, we can apply Step 1 of the Weiszfeld method repeatedly until we find that two consecutive x, y values are equal.


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Optimal location


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Facility Location Case Study (1)A small manufacturing company currently located in a university “tech park” has witnessed major growth since introducing an innovative technology into the marketplace. Its owner now wants to find a new location and build a bigger facility. In January she hired senior industrial and management engineering (IME) students at the university to investigate several potential locations and select the one that est suits her needs. The student group adopted the following five-step approach, which based on the hybrid analysis discussed earlier. (see Heragu, pp 546 – 551)

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Facility Location Case Study (2)Step 1 : determine of requirements (the students

conducted interviews with the owner and facility manager to determine these company-spesific requirements for the new facility)

Step 2 : classification of location factors (the requirements classified into three categories)

Step 3 : data collection (this step requires the most time, but it is very important and should be done carefull)

Step 4 : elimination of sites not meeting critical objectives and development of a rating chart

Step 5 : site visits and site evaluation

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