Facilty Location

8/8/2019 Facilty Location

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FACILITY LOCATION

Presented By: Shreyas Todankar Gaurang SampatNikhil Kawde


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What is me ant by Fac ility?

A building or place that provides aparticular service or is used for a

particular industry.

A real property entity consisting of oneor more of the following: a building, astructure


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What is me an ing of lo cat io n ?

A place where something is or could belocated.

A site or position.

A determination of the location of something.


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On w hat p ara me te rs you will de cide

that you requi re addi t io na l f ac ilit y???

O pening of a new venture .

Expansion of existing business .Significant change in existing demand , supplyand marketing location .

Significant change in cost structure .Government policies .

http://www.gyte.edu.tr/dersler/546/ISL536/%C3%9Cretim%205


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FACILITY LOCATION

O nce a firm has decided to open a new facilityOR relocate an existing facility. It must decidewhere that facility should be located.

Facility location problem involves theevaluation of various sites for a new facility.There are several factors that influence the

Facility Location Decision.WHAT ARE THESE FACTORS?????



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FACTORS

Factors Related to Resources

Factors Related to the Market

Factors Related to the Infrastructure


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Fact o rs Rel at ed to Resou rces

Labor availability, Labor cost, Labor Skills;Materials Availability, Material cost, materialquality;Equipment availability, Equipment Cost;Land availability, Land suitability, Land cost;Energy availability, energy cost;Water availability, water quality, water cost.



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Fact o rs Rel at ed to th e M ark e t

P roximity to the firm s market.Size of the market.P otential needs of the market.



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Fact o rs Rel at ed to th e In f ra str uct u re

Availability of Financial Institutions , Strengthof Financial Institutions.Government Stability, Government taxes,Import and Export restrictions.Quality of life , Cultural issues.Environmental regulations , Transportation

availability, Transportation cost.And finally, Competitors size , strength andattitude in that region.



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FACILITY LOCATION

There are many analytical techniques that can be used infacility location decision.Some of these are:

1) Break Even analysis2 ) Single Facility Location Problem3) Factor R ating4) Multifacility Location Problem5) MiniMax Location Problem6) Gravity Location Problem7) Euclidean-Distance Location P roblem8) Covering P roblem9) Model for Warehouse Location P roblem


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B REAK EVEN ANALYSIS

BR EAK EVENanalysis is used in comparingseveral potential locations on an economicbasis .

When the fixed and variable costs for each sitediffer, B R EAK EVENanalysis can be used toidentify the location with the lowest cost.



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Exa mple

A company is considering three alternativesites for its new production facility.T

he AnnualP

roduction Cost associated witheach alternative is a linear function of theproduction volume.

Total P roduction Cost = ( Fixed Cost per year )+ (variable cost per unit ) x (annual productionvolume )



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Example

Plant A B C

Fixedcostper

year

1,00,00,000

2,50,00,000

6,00,00,000

Assume that Theexpected annualproduction volume is2 ,50,000 units.And further assumethat:

( production volume =x = 2 ,50,000 )



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Example

For Site A: P rod. Cost = 1,00,00,000 + 2 50xFor Site B: P rod. Cost = 2 ,50,00,000 + 150x

For Site C: P rod. Cost = 6,00,00,000 + 50x

Based on these information, select which site

has the lowest cost !



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Exa mple

For Site A: P rod. Cost =1,00,00,000 + 2 50(2 ,50,000) = 7, 2 5,00,000.

For Site B:P

rod. Cost =2

,50,00,000+ 150(2 ,50,000) = 6,2 5,00,000 .For Site C: P rod. Cost = 6,00,00,000 + 50(2 ,50,000) = 7, 2 5,00,000.At a production volume of 2 ,50,000 units, siteB has the lowest cost .



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Exa mple



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Example

This graphic shows that annual production costchanges with different production volumes.-If the expected annual production volume is below1,50,000 units, then choose site A.-If the expected annual production volume isbetween 1,50,000 and 3,50,000 units, then choosesite B.-If the expected annual production volume is over3,50,000 units, then choose site C.



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Sing le Fac ilit y Locat io n Problem

Single Facility Location problem helps todetermine the optimal location for the newfacility.It is useful when there are existing facilities &when we have to move the materials fromnew facility to all the existing facilities.

http://books.google.co.in/books?id=6tDjhiQd_WoC&pg=PA98&dq=facility+location+panneerselvam&hl=en&ei=N6inTLS9OouPcbb2kdsN&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDMQ6AEwAA#v=onepage&q=facility%20location%20panneerselvam&f=false


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ExampleSuppose there are 5 existing plants, which have amaterial movement relationship with new plant .Let theexisting plants have locations of (400, 2 00) ,(800,500) ,(1100,800) ,(2 00,900) and(1300,300) .The number of tons of materials transported per yearfrom the new plant to various existing plants are450,1 2 00,300,800 and 1500 .O ur objective is to determine optimum location for thenew plant such as the distance moved (cost) isminimized .



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Example

Let(X,Y) be the coordinate of the new plant.The optimum X coordinate forthe new plant is determined asfollows:The data of existing plants areordered according to their Xcoordinate values.

Next weights are accumulated.The total number of tonstransported per year is 4 2 50.

ExistingPlant

X-Coordinate

Weight CumulativeWeight

4 200 800 800

1 400 450 1250

2 800 1200 2450

3 1100 300 2750

5 1300 1500 4250

Total 4250



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Example

Thus the median location corresponds to acumulative weight of 4 2 50/ 2 =2 12 5.From the above table, the corresponding Xcoordinate value is 800.Since the cumulative weight first exceeds 2 12 5 at X=800



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Example

Similarly, thedeterminationof Y-Coordinate

is as shown :

ExistingPlant

Ycoordinate

Weight Cumulative Weight

1 200 450 450

5 300 1500 1950

2 500 1200 3150

3 800 300 3450

4 900 800 4250

Total 4250http://books.google.co.in/books?id=6tDjhiQd_WoC&pg=PA98&dq=facility+location+panneerselvam&hl=en&ei=N6inTLS9OouPcbb2kdsN&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDMQ6AEwAA#v=onepage&q=facility%20location%20panneerselvam&f=false


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Example

The median location on Y axis corresponding to thecumulative weight 4 2 50/ 2 =2 12 5 is 500.Hence, the optimal Y coordinate for new facility is500.Thus, optimal (X*,Y*) =(800,500) .The new facility location should be at ( 800,500 ) co-

ordinates.



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Me th od of F act o r Rat ing

In factor rating method, first we must identify theMost Important Factors in evaluating alternative sitesfor the new facility.Then we should assign a weight between 0 and 100to each of these factors.Each alternative location will then be rated based onthese factor weights.The most weighted alternative is selected as the bestalternative .



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Example

Samsung Ltd. is considering three alternativesites for its new facility.After evaluating the firm s Needs , theManagers have Narrowed the list of ImportantSelection Criteria down into three majorFactors.

- Availability of skilled labor .- Availability of R aw materials .- P roximity to the firm s markets .



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ExampleWeights reflecting the relative importanceof each factor have been assigned asfollows:

FACTOR WEIGHT Availability of skilledlabor

0.50

Availability of Raw

materials

0.30

Proximity to the firmsmarkets.

0.20

TOTAL 1.00http://www.gyte.edu.tr/dersler/546/ISL536/%C3%9Cretim%205


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Example

Based on these criteria, the three Alternative siteswere scored between 0 and 100 points:



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Exa mpleNow we will multiply each score by its correspondingfactor weight:Weighted scores = (Site Score) x (Factor Weight)



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Example

From these results, the largest total weight isfor Site A .

It appears to be the best location.Since factor weights, selected factors andassigned scores are all determinedsubjectively, the managers should be verycareful in selecting these items and numbers.



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Mul t if ac ilit y Locat io n Problem

In this problem our objective is to locateseveral new facilities in relation to a set of existing facilities, such that the total cost of

transportation between the new facilities andthe set of existing facilities in minimised.



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Mi nim ax Locat io n Problem

Minimax Location problems gives us the idea how tolocate a new emergency facility that will serve thealready existing facility.

Thus, it helps to locate the new emergency facility suchthat the maximum distance from the new emergencyfacility to any of the existing facilities is minimized.The distance between the new facility and the existing

facilities may be rectilinear or euclidean.



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Example

In a foundry, there are seven shops whose coordinatesare summarized in the following table:Sr. No Exist ing Fac ilit y Coo rdinat es of Ce ntr oid

1 Sand P lant 10, 2 0

2 Moulding Shop 30,40

3 P attern Shop 10,1 2 0

4 Melting Shop 10,60

5 Felting Shop 30,100

6 Gouging Shop 30,1407 Annealing Shop 2 0,190

T he Company is interested in locating a new costly fire fighting equipmentin the foundry. Determine the minimax location for the new equipment.



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The P roblem can be solved by using the followingformulas:

To find C1,C 2 ,C3,C4 and C5 the following formulas can beused:

C1=min (ai +bi)C2 =max (ai+bi)

C3=min (-ai+bi)C4=max (-ai+bi)C5=max(C 2 -C1,C4-C3)

To find the points

P1 and

P2using the following formulaP 1=[1/ 2 (C1-C3),1/ 2 (C1+C3+C5)]

P2 =[1/ 2 (C2 -C4),1/ 2 (C2 +C4-C5)]



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(a1,b1)x

(a2 ,b2 )x

L1

L2

L3

L4(x,y)

(a3,b3)

x

x

(a4,b4)

The objective is to minimize Fmax ( x , y ). We have toidentify x*, y* such that max ( L1, L 2 , L3, L4) isminimized.

Exa mple



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Example

The company is interested in locating a new costly fire fightingequipment in the foundry. Determine the minimax locationfor new equipment.Since, the movement of the new equipment is constrainedwithin the foundry, the assumption of rectilinear distance ismore appropriate.The coordinates of the centroids of the existing shops are asfollows :

(a1,b1)=10, 2 0 (a5,b5)=30,100

(a2 ,b 2 )=30,40 (a6,b6)=30,140(a3,b3)=10,1 2 0 (a7,b7)= 2 0,190(a4,b4)=10,60



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Example

C1=min[ai+bi]=min[(10+ 2 0),(30+140),(10+1 2 0),(10+60),(30+100),(30+140),( 2 0+190)]

= min[30,70,130,70130,170, 2 10]= 30

C2 = max[ai+bi]=max[(10+ 2 0),(30+40),(10+1 2 0),(10+60),

(30+100),(30+140),(2

0+190)]= max[30,70,130,70,130,170, 2 10]= 2 10

C3=min[-ai+bi]=min[(-10+ 2 0),(-30+40),(-10+1 2 0),(-10+60),(-30+100)(-30+140),(- 2 0+190)

= min[10,10,110,50,70,110,170]= 10

C4=max[-ai+bi]=max [(-10+ 2 0),(-30+40),(-10+1 2 0),(-10+60),(-30+100),(-30+140),(- 2 0+190)]

=max[10,10,110,50,70,110,170]= 170



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Exa mpleC5=max[C2 -C1),(C4-C3)]

=max[( 2 10-30),(170-10)]max[180,160]

=180Step 2

P 1=[1/ 2 (C1-C3),1/ 2 (C1+C3+C5)]=[1/ 2 (30-10),1/ 2 (30+10+180)]=(10,110)

P2 =[1/ 2 (C2 -C4),1/1(C 2 +C4-C5)]=[1/ 2 (2 10-170),1/ 2 (2 10+170-180)]

=(2 0,100)

Any point X*,Y* on the line segment joining points (10,110)and ( 2 0,100)isa minimax location for the fighting equipment



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G rav it y Locat io n Problem

The center of gravity method is used to find alocation that Minimizes the Sum of Transportation Cost in between new facility

and old facilities.The location of the firm s existing facilities areconverted into x and y coordinates.T

he following center of gravity equations arethen used for calculating the x and ycoordinates for the new facility:



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Cent e r of G rav it y Me th od

Cx : x coordinate for new location.Cy : y coordinate for new location.i: index for existing locations.n: total number of existing locations.xi: x coordinate of i th existing location.yi: y coordinate of i th existing location.Vi: weight associated with the existing

location i .



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Cent e r of G rav it y Me th od



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Example

Five facilities areto be served by asingle new facility.

The details aregiven below:

Existingfacility

(i)

Coordinates(xi,yi)

No. of tripsof loads/year

(Vi)

1 5,10 100

2 20,5 3003 15,20 200

4 30,25 300

5 25,5 100http://www.gyte.edu.tr/dersler/546/ISL536/%C3%9Cretim%205


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Example

Cx=(100*5+300* 2 0+2 00*15+300*30+100* 2 5)( 100+300+ 2 00+300+100 )

=2 1000/1000

=2 1Cy=(100*10+300*5+ 2 00 2 0+300* 2 5+100*5)

(100+300+ 2 00+300+100 )

=14500/1000=14.5The optimal location of the new facility is ( 2 1,14.5).



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Euclide an-D istanc e Lo cat io n Problem

The objective of this problem is to locate thenew(single)facility in relation to the set of existingfacilities such that the total cost of materials handling is

minimized based on euclidean distance.The formula to compute the euclidean distance is:euclidean distance = [( p r ) 2 + ( q s ) 2 ] 1/ 2

Where (p , q) & (r , s) are the coordinates of the two

locations.



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Euclide an Distanc e

The formula to compute the total weighted Euclideandistance is:

Where: m= no of existing facilitiesa i= x coordinate of i th existing facility.b i= y coordinate of i th existing facility.

x= x coordinate of new facility.y= y coordinate of new facility.w i= weight associated with the existing facility i.



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The objective is to find (x*,y*) such that f(x,y)isminimized. The O bjective is in quadratic form, partialderivates of the objective function with respect to x* andy* are to be equated to zero to find the optimal x*,y*. Thepartial derivatives are shown below:

For any i,if x*=a1 and y*=b1,then the denominator of the partial derivatives will be zero.So the x* and y* values will be infinite



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Covering P roblem

Total Covering P roblem: The aim is to cover allthe customers with minimum number of facilities .

P artial Covering P roblem: The aim is to coveras many customers as possible with a givenmaximum number of facilities .



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Total Covering P roblem

Consider a set of residential regions in a statewhich are to be covered by set of dealersIf the dealer is said to located in the distanceof say 30 Km from the residential areaIn this example, if the objective is to cover allthe residential regions with minimum numberof dealers then it is TO TAL CO VER INGP RO BLEM



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Examples of covering problem

Locating minimum number of fire extinguishers tocover various departments in large scale industryLocating various number of health centres to cover

various areas in a stateLocation minimum number of schools to covervarious villages in districtLocating minimum number of emergency food grainreserve stations to supply food grains to variousregions worldwide.



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The table summarizes the distance between30 major areas in a state it is desired to locatefacilities among the areas such that no area ismore than, say, 69 miles from the facility. Thismeans that if d ij < 69 miles, then the area i iscovered by area j; otherwise the area i is not

covered by area j.



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Thank You!

Facilty Location

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