Location Planning and Analysis

DefinitionDefinition of Facility Planningof Facility Planning

Facility Planning determines how an activity’s tangible fixed assets

best support achieving the activity’s objectives.

Examples:

a. In manufacturing, the objective is to support production.

b. In an airport, the objective is to support the passenger airplane

interface.

c. In a hospital, the objective is to provide medical care to patients.

Hierarchy of Facility PlanningHierarchy of Facility Planning

Location: is the placement of a facility with respect to customers, suppliers, and other facilities with which it interfaces.

Structure: consists of the building and services (e.g., gas, water, power, heat, light, air, sewage).

Layout: consists of all equipment, machinery, and furnishings within the structure.

Handling System: consists of the mechanism by which all interactions required by the layout are satisfied (e.g., materials, personnel, information, and equipment handling systems).

Facility Planning

Structural Design

Facility Location

Facility Design

Layout Design

Handling System Design

Need for Location DecisionsNeed for Location Decisions

Marketing Strategy

Cost of Doing Business

Growth

Depletion of Resources

Making Location DecisionsMaking Location Decisions

Decide on the criteria Identify the important factors Develop location alternatives Evaluate the alternatives Make selection

Location Decision FactorsLocation Decision Factors

Regional Factors

Site-related Factors

Multiple Plant Strategies

Community Considerations

Evaluating LocationsEvaluating Locations

Transportation Model Decision based on movement costs of raw

materials or finished goods Factor Rating

Decision based on quantitative and qualitative inputs

Center of Gravity Method Decision based on minimum distribution costs

Factor RatingFactor Rating

General approach to evaluating locations that includes quantitative and qualitative inputs.

ExampleExample 1 1

A photo-processing company intends to open a new branch store. The following table contains information on two potential locations. Which is the better alternative?

Alternative 2 is better because it has the higher composite score.

Example 2Example 2

Using the following factor ratings, determine which location alternative should be chosen on the basis of maximum composite score, A, B, or C.

Example 2Example 2

Solution:

Therefore, Location A is better.

The Center of Gravity MethodThe Center of Gravity Method

The method use to determine the location of a facility that will minimize shipping costs or travel time to various destinations.

If the quantities to be shipped in every If the quantities to be shipped in every location are equallocation are equal

where:

n = Number of destinations.

xi = x coordinate of destination i.

yi = y coordinate of destination i.

n

x

xi

n

y

yi

When the number of units to be When the number of units to be shipped is not the same for all shipped is not the same for all

destinationsdestinations

i

ii

Q

Qx

x

i

ii

Q

Qy

y

whereQi = Quantity to be shipped to destination ixi = x coordinate of destination iyi = y coordinate of destination i

ExampleExample 1 1Destination x, y

D1 2, 2

D2 3, 5

D3 5, 4

D4 8, 5

18 16

5.44

18

n

x

xi

44

16

n

y

yi

Hence, the center of gravity is at (4.5,4).

Example 2Example 2Destination x, y Weekly Quantity

D1 2, 2 800

D2 3, 5 900

D3 5, 4 200

D4 8, 5 100

2000

3) to(round05.32000

6100

2000

)100(8)200(5)900(3)800(2

i

ii

Q

Qx

x

70.32000

7400

2000

)100(5)200(4)900(5)800(2

i

ii

Q

Qy

y

Hence, the center of gravity are approximately (3,3.7). This would place it south of destination D2, which has coordinates of (3,5).

Example 3Example 3

Destination x,yCoordinates

Weekly Quantity

D1 3,5 20

D2 6,8 10

D3 2,7 15

D4 4,5 15

60

5.360

210

60

)15(4)15(2)10(6)20(3

i

ii

Q

Qx

x

0.660

360

60

)15(5)15(7)10(8)20(5

i

ii

Q

Qy

y

Hence, the center of gravity has the coordinates x = 3.5 and y = 6.0

The Transportation Model

Requirements for Transportation Requirements for Transportation ModelModel

List of origins and each one’s capacity

List of destinations and each one’s demand

Unit cost of shipping

Transportation Model AssumptionsTransportation Model Assumptions

1. Items to be shipped are homogeneous

2. Shipping cost per unit is the same

3. Only one route between origin and destination

The Transportation ProblemThe Transportation Problem

D(demand)

D(demand)

D(demand)

D(demand)

S(supply)

S(supply)

S(supply)

m- number of sources n- number of destinations ai- supply at source I

bj – demand at destination j

cij – cost of transportation per unit from source i to destination j

Xij – number of units to be transported from the source i to destination j

DESTINATION j

cc1111 cc1212 cc1j1j cc1n1n

cci1i1 cci2i2 ccijij ccinin

ccm1m1 ccm2m2 ccmnmn

SOURCE i

12

i

m

1 2 j n

Demand b1 b2 bj bn

Supply a1

a2

ai

am

Transportation problem: Transportation problem: represented as an LP modelrepresented as an LP model

njandmiforX

njbX

miaXtosubject

XcZMinimize

ij

j

m

iij

i

n

jij

ij

m

i

n

jij

,..1,...10

,.....,2,1

,....,2,1

:

1

1

1 1

Summary of ProcedureSummary of Procedure

Make certain that supply and demand are equal

Develop an initial solution using intuitive, low-cost approach

Check that completed cells = m+n-1

Evaluate each empty cell

Repeat until all cells are zero or positive

Determination of Starting Basic Feasible Determination of Starting Basic Feasible SolutionSolution

•NORTH-WEST Corner MethodNORTH-WEST Corner Method - - is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North – West corner.

•LEAST COST Method - LEAST COST Method - This method takes consideration the lowest cost and therefore takes the less time to solve the problem.

•Vogel’s Approximation Method (VAM) - Vogel’s Approximation Method (VAM) - This method also takes costs into account in allocation.

VAM usually produces an optimal or near- optimal starting solution. One study found that VAM yields an optimum solution in 80 percent of the sample problems tested.

The Amulya Milk Company has three plants located throughout a state with production capacity 5000, 2000 and 3000 gallons. Each day the firm must furnish its four retail shops with at least 3000, 3000 , 2000, and 2000 gallons respectively.

Example 1Example 1

33 77 66 44 55

22 44 33 22 22

44 33 88 55 33

33 33 22 22

Destination 1 2 3 4 Supply Row Penalties

Source

1

2

3

Demand

Total shipping cost = 32

Column Penalties

1

0

1

1 1 3 2

2

0

1

-

1

1 4 - 1

3

0

3 0 0 2

TOFROM

A B C SUPPLY

W 9 8 525

X 6 8 435

Y 7 6 940

DEMAND 30 25 45 100100

ROW/COLUMN SEC-LOWEST COST ━ LOWEST COST = OPPORT-CST

ROW W 8 5 3 LARGEST

ROW X 6 4 2

ROW Y 7 6 1

COLUMN A 7 6 1

COLUMN B 8 6 2

COLUMN C 5 4 1

25

20

Example 2Example 2

VAM: VOGEL APPROXIMATION METHOD

TOFROM

A B C SUPPLY

W 9 8 525

X 6 8 435

Y 7 6 940

DEMAND 30 25 45 100100

ROW/COLUMN SEC-LOWEST COST ━ LOWEST COST = OPPORT-CST

ROW X 6 4 2

ROW Y 7 6 1

COLUMN A 7 6 1

COLUMN B 8 6 2

COLUMN C 9 4 5 LARGEST

25

20

20

15

VAM: VOGEL APPROXIMATION METHOD

TOFROM

A B C SUPPLY

W 9 8 525

X 6 8 435

Y 7 6 940

DEMAND 30 25 45 100100

ROW/COLUMN SEC-LOWEST COST ━ LOWEST COST = OPPORT-CST

ROW X 8 6 2 LARGEST

ROW Y 7 6 1

COLUMN A 7 6 1

COLUMN B 8 6 2 LARGEST

25

20

25

15

15

20

TOFROM

A B C SUPPLY

W WA 9 WB 8 WC 525

X XA 6 XB 8 XC 435

Y YA 7 YB 6 YC 940

DEMAND 30 25 45 100100

25

20

2515

15

Q X COST / UNIT = TC ($)

WC 25 5 125

XA 15 6 90

XC 20 4 80

YA 15 7 105

YB 25 6 150

TOTAL TRANSPORTATION COST 540

15

15

20