facility location operations management. location decisions long-term decisions difficult to reverse...

Facility Location

Operations Management

Location Decisions

Long-term decisions Difficult to reverse Affect fixed & variable costs

Transportation costs (25% of price)Other costs: taxes, wages, rent

Objective: maximize benefit of location to firm

What factors should we consider?

Skilled workforce Environmental laws / cost of compliance Cost of utilities, labor, taxes Suppliers close by – fast & cheap access Customers close by Competitors close by? Skilled labor pool International - control issues?

Service Facilities – Traffic focus Revenue changes a huge amount, depending on the

location. Old Navy in Stead because of cheap land? Location, location, location: you need traffic Make it convenient! vitamins: need enough, but it has to be the right kind people who would want to buy your products when they are

there. Cost probably doesn’t change nearly as much, by

location All malls have high rent

Cost Focus

Revenue does not vary much, depending on the location.Customers don’t care if your warehouse is in

Sparks or Sacramento Location is a major cost driver

Impacts shipping, labor, production costsVaries greatly by location

Cost Minimization

Identify the costs that will vary most with the location you choose. Transportation, taxes, labor, Facility construction cost, utilities

Other considerationsProximity of services, suppliersQuality of lifeGovernment incentives

Cost Focus Process Overview

1. Identify general region to locate in Usually based on mostly on transp. costs

2. Identify a list of candidate cities Choose cities with good transp. Access Estimate labor cost & availability, facilities costs

3. Select metro area, identify candidate properties.

Find cost of building or leasing individual properties

Distribution Center Location

Minimize demand-weighted distance: distance to each customer times the volume of shipments to the customer

How many to build? Where to build?

Location Methods

Minimize demand-weighted distance Center of Gravity – minimizing demand-weighted

distances of one facility Ardalan – minimize transportation of multiple facilities,

but must locate by customers

Factor Weighting – consider qualitative factors Break-even – Consider fixed & variable costs

Center of Gravity

Compute X and Y coordinates separately

dix is the X coordinate of location i.

diy is the Y coordinate of i.

Wi is the X demand at i.

CX and CY are the coordinates of the DC.

ii

iiix

X W

WdC

ii

iiiy

Y W

WdC

Center of Gravity Example 1

You need to decide where to build a new DC for Motorola.

It needs to serve wholesalers in Reno, Dallas, and Chicago.

Locate these cities on an unscientific, rectangular grid.

Grid must maintain relative distances, but X and Y grids could be different.

0 20 40 60 80 100 120 140 160

80

20

40

60

0

100

Center of Gravity Method

City Demand Reno is at 17, 55 100 Fort Worth is at 78, 20 90 Chicago is at 110, 65. 120

Demand is TL/month

Center of Gravity

7.70310

920,21

310

200,13020,7700,1

12090100

120*11090*78100*17

X

ii

iiix

X

C

W

WdC

7.48310

100,15

310

800,7800,1500,5

12090100

120*6590*20100*55

Y

ii

iiiy

Y

C

W

WdC

0 20 40 60 80 100 120 140 160

80

20

40

60

0

100

Center of Gravity Example 2

You need to decide where to locate a DC in South Dakota

X Y Demand Pierre 78 47 50 Watertown 150 65 8 Sioux Falls 160 25 90 Rapid 12 42 60

0 20 40 60 80 100 120 140 160

80

20

40

60

0

100

Center of Gravity

2.97208

220,20

208

720400,14200,1900,3

6090850

60*1290*1608*15050*78

X

ii

iiix

X

C

W

WdC

7.36310

640,7

208

520,2250,2520350,2

6090850

60*4290*258*6550*47

Y

ii

iiiy

Y

C

W

WdC

0 20 40 60 80 100 120 140 160

80

20

40

60

0

100

Ardalan Heuristic

Need a matrix of distances or costs from each customer location to every other location

Demand at each location Weight – give higher weight to more important

customers – their pain of traveling a longer distance is worth more.

Only consider locating where customers are Identify the one best place to locate at, then the

second one to add, then the third, etc.

Ardalan Heuristic Minimize weighted distance traveled

To

FromA B C D Dem.Weight

A 0 11 8 12 10 1.1

B 11 0 10 7 8 1.4

C 8 10 0 9 20 0.7

D 9.5 7 9 0 12 1.0

Ardalan Method Expected demand at each location. Weight represents importance of serving

location (bigger = more important) Step 1: Multiply distances * weights *

demand A to B: 11 * 1.1 * 10 = 121

Ardalan MethodStep 2. Add up values in columns

FromA B C D

A 0 121 88 132

B 123.2 0 112 78.4

C 112 140 0 126

D 114 84 108 0

349.2 345 308 336.4

Ardalan MethodChoose smallest value as first site.

FromA B C D

A 0 121 88 132

B 123.2 0 112 78.4

C 112 140 0 126

D 114 84 108 0

349.2 345 308 336.4

Ardalan Method3. If larger, set each cost equal to cost in same row

in the chosen column

FromA B C DA 0 88 88 88B 112 0 112 78.4C 0 0 0 0D 108 84 108 0

220 172 308 166.4

Ardalan Method

Get rid of previously chosen column.Sum, choose smallest sum.FromA B D

A 0 88 88B 112 0 78.4C 0 0 0D 108 84 0

220 172 166.4

Ardalan Method

Repeat 3 & 4 until enough sites chosen.

FromA B D

A 0 88 88

B 78.4 0 78.4

C 0 0 0

D 0 0 0

78.4 88 166.4

Ardalan Method

Repeat 3 & 4 until enough sites chosen.

From A B

A 0 88

B 78.4 0

C 0 0

D 0 0

78.4 88

Ardalan Summary

What we decided is that if we only want to build one location, it should be in C.

If we want to build two, they should be in C and D. If we add a third one, it should be in A.

Ardalan Summary

Assumes that we have to locate in the same city as one of our customers, which is not always the case.

However, it can be used to find more than one location. Center of Gravity does not try to locate in the same city

as one of the customers, but can only set one site. If we choose the same sites as customers A and X, we

obviously don’t really have to put the warehouses in those exact cities.

Factor Rating Example

We need to decide where to build a new coffee roasting plant. There are two possible locations: Dallas, and Denver.

We consider the following factors Transp: annual trucking costs in $k Lease: annual costs in $k Labor availability: scale 1-10, unemployment, related

industries Quality of life: scale 1-10: outdoor activities, cultural,

sports, education

Factor Rating Example

Using a scoring system we developed, we have the following.

Factor Weight TX CO

Transportation 0.5 900 1,023

Plant Lease Cost 0.3 45 39

Labor availability 0.2 10 8

Quality of Life 0.1 7 9.5

Normalizing Scores

All factors must be scored on the same scale, like 1-10, or 0-1.0, etc.

Costs need to be re-scaledLowest cost site gets a 10.More expensive site gets less than 10

Factor Rating Example

TX CO

Factor Wt Raw Wtd Raw Wtd

Tr 0.4 10 4.00 8.80 3.52

Plant 0.3 8.7 2.61 10 3.00

Labor 0.2 10 2.00 8 1.60

Q Life 0.1 7 0.70 9.5 0.95

TOTAL 9.31 9.07

TX is best

Possible Approach Use Ardalan to find out which general

regions to locate in (state / county). Use factor weighting to choose city. Ardalan has disadvantage of choosing

weights -- difficult to set levels.

Break-Even Analysis

Determine fixed and variable costs for each location

Fixed cost: how much it would cost to open a facility there

Variable cost: how much total costs would increase as production increases: Transportation costs Labor costs Taxes Increased construction costs

Locating Service FacilitiesUsing Linear Regression Collect data about your current facilities Use regression to determine which

variables have a significant impact on profits

Choose new facilities which have these characteristics

Method Comparison Center of gravity minimizes average distance

for one facility only. Ardalan Minimizes weighted distances for

more than one facility. Breakeven: fixed & variable costs. Factor weighting considers many other

important aspects of location, but does not minimize distance.

Transportation Method

You have 3 DCs, and need to deliver product to 4 customers.

Find cheapest way to satisfy all demand

A 10

B 10

C 10

D 2

E 4

F 12

G 11

Solving Transportation Problems

Trial and Error Linear Programming

– ooh, what’s that?! Tell me more!

D E F G

A 10 9 8 7

B 10 11 4 5

C 8 7 4 8