Facility Location

Operations Management

Dr. Ron Tibben-Lembke

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

Wal-Mart

WinCoOfficeMax

ToysParty

A Tale of Two Stores

K

W

“I-80 & McCarran” sounds great.

Kmart Sins:Can’t see from anywhere- see where we’re goingVery circuitous entry- feels inconvenient, no matter how long it actually takes

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

Case Study:Importing from China to E. Coast

Customer Location

InterstateDetail

New Orleans $3,20036 days

NY / NJ $3,60036 days

Wilmington DE $3,95036 days (door)

Norfolk $3,60034 days

Charleston $3,60035 days

China to U.S. Container Rates

Atlanta$3,20037 days (door)

Roanoke

Norfolk

Philadelphia

Baltimore

Allentown

Harrisburg

750

850

850

750

750

825

Elizabeth, NJ

350

656375

950

575 305

1125

305

780

375

305

428

888

725

265

343 295

950

DrayageRates North Wilmington

China to Long Beach

Cincinnati $2925, 21d

Columbus $3000, 21days

Atlanta $3300, 23d

Memphis $2900, 18.5d

Murray $3350, 22d

Nashville$3300, 22d

Louisville $3050, 20d

Landbridge Data

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?

Case Study: Retailer

Location of a 5th returns processing facility Addresses of 2125 Continental U.S. stores Location of 4 Return Goods Processing

Centers List of all return shipments from each

store, including pounds and # pallets Calculated actual highway distances from

every store to its DC

Local Streets

Transportation Cost Approx.

Current Pallets: 205,254 Current Pallet Miles: 77.9m Cost / pallet-mile 11.68 cents Pallet-Mile = 1 pallet traveling 1 mile Minimize average distance traveled

Solution Software

Some locations must have a facility Considers adding a facility at every existing

store We won’t really build next to a store, but that’s ok

Finds one best facility to add Finds second best facility to add Reconsider first added facility, then second, etc. Improvement heuristics, optimal methods

Current RCs

Dallas Realignment

Close 1 existing RDC

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 (P-Median Problem, Maximum Covering)

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 X Y Demand Reno is at 17, 55 100 Dallas is at 78, 20 90 Chicago is at 110, 65 120

Demand is TL/month

Center of Gravity

12011090

120*110*90

ii

iiix

X W

WdC

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

Salina KS

North Platte

SharonSprings

Compromise Solution

Closest town is Sharon Springs, KNPopulation 87230 miles from I-70.Probably not a good choice

Salina, KN puts us at I-70 and I-35 North Platte NE is at I-80 and 83.

Access to Dallas less convenient

0 20 40 60 80 100 120 140 160

80

20

40

60

0

100

Finalizing City

Go where other warehouses are More choice in pre-built buildings Cheaper, easier to build a new one More trucks to and from town, means more carriers

there, means cheaper rates. Backhaul situation

Get estimates of inbound, outbound trucking costs. Provide lists of # loads per year to each destination,

from each source

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

12011090

120*110*90

ii

iiix

X W

WdC

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 HeuristicMinimize cost (distance) traveled

From

To A B C D Dem.

A 0 11 8 12 10

B 11 0 10 7 8

C 8 10 0 9 20

D 9.5 7 9 0 12

The distance from A to A is shown as 0, but there is no reason we couldn’t put the actual mileage in.

Carriers might charge more on popular routes, so costs may not be symmetrical.Cost to serve A from D is $12.Cost to serve D from A is $9.5.

Ardalan Method Expected demand at each location. Step 1: Multiply distances * demand A to B: 11 * 10 = 110

Ardalan Heuristic Multiply distances times demand, and sum

To A B C D * Dem = AB C D

A 0 11 8 12 * 10 0110 80 120

B 11 0 10 7 * 8 880 80 56

C 8 10 0 9 * 20 160200 0 180

D 9.5 7 9 0 * 12 11484 108 0

Total 362 394268 356

Ardalan Heuristic Choose smallest total as first location

A B C D

A 0 110 80 120

B 88 0 80 56

C 160 200 0 180

D 114 84 108 0

Total 362 394 268 356

If we only build one facility, we should build it in C, and the total transportation costs will be 268. (This is in dollars, or truckload miles, or whatever the units in the table were.)

Notice that even if we built a facility in B or D, it will continue to be cheaper to serve A from C.In the next step, we will make use of that.

Ardalan Heuristic Compare each cost in row to the cost in

the chosen cost, and switch is lower

A B C D

A 0 80 80 80

B 80 0 80 56

C 0 0 0 0

D 108 84 108 0

Total 188 164 268 136

Why do we do that? Before, the first row said “0, 110, 80, 120.”We’ve decided to build in CIf we build in A, B, or D, how much will we spend to haul to A? No matter what, we’ll spend 80.

If we locate in D, we’ll serve B from D, but otherwise, we’ll serve B from C, because it’s cheaper.

Ardalan Heuristic Don’t need first chosen city any more. Choose second cheapest city

A B D

A 0 80 80

B 80 0 56

C 0 0 0

D 108 84 0

Total 188 164 136

This means that if we locate #2 in D (and we already decided to locate one in C), total costs will be $136. How? A served at cost of $80 by C.B served at cost of $56 by D.C served at cost of $0 by C.D served at cost of $0 by D.

This is why we needed to change the costs above.

Ardalan Heuristic Compare non-chosen cities’ costs to cost

of chosen, and choose the lower cost

From A B D

A 0 80 80

B 56 0 56

C 0 0 0

D 0 0 0

Total 56 80 136

Ardalan Heuristic Compare non-chosen cities’ costs to cost

of chosen, and choose the lower cost

From A B

A 0 80

B 56 0

C 0 0

D 0 0

Total 56 80

If we locate the third facility in A, we will have facilities in C, D, and A. B is the only city without a DC, and it will be served at a cost of $56.

What happens if we do the method one more time?

Ardalan Heuristic Compare non-chosen cities’ costs to cost

of chosen, and choose the lower cost

From A B

A 0 0

B 56 0

C 0 0

D 0 0

Total 56 0

After we get rid of the now-unnecessary column A, there is only column B, with total costs of 0.Does that make sense? Well, yes: every city gets served by the DC located in that city, so if the cost of serving a city from that city is 0, then yes, it makes sense.

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.

P-Median Problem

Minimize average weighted distance to customers, when locating P facilities, where P>=1.

Can consider 100s of locations. Complex to solve – there is software for

this.

Maximum Covering Problem

A facility can “cover” a customer if the customer is within X miles of the facility.

Try to find the best location, and minimum number of facilities to cover all demands.

Cover a table with plates. Math also very hard.

90.00%

91.00%

92.00%

93.00%

94.00%

95.00%

96.00%

97.00%

98.00%

99.00%

100.00%

15 16 17 18 19 20 21 22 23 24 25 26

Lower Bound

Greedy Solution

Upper Bound

Comparison of Results

Number of Facilities

Dem

and

Cov

ered

(Using Distances of 150, 200, 250,250)

Solving large problems

Incremental or clean-slate apprach

Take into account existing facilities What is the best location to add, given the

existing facilities? What is the best to add, if we were to

close down one of the current facilities? Unfortunately, only P-Median or Maximum

Covering can deal with these.

Factor Rating Method

Most widely used method? Useful for service or industrial facilities: can

include intangible, qualitative factors List relevant factors, assign a weight Develop a scale for each factor Score each factor using the scale Multiply scores by weights, add up Choose location with highest total score Kind of like “Miss America”

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 1023

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

Plant Lease: 39/45 * 10 = 8.7 Transportation: 900/1,023 * 10 = 8.8

Multiply these raw scores by the weights for weighted scores

Factor Rating Example

TX CO

Factor Wt Raw Wtd Raw Wtd

Transp. 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, but not by a huge amount

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

Hey – this sounds familiar!

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