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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

“I-80 & McCarran” sounds great.

- Kmart Sins:
- Can’t see from anywhere
- - see where we’re going
- Very 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 costs
- Varies 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 considerations

- Proximity of services, suppliers
- Quality of life
- Government incentives

Cost Focus Process Overview

- Identify general region to locate in
- Usually based on mostly on transp. costs
- Identify a list of candidate cities
- Choose cities with good transp. Access
- Estimate labor cost & availability, facilities costs
- Select metro area, identify candidate properties.
- Find cost of building or leasing individual properties

Interstate

Detail

China to U.S. Container Rates

NY / NJ $3,600

36 days

Wilmington DE $3,950

36 days (door)

Norfolk $3,600

34 days

Charleston $3,600

35 days

Atlanta

$3,200

37 days (door)

New Orleans $3,200

36 days

Allentown

305

575

428

DrayageRates

North

Elizabeth, NJ

850

Harrisburg

295

343

350

Philadelphia

305

265

375

850

Wilmington

656

825

750

Baltimore

305

375

750

780

950

1125

725

950

888

Roanoke

750

Norfolk

Landbridge Data

Columbus $3000, 21days

Cincinnati $2925, 21d

Louisville $3050, 20d

Murray $3350, 22d

Nashville

$3300, 22d

Memphis $2900, 18.5d

Atlanta $3300, 23d

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

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

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.

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.

Center of Gravity Method

City X YDemand

- Reno is at 17, 55100
- Dallas is at 78, 2090
- Chicago is at 110, 65120
- Demand is TL/month

Compromise Solution

- Closest town is Sharon Springs, KN
- Population 872
- 30 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

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

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 cost (distance) traveled

From

ToA B C DDem.

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

ToA B C D * Dem = A B C D

A 0 11 8 12 * 10 0 110 80 120

B 11 0 10 7 * 8 88 0 80 56

C 8 10 0 9 * 20 160 200 0 180

D 9.5 7 9 0 * 12 114 84 108 0

Total 362 394 268 356

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 C

If 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.

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-scaled
- Lowest 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

TXCO

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 Facilities

Using 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

D 2

A 10

E 4

B 10

F 12

C 10

G 11

Solving Transportation Problems

- Trial and Error
- Linear Programming – ooh, what’s that?!
- Tell me more!

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