facility location operations management dr. ron tibben-lembke
Post on 19-Dec-2015
233 views
TRANSCRIPT
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 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
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
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
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.
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.
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
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
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
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
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)
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