Warehouse Location - The FMC Corporation*
The FMC Corporation is a large diversified producer ofmachinery, chemicals, films, and fibers such as nylon. The companyhas annual sales which place it in the top hundred corporations inthe nation. The study presented in this case was done for FMC'sLink-Belt Products Division, manufacturers of a broad line ofindustrial equipment. The study was done by FMC's own consultants,people who are available to work with any of the company'sdivisions.
A few years before the beginning of this study, Link-Beltmanagement began to feel that perhaps it should reduce the numberof warehouses. This feeling was based on several factors, includingthe decrease in transportation time necessary to reach customers,the lower cost of communication services, higher labor costs, andimprovements in techniques of automating warehouses.
The company had warehouses in Philadelphia; Atlanta; Columbus,Ohio; Chicago; Kansas City; Dallas; Reno; Seattle; Houston; andPortland, Oregon. The question presented by the Link-Beltmanagement to the consultants: Should any of the current warehousesbe closed, and, in general, what possible configuration ofwarehouse sites would provide the lowest possible cost while stillproviding good service to customers?
Dollar amounts reflecting total warehouse sales, tonnageshandled, and total operating costs are considered confidential byFMC. However, in the most recent year for which an analysis offigures could be made, the percentage breakdown for Link-Belt'swarehouse operating costs were as follows: 19% for freight, 42% forinventory investment, and 39% for operating expenses.
To begin the analysis, 17 additional cities were selected aspotential warehouse sites. Since construction and land costs varyfrom city to city, it was necessary to develop for each city anequation which represented the local costs of construction. Indeveloping this equation, we shall use the following variable.
A = warehouse floor area (in thousands of square feet)
Cc = cost of labor and materials to build a warehouse (in thousandsof dollars)
L = amount of land needed for warehouse (in acres)
C1 = cost of land (in thousands of dollars)
I = inventory in a warehouse at a given time (in pounds)
T = total quantity of merchandise going through a warehouse in ayear (in thousands of pounds)
For example, if A represents the warehouse area in thousands ofsquare feet, and Cc represents the cost of labor and materials inthousands of dollars, then
Cc = 12.5 + 3.75A
was found to provide a good approximation to the cost for labor andmaterials in Atlanta, while
Cc = 18.75 + 5.6A
is a similar equation for Chicago. These equations were obtained bystudying construction costs in the cities in question.
Land prices also vary from city to city. Again using informationobtained about each of the cities in question, it was estimatedthat the amount of land, L, in acres, needed for a warehouse ofarea A, in thousands of square feet, is given by
L = 0.875 + 0.0315A.
For Chicago, the cost of this land, C1, in thousands of dollars, isgiven by A, in thousands of square feet, is given by
C1 = 30.6 + 1.10A,
while the cost equation for Atlanta is
C1 = 14.8 + 0.94A.
Based on past records, the company knows that one square foot ofwarehouse area can store about 70 pounds of merchandise, or, if Irepresents inventory measured in pounds in a warehouse at a giventime, then
I = 70A.
The inventory at a given time, again from experience, is also givenby
I = 180 + 0.1435T,
where T is the total weight of merchandise in thousands of poundsthat go through the warehouse in a year.
Using the above equations, we can find the cost of land, labor,and materials for a new warehouse in Chicago in terms of T—that is,we can find the cost in terms of the quantity of merchandise goingthrough the warehouse in a year. To find the cost for labor andmaterials, we begin with
Cc = 18.75 + 5.6A,
and since I = 70A, or A = I/70, we get
We also know that I = 180 + 0.1435T; thus
which simplifies to
Cc = 33.15 + 0.0115T.
To find the cost of land, go through the same steps to obtain
C1 = 33.47 + 0.00225T
for the equation which gives the cost of land for a warehouse inChicago.
Using these equations, the analysts prepared the followingchart.
Cost of a Warehouse in Chicago FixedCost Variable cost (dollars per 1000 pounds)
Labor, materials $33,000 $11.50
Land $33,500 $2.25
Total $66,500 $13.75
The numbers in this chart were obtained as follows. We know thatthe cost of land in Chicago is given by C1 = 33.47 + 0.00225T. Thefixed cost is found by letting T = 0: C1 = 33.47 + 0.00225(0) =33.47, which represents a fixed cost of about $33,500. The variablecost is given by 0.00225 thousands of dollars, which is about $2.25per thousand pounds of merchandise.
Charts similar to the one above could be made for each of theother cities under discussion. Using all these results, and aprocess called linear programming, the analysts recommended thefollowing consolidation of warehouse sites. All warehousing shouldbe centralized in five warehouses, located in Philadelphia,Atlanta, Indianapolis, Dallas, and San Francisco. Operating fromthese five cities will save $600,000 annually, with an additional$730,000 to be realized from selling the warehouses which would beclosed. The analysts estimated that service to customers would beas follows: it would be possible to reach eighty-seven percent ofthe market from these five warehouses in two days or less (comparedto current delivery times of one day or less for 89% of allcustomers), with the remaining 13% reached in three days. Abouthalf the market will have delivery times of one day or less.
Exercises
1.
Complete each of the following steps.
(a) Cost of labor and materials in Atlanta:
Cc = ____________________.
(b) Since A = I/70 and I = 180 + 0.01435T, we have
(c) The equation for the cost of land in Atlantais
Cl = ______________________________________.
(d) We have
2.
Complete the following chart.
Cost of a Warehouse in Atlanta FixedCost Variable cost
Labor, materials
Land
Total
3.
Suppose the cost equations for a Sacramento warehouse can be givenby
Cc = 11.4 + 4.20A,
C1 = 12.9 + 0.90A.
(a)
Obtain Cc and C1 in terms of T. (Hint: Go through the steps ofExercise 1 above.)
(b)
Complete a table, similar to the one of Exercise 2, for a warehousein Sacramento.
4.
Show that warehouse area A, in thousands of square feet, needed fora certain annual total quantity of goods, T, in thousands ofpounds, is given by
A = 2.57 + 0.00205T,
or T = 487A - 1250.
