Chapter 8: Distribution Center, Warehouse, and Plant Location
Chapter 8: Distribution Center, Warehouse, and Plant Location
PART II
ANSWERS TO END-OF-CHAPTER QUESTIONS
CHAPTER 8: DISTRIBUTION CENTER, WAREHOUSE, AND PLANT LOCATION
1. How can advances in technology and communication influence the facility location decision?
The text cites an example of a manufacturer that used the Internet to gather the relevant data for choosing a new production facility to serve their customers east of the Rocky Mountains. Advances in technology and communication allow companies the ability to collect data inexpensively and relatively quickly.
2. Discuss the factors that influence the number of facilities that a firm chooses to operate.
Rather than asking, “Where should a new facility be located?” organizations should be thinking about the optimal number of facilities in the system. The need for additional facilities often arises when an organization’s service performance from existing facilities drops below “acceptable” levels. The general trend in recent years has been for companies to reduce the number of facilities in their distribution networks.
3. Briefly describe the general factors influencing facility location.
The cost and availability of natural resources may be a factor, particularly for manufacturing facilities. An area’s population is also important; population serves as a market for goods as well as a source of labor. Taxes and subsidies are yet another general factor, as is the cost and availability of transportation. Over the past two decades, many organizations have identified proximity to key suppliers as an important determinant when locating a facility. Trade patterns, such as commodity flows, can be studied to determine changes occurring in the movement of raw materials and finished goods. An increasingly important locational factor can be broadly called quality-of-life considerations and can include access to commercial air travel, an area’s cost of living, and its crime, among others.
4. How does a raw material’s status as pure, weight-losing, or weight-gaining influence the facility location decision?
A pure raw material is one that loses no weight in manufacturing and, because of this, the processing point can be anywhere near the raw material source and the market. Weight-losing products lose weight during processing; the processing point should be near their source in order to avoid payment of unnecessary transportation charges. Weight-gaining products gain weight during processing; the processing point should be close to the market.
5. Discuss how environmental considerations might influence the facility location decision.
One set of environmental considerations involves various types of pollution—air, water, and noise. Another is the conservation of natural resources—sometimes with respect to those used in production and other times for various reasons. Developing nations often have lax environmental regulations, a situation that can foster economic growth and improve standards of living. These lax environmental regulations may have long-term consequences, such as depletion of key natural resources—which could render certain facilities meaningless.
6. Discuss how population can be viewed as both a market for goods and a source of labor.
With respect to a market for goods, attributes of current and potential customers are important. Things such as changes in population size as well as changes in population characteristics are important. In terms of population size, for example,
There are myriad concerns associated with population as a source of labor, to include the size of the workforce; the unemployment rate; the age profile; its skills and education; prevailing wage rates; and union status.
7. How might the factors considered important for locating manufacturing facilities differ from the factors considered important for locating a distribution facility?
There are a number of possible answers for this question. For example, the availability of natural resources is probably much more important for a manufacturing facility than a distribution facility. Population is likely to be an important factor regardless of whether one is looking at a manufacturing facility or a distribution facility—but the relevant attributes may differ. Access to low cost labor might be a greater consideration for a manufacturing facility than for a distribution facility. The impact of taxes and subsidies is likely to be different as well. For instance, certain regions may develop subsidy/incentive plans to attract manufacturing facilities (e.g., foreign automakers locating in the Southern United States) while inventory taxes could be a concern with distribution facilities.
8. Discuss the advantages and disadvantages of locating manufacturing, assembly, or distribution facilities in countries with relatively low wages.
Labor wage rates appear to be a key locational determinant as supply chains become more global in nature. Although absolute wage comparisons are important, relative comparisons can be quite insightful. For example, at prevailing wage rates, a company could have approximately similar compensation costs by hiring nine Mexican workers or one
One possible disadvantage is that there are sometimes limits on the number of supervisory personnel that can be brought in from outside the country. There may also be regulations that specify that nationals be trained for and employed in supervisory posts. Countries with low labor costs may also have a number of sweatshops, which can be viewed as organizations that exploit workers and that do not comply with fiscal and legal obligations towards employees.
9. What are right-to-work laws? How do they influence locational decisions?
Right-to-work laws refer to situations where an individual cannot be compelled to join a union as a condition of employment. Right-to-work laws tend to make particular locations more attractive to potential employers; in recent years several non-U.S. automakers have constructed production facilities in right-to-work states such as Alabama,
10. What are expatriate workers? What challenges do they face?
Expatriate workers are those employees who are sent to other countries to work for extended periods of time. It appears that most expatriate turnover is caused not by technical factors (knowledge and skills) but, rather, by socialization issues. These socialization concerns can be magnified if the expatriate’s family comes along on the work assignment; it’s vital that the expatriate and his/her family are comfortable with the social and cultural factors of the country where they will be employed.
11. Do you think inventories should be taxed? Why or why not?
Students can take either side in answering this question. An inventory tax may be a disincentive in the sense that it adds to the cost of doing business and may cause a certain location to be viewed as less “business friendly.” Moreover, as this manual is being prepared, there are suggestions that inventory taxes might be obsolete by 2010, in part because of lack of agreement of what is meant by inventory.
12. What are empowerment zones? What is their relevance to locational decisions?
Empowerment zones were created by the U.S. Department of Housing and Urban Development to encourage business development, through tax credits, in economically depressed portions of individual cities. They represent one type of incentive for locating a facility in less-than-desirable areas.
13. What mode of transportation do you think is the most important to firms when evaluating new sites? Why?
The answer to this question will depend on the type of facility that is being considered. A manufacturing plant might need both rail service (in order to bring in raw materials) and truck service (to carry the finished goods). A distribution center for repair parts might, by contrast, need highway and air service.
14. What are supplier parks? Give some examples.
Supplier parks require key suppliers to locate on, or adjacent to, assembly plants which helps to reduce shipping costs as well as inventory carrying costs. They have been popular in Europe, have spread to other continents, and have often been associated with automakers and their suppliers.
15. Discuss how multicountry trade agreements have influenced the location of production or distribution facilities.
The North American Free Trade Agreement (NAFTA) has seen
The virtual elimination of trade barriers among members of the European Union (EU) has allowed many companies to reduce the number of relevant distribution facilities. When the EU consisted of 14 countries, the Benelux countries were a favored location for distribution facilities. However, since the EU’s addition of 10 Central and Eastern European countries in 2004, the
16. What quality of life considerations do you think are the most important for locational decisions? Why?
There are a number of acceptable answers for this question, and the answer may vary from student to student. An unmarried student with no children, for example, might have a much different response from a married student with children.
17. Beyond the general factors discussed in this chapter, what additional considerations are important when a firm is thinking of locating a facility (facilities) in other countries?
The considerations include the relevant legal system; political stability; bureaucratic red tape; corruption; protectionism; nationalism; privatization; expropriation (confiscation); treaties and trade agreements.
Social unrest and crime may also be important considerations, as are culture, customs, holidays, language, level of education, and religion. Currency fluctuations and devaluations can result in frequent cost changes for expatriate workers. The laws in the host country, and the ability to repatriate profits, limit one’s ability to use profits that operations in the host country might generate.
18. What is a free trade zone? What functions might be performed in it?
Free trade zones refer to highly specialized sites where a company can locate without being subjected to duties and quotas until the goods or their products enter the customs territory of the zone country. Functions that might be performed include storing, processing, exhibiting, and/or manufacturing.
19. Discuss advantages and disadvantages to grid systems such as the center-of-gravity and weighted center-of-gravity approaches.
As a general rule, grid systems can be used for locating a single facility so that the distance to existing facilities is minimized—and by extension, transportation costs are minimized as well. In addition, grid systems are relatively simple to apply, and calculations can be done relatively quickly.
Alternatively, the relative simplicity means that adjustments have to be made to take into account real-world considerations such as taxes, wage rates in particular locations, volume discounts, the cost and quality of transport services, and the fact that transport rates taper with increased distances.
20. Distinguish between facility relocation and facility closing. How should companies deal with their human resources (workers) in both situations?
Facility relocation occurs when a firm decides that it can no longer continue operations in its present facility and must move operations to another facility in order to better serve suppliers and/or customers. Facility closing, by contrast, occurs when a company decides to discontinue operations at a current site because the operations may no longer be needed or can be absorbed by other facilities.
Regardless of whether we are talking about relocation or closing, current employees should be kept informed—by their employer—about relevant issues. Information from other sources could cause confusion, anger, and lower morale and could easily offset the productivity of the existing facility. Additional information is generally required for facility closings, in the sense that the Worker Adjustment and Retraining Notification Act mandates that employers give 60 days notice about closings and mass layoffs.
PART III
EXAMINATION QUESTIONS
CHAPTER 8: DISTRIBUTION CENTER, WAREHOUSE, AND PLANT LOCATION
Multiple Choice Questions
1. The major factors influencing locational decisions are ____ and____.
a. markets; resource availability
b. labor; transport services
c. markets; labor
d. transport services; resource availability
e. none of the above
(a; p. 188)
2. Each of the following is a dimension in facility location except:
a. time
b. cost
c. value
d. size
(d; p. 189)
3. With respect to facility location decisions, firms are seeking the most ____ at the least ____ in the least elapsed amount of time.
a. customers; cost
b. value; effort
c. value; cost
d. sites; distance
(c; p. 189)
4. The initial focus in facility location is on a____.
a. city
b. county
c. state
d. region
(d; p. 189)
5. The general trend in recent years has been for companies to do what with their distribution networks?
a. maintain the status quo
b. reduce the number of facilities
c. slightly increase the number of facilities
d. relocate their facilities
(b; p. 191)
6. Chicago Consulting is known for its annual list of “The 10 Best Warehouse Networks” for serving the
a.
b.
c.
d.
(b; p. 191)
7. A pure material:
a. is one that loses no weight in manufacturing
b. cannot be mixed with other materials
c. is soluble in water
d. comes from the ocean
e. none of the above
(a; p. 193)
8. The processing point for a pure material:
a. should be near its source
b. should be near the final market
c. can be anywhere in the world
d. can be anywhere near the source and the market
(d; p. 193)
9. The processing point for a weight-losing raw material:
a. can be anywhere near the source and the market
b. should be near its source
c. should be near the final market
d. should be equidistant between the source and the market
(b; p. 193)
10. The processing point for a weight-gaining raw material:
a. can be anywhere near the source and the market
b. should be near its source
c. should be near the final market
d. should be equidistant between the source and the market
(c; p. 193)
11. Over the past quarter century, discussion of natural resources and facility location has increasingly factored in ____ considerations.
a. cost
b. supply chain
c. ethical
d. environmental
(d; p. 193)
12. What two countries account for approximately one-third of the world’s population?
a.
b.
c.
d.
(b; p. 194)
13. According to a recent update to the 2000
a. Great Lakes
b. Northeast
c. West
d. Southeast
e. none of the above
(c; p. 194)
14. Which of the following countries has the highest hourly worker compensation?
a.
b.
c.
d.
(a; p. 195)
15. ____ plants, which are located just south of the U.S.–Mexican border, provide much needed jobs to Mexican workers and allow for low-cost, duty-free production so long as all the goods are exported from Mexico.
a. Expatriate
b. Trade zone
c. Nationalization
d. Maquiladora
(d; p. 195)
16. Right-to-work laws refer to a situation where:
a. an individual cannot be compelled to join a union as a condition of employment
b. each state provides employment to those people receiving public assistance
c. every person who wants a job is guaranteed a job
d. worker strikes are illegal
(a; p. 195)
17. All of the following are true, except:
a. countries with low labor costs often have a multitude of sweatshops
b. a workforce’s union status may be a key locational determinant for some organizations
c. expatriate work assignments can be costly
d. there has been declining union membership in industrialized nations
e. all are true
(e; pp. 195-196)
18. An expatriate refers to a person:
a. who holds dual citizenship
b. who is sent to work in other countries for extended periods of time
c. who is ISO 9000 certified
d. who has renounced union membership
e. none of the above
(b; p. 196)
19. Logisticians and supply chain managers have a particular interest in ____ taxes.
a. real estate
b. corporate income
c. inventory
d. severance
(c; p. 196)
20. A general rule of thumb is that the services being received in exchange for taxes represent about ____% of the taxes paid.
a. 80
b. 70
c. 60
d. 50
(d; p. 197)
21. The purpose of ____ zones is to encourage business development in economically depressed portions of a particular city.
a. commercial
b. free trade
c. privatization
d. empowerment
(d; p. 197)
22. Which of the following is not a general factor influencing facility location?
a. transportation considerations
b. natural resources
c. proximity to key suppliers
d. trade patterns
e. all are general factors
(e; pp. 193-199)
23. It has been suggested that all things being equal, the best locations are generally those where the best ____ are located.
a. skilled workers
b. warehousing facilities
c. transportation services
d. natural resources
(c; p. 197)
24. The existence of transportation competition, whether intermodal or intramodal, tends to:
a. have cost, but not service, benefits to a user
b. have service, but not cost, benefits to a user
c. have both cost and service benefits to users
d. have neither cost nor service benefits to users
(c; p. 197)
25. Supplier parks are a concept that developed around ____ and their suppliers in Europe.
a. supermarkets
b. apparel makers
c. computer makers
d. automakers
(d; p. 199)
26. With respect to commodity flows, logisticians are especially interested in ____ and ____.
a. what is being produced; where it is being produced
b. how much is being produced; where it is being shipped
c. how much is being produced; where it is being produced
d. what is being produced; where it is being shipped
(b; p. 199)
27. Since the European Union’s expansion into 10 Central and Eastern European countries in 2004, ____ has become a favored production and distribution site because of its relatively central location.
a. Czech Republic
b.
c.
d.
(a; p. 200)
28. Which of the following is not a possible quality of life consideration?
a. access to commercial air travel
b. cost of living
c. crime rate
d. educational opportunities
e. all are quality of life considerations
(e; p. 200)
29. A “brownfield” is:
a. a term for where crushed boxes are kept before recycling
b. a term that refers to a potential facility site that has no trees needing to be cleared before construction
c. a property for which use and redevelopment is complicated by past use
d. an airport that lacks paved runways
(c; p. 201)
30. A free trade zone refers to:
a. an area that is home to businesses that are owned and operated by large concentrations of a particular ethnic group
b. an area in which products can be stored, exhibited, or processed without being subjected to duties and quotas unless they enter the customs territory of the zone country
c. an area in which the federal government disregards all import and export quotas for products coming from, or destined to, “favored” nations
d. an area outside the legal jurisdiction of federal, state, and/or local governments
e. none of the above
(b; p. 202)
31. Each of the following statements about free trade zones are false, except:
a. they must be located adjacent to ports or airports
b. they cannot be used for processing or manufacturing
c. they require duties to be paid prior to leaving the trade zone
d. they have become less popular in recent years
e. all are false
(e; p. 202)
32. The center-of-gravity approach to location analysis minimizes:
a. labor costs
b. warehousing costs
c. taxes
d. distance to existing facilities
(d; p. 204)
33. How does the weighted center-of-gravity approach to location analysis differ from the center-of-gravity approach to location analysis?
a. the weighted approach considers taxes
b. the weighted approach is less complicated
c. the weighted approach considers shipment volume
d. the weighted approach considers tapering rates
(c; p. 204)
34. Location within another firm’s channel is feasible assuming that the products involved are ____.
a. complementary
b. supplemental
c. very similar
d. very different
(a; p. 205)
35. Which of the following is not a possible reason for facility closings?
a. eliminating redundant capacity in mergers and acquisitions
b. poor planning
c. improving supply chain efficiency
d. insufficient volume of business
e. all of the above are possible reasons
(e; p. 206)
True-False Questions
1. The major factors influencing locational decisions are markets and resource availability. (True; p. 188)
2. With respect to facility location decisions, firms are seeking the most value at the least cost in the least elapsed amount of time. (True; p. 189)
3. The initial focus in facility location is on the region. (True; p. 189)
4. The general trend in recent years has been for companies to increase the number of facilities in their distribution networks. (False; p. 191)
5. Chicago Consulting’s “The 10 Best Chinese Warehouse Networks” suggests that going from two to five warehouses allows a company to save nearly one day of lead time to the Chinese population. (True; p. 191)
6. A pure material is one that is totally water soluble. (False; p. 193)
7. The processing point for a pure material can be anywhere between the source and the market. (True; p. 193)
8. The processing point for a weight-losing raw material can be anywhere between the source and the market. (False; p. 193)
9. The processing point for a weight-gaining raw material should be close to the market. (True; p. 193)
10. Over the past quarter century, discussion of natural resources and facility location has increasingly factored in supply chain considerations. (False; p. 193)
11. Population can be viewed as both a market for goods and a potential source of labor. (True; p. 194)
12. Population size is an irrelevant consideration in the facility location decision. (False; p. 194)
13. Labor wage rates appear to be a key locational determinant as supply chains become more global in nature. (True; p. 195)
14. The
15. Maquiladora plants have experienced resurgence in recent years because of a focus on manufactured products that depend on fast time to market. (True; p. 195)
16. Sweatshops are organizations that exploit workers and that do not comply with fiscal and legal obligations. (True; p. 195)
17. Right-to-work laws mean that every person who wants a job is guaranteed a job. (False; p. 195)
18. An expatriate is a person who holds dual citizenship. (False; p. 196)
19. Turnover rates for expatriate workers currently range between 20% and 40%. (True; p. 196)
20. The inventory tax is based on the average amount of inventory during a six-month period. (False; p. 196)
21. There are suggestions that inventory taxes may be obsolete by 2010 in part because of lack of agreement as to what is meant by inventory. (True; p. 196)
22. The services received from business taxes represent only about 50% of the taxes that were paid. (True; p. 197)
23. The purpose of empowerment zones is to encourage business development in economically depressed portions of a city. (True; p. 197)
24. Transportation considerations, in the form of transportation availability and costs, tend to play a relatively minor role in facility location decisions. (False; p. 197)
25. Intermodal competition refers to the number of carriers within a particular mode of transportation. (False; p. 197)
26. Centralized facilities tend to minimize total transit distances, which likely results in minimum transportation cost. (True; p. 197)
27. Supplier parks refer to places where main component makers locate in specially created industrial complexes adjacent to assembly plants. (True; p. 199)
28. With respect to commodity flows, logisticians are especially interested in what is being produced and where it is being produced. (False; p. 199)
29. The development and implementation of multicountry trade agreements has had profound impacts on trade patterns. (True; p. 199)
30. Since the European Union’s expansion into 10 Central and Eastern European countries in 2004,
31. Quality of life considerations play a limited role in locational decisions. (False; p. 200)
32. Government considerations such as the relevant legal system, political stability, and protectionism are important when companies are thinking of facility locations in non-domestic countries. (True; p. 200)
33. Zoning classifications can be changed in an effort to encourage or discourage business activity. (True; p. 201)
34. Brownfields refer to a place where flattened cartons are stored until they are recycled. (False; p. 201)
35. Free trade zones must be adjacent to a port or airport. (False; p. 202)
36. Grid systems are important to locational analysis because they allow one to analyze spatial relationships with relatively simple mathematical tools. (True; p. 202)
37. The idea behind a weighted center-of-gravity approach is that a prospective warehousing facility will be located closer to the existing sites with the greatest current demand. (True; p. 204)
38. Location within another firm’s channel is feasible assuming that the products involved are supplementary in nature. (False; p. 205)
39. Facility relocation is associated with business growth, while facility closing is associated with business contraction. (True; p. 205)
40. Communication with employees is more important for facility closings than for facility relocations. (False; p. 206)
PART IV
CASE SOLUTIONS
CASE 8-1 AERO MARINE LOGISTICS
Question 1: What would the first-year costs be to AML if they purchased the 10 used 20-foot containers? How long would it take to recoup the investment, assuming that the mushroom traffic continued?
Cost category
Monthly cost ($
Annual cost ($
Inbound transportation
20,000
240,000
Outbound transportation
10,000
120,000
Maintenance
22,220
Energy
33,330
Total
415,550
Revenue category
Monthly revenue ($
Annual revenue ($
Mushroom sales
30,000
360,000
Backhaulsa
12,000
Total
372,000
a: based on 120 container shipments per year; 10% of return loads, or 12 containers, would generate revenues equal to the associated costs
According to the above data, the proposed service is a money loser and the relevant investment ($255,530 in
Question 2: What would the first-year costs be to AML if they purchased 5 new 40-foot containers? How long would it take to recoup the investment, assuming that the mushroom traffic continued?
Cost category
Monthly cost ($
Annual cost ($
Inbound transportation
15,500
186,000
Outbound transportation
7,750
93,000
Maintenance
0
Energy
33,330
Total
312,330
Revenue category
Monthly revenue ($
Annual revenue ($
Mushroom sales
30,000
360,000
Backhaulsa
9,300
Total
369,300
a: based on 60 container shipments per year; 10% of return loads, or 6 containers, would generate revenues equal to the associated costs
According to the above data, the proposed service would generate an annual “profit” of $56,970 ($369,300 minus $312,330). The investment in for 5 containers is as follows: 5 containers @ 15 lakh = 75 lakh, plus 5 re-equipped flatcars @ 9 lakh = 45 lakh, for a total of 130 lakh. 130 lakh = $288,860; this divided by $56,970 yields a payback time of approximately 5.1 years.
Question 3: Is either of the alternatives covered in questions 1 and 2 riskier? Why?
Given that the 10-container option yields an annual loss—which precludes recouping any part of the relevant investment—it appears to be the riskier of the two alternatives.
Question 4: Mr. Singh has read about the supply-chain concept that attempts to identify and link all the participants from suppliers’ suppliers to customers’ customers. Who are all of the participants in the supply chain, a part of which has been discussed in the case?
The participants could include, but are not limited to: mushroom suppliers, such as the farmers, mushroom pickers, and mushroom packers; Freshfoods; consolidators in Amsterdam; transportation carriers bringing the mushrooms to the consolidators; ocean carrier from Amsterdam to Mumbai; transportation provider(s) from Mumbai to Delhi; AML; the container leasing company; stores, open-air markets, hotels, and restaurants in Northern India.
Question 5: Logistics partnerships involve sharing costs and risks. What are all the costs and risks that this venture entails? How might they be shared?
Some of the costs include accessorial and linehaul transportation costs; the investment costs for the containers; energy costs to provide power for the refrigerated containers; reconfiguration costs for the flatcars; maintenance costs for the containers. Another cost, which appears not to have been mentioned, is the cost of capital.
Some of the relevant risks include irregularities in product supply due to poor growing conditions for mushrooms; product spoilage due to refrigeration problems; lack of demand for the product; higher than expected maintenance for the containers (because of the high temperatures in India); theft, perhaps not so much for the mushrooms but because containers can serve as shelter; dramatic changes in the cost of capital, particularly if capital costs increase substantially.
The sharing of the costs and risks depends on which parties are impacted by a particular cost or risk. For example, lack of demand for the mushrooms is a risk that might be shared by Freshfoods and AML. Alternatively, the risk of refrigeration inadequacies might be shared by AML, the container supplier, and perhaps the company installing the power equipment on flatcars (if different from AML).
Question 6: With some help from your instructor, divide into groups representing most or all of the supply chain members identified in question 4, and negotiate an agreement or agreements that share the costs, risks, and possible profits and losses from the venture being considered.
There is any number of acceptable responses.
CASE 8-2 ALBERTA HIGHWAY DEPARTMENT, REGION VI
One student developed the following drawing to guide her analysis:
6000’\
\ Mile 6 (700 tons)
\
5500’ A \
\ Mile 5 (650 tons)
\
5000’ B \
\ Mile 4 (580 tons)
\
4500’ C \
\ Mile 3 (530 tons)
\
4000’ D \
\ Mile 2 (480 tons)
\
3500’ E \
\ Mile 1 (400 tons)
\
3000’------------------------------|-----------------> Bear Valley
1 mile 40 miles
Lake
Louise
Silo
Question 1: Should one portion of sand silos at the Lake Louise maintenance station be relocated to a point to the west, at a higher elevation? If yes, where should it be relocated, how much capacity should it have, and what are the projected annual savings in truck operating costs? Show your work.
The answer is that a portion of the Lake Louise sand silos should be relocated to Point B. The capacity should be 2,460 tons (plus reserves—actual amount unspecified). The following table shows the cost calculations for each alternative.
New silo at
Sectors served by new silo and by Lake Louise
Average tonnage each
Inbound costs from Bow Valley
Outbound costs to sectors beyond one mile from silo
Total costs
A
A-6,5,4,3
2460
2460 x 46 x .03 = $3,395
A to 4: 580 x 1 x .10 = $58
A to 3: 530 x 2 x .10 = $106
A
LL-2,1
880
880 x 40 x .03 = $1,056
LL to 2: 480 x 2 x .10 = $96
LL to 1: 400 x 1 x .10 = $40
$4,751
B
B-6,5,4,3
2460
2460 x 45 x .03 = $3,321
B to 6: 700 x 1 x .10 = $70
B to 3: 530 x 1 x .10 = $53
LL-2,1
880
880 x 40 x .03 = $1,056
LL to 2: 480 x 2 x .10 = $96
LL to 1: 400 x 1 x .10 = $40
$4,636
C
C-6,5,4,3,2
2940
2940 x 44 x .03 = $3,881
C to 6: 700 x 2 x .10 = $140
C to 5: 650 x 1 x .10 = $65
C to 2: 480 x 1 x .10 = $48
LL-1
400
400 x 40 x .03 = $480
LL to 1: 400 x 1 x .10 = $40
$4,654
D
D-6,5,4,3,2
2940
2940 x 43 x .03 = $3,793
D to 6: 700 x 3 x .10 = $210
D to 5: 650 x 2 x .10 = $130
D to 4: 580 x 1 x .10 = $58
LL-1
400
400 x 40 x .03 = $480
LL to 1: 400 x 1 x .10 = $40
$4,710
E
E-6,5,4,3,2,1
3340
3340 x 42 x .03 = $4,208
E to 6: 700 x 4 x .10 = $280
E to 5: 650 x 3 x .10 = $195
E to 4: 580 x 2 x .10 = $116
E to 3: 530 x 1 x .10 = $53
$4,852
No new silo
LL-6,5,4,3,2,1
3340
3340 x 40 x .03 = $4,008
LL to 6: 700 x 6 x .10 = $420
LL to 5: 650 x 5 x .10 = $325
LL to 4: 580 x 4 x .10 = $232
LL to 3: 530 x 3 x .10 = $159
LL to 2: 480 x 2 x .10 = $96
LL to 1: 400 x 1 x .10 = $40
$5,280
Question 2: Assume that it is discovered that it would be impossible to split the silo into sections. However, it would be feasible to move the entire silo to a site farther up the slope. The section of highway from the Lake Louise maintenance station stretching west 1 mile to where it reaches the 3,000-foot elevation point must be sanded for 30 days per year. All points east of the Lake Louise maintenance station can be serviced from other points. Should the entire silo be moved to another point? If so, to where? What will the savings be? Show your work.
This is handled the same way as question 1 except that we must also supply 300 tons of sand for the mile between the Lake Louise silo and the start of the hill. The combined hauling and spreading costs for each silo are: A, $5,641; B, $5,373; C, $5,228; D, $5,194 (the lowest cost); E, $5,260; and leaving the silo at Lake Louise, $5,640. The “leaving the silo at Lake Louise” cost is higher than given in question 1 because we now must include costs of sanding the mile just west of the silo.
Question 3: Ignore all statements made in question 2 and assume, instead, that the silo can be divided into three sections: one remaining at Lake Louise and other two located somewhere along the 6-mile stretch. If two sections are to be located within the 6-mile section, where should they be placed? What will the savings be over the present system? Show your work.
Because larger tonnages are used at the top, it would be the cheapest to place the split silos closer to the top: at site A which would serve miles 6 and 5, and at site C which would serve miles 4 and 3. Other sites would be served from Lake Louise.
Question 4: This case was written some time ago, when fuel costs were very low. Assume now that the spreader dump truck costs $.35 per ton-mile to operate (compared to $.10) and that the trailer dump truck used to move sand from the quarry costs $.20 per ton-mile to operate (up from $.03). Answer question 1 again, but this time take into account the new truck operating costs.
The problem is set up as in question 1, although the costs have changed. The new “low cost” silo site is D, with annual costs of $30,027, which should be compared with the annual costs of $31,185 to keep the site at Lake Louise.
Question 5: Answer question 2 again but using the new trucking costs outlined in question 4.
The new site is E, with annual costs of $32,947, compared with annual costs of $33,589 of keeping the silo at Lake Louise. With respect to both answers 4 and 5, note that the costs of the hauling trucks has increased more than the costs of spreading trucks; hence the most advantageous sites are lower on the hill.
Question 6: Answer question 3 again, taking into account the new trucking costs outlined in question 4.
The answer for question 3 applies here as well.
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