The Darby Company manufactures and distributes meter used tomeasure electric pow

Question

The Darby Company manufactures and distributes meter used tomeasure
electric power consumption. The company started with a smallproduction
plant in El Paso and gradually built a customer base throughoutTexas.
A distribution center was established in Ft. Worth, Texas later,as
business expanded to thenorth, a second distribution center was
established in Santa Fe, New Mexico.
The El Paso plant was expanded when the company began marketing
itsmeters in Arizona, California, Nevada, and Utah. With the growthof the
West Coast business, the Darby Company opened a third distributioncenter
in Las Vegas and just two years ago opened a second productionplant in
San Bernardino, California.
Manufacturing costs differe between the company's productionplants.
The cost of each meter produced at the El Paso plant is $10.50.The
San Bernardino plant utilizes newr and more efficient; as aresult,
manufacturing costs are $.50 per meter less than at the El Pasoplant.
The company's rapid growth meant that not much attention was paidto
the efficiency of the distribution system. Darby's managementdecided
it is now time to address this issue. The cost of shipping ameter
from each of the two plants to each of the three distribtioncenters is
shown in Table 1 below.
The quarterly production capacity is 30,000 meters at the olderElPaso
plant and 20,000 meters at the San Bernardino plant. Note thatno
shipments are allowed from the San Bernardino plant to the Ft.Worth
distribution center.
The company serves nine customer zones from the threedistribution
centers. The forecast of the number of meters needed in eachcustomer zone
for the next quarter is shown in Table 2.
The cost per unit of shipping from each distribution center toeach
customer zone is given in Table 3. note that some of thedistribution
centers cannot serve certain customer zones.
In the current distribution system, demand at the Dallas, SanAntonio,
Wichitia, and Kansas City customer zones is satisfied by shipmentsfrom
the Ft. Worth distribution center. In a similar manner, theDenver,
Salt Lake City, and Phoenix customer zones are served by the SantaFe
distribution, and the Los Angeles and San Diego customer zones areserved
by the Las Vegas distibution center. To determine how many unitsto
ship from each plant, the quarterly customer demand forecastsare
aggregated at the distribution centers. and a trnspration model isused to
minimze the cost of shipping from the production plants to the
distribution centers.

Table 1
Shipping cost per unit from production plants to distributioncenters
($)
Distribution Center
Plant Ft Worth Sante Fe Las Vegas
El Paso 3.20 2.20 4.20
San Bernardino --- 3.90 1.20

Table 2
Quarterly Demand Forecast
Customer Zone Demand (meters)
Dallas 6300
San Antonio 4880
Wichitia 2130
Kansas City 1210
Denver 6120
Salt Lake City 4830
Phoenix 2750
Los Angeles 8580
San Diego 4460

Table 3
Shipping cost from the distribution centers to the customer zones($)

Customer Zone
San Kansas Salt Lake
Dallas Antonio Wichita City Denver City Phoenix LA SD
Ft Wor 0.3 2.1 3.1 4.4 6.0 -- -- -- --
Sante Fe 5.2 5.4 4.5 6.0 2.7 4.7 3.4 3.3 2.7
Las Vegas - - - - 5.4 3.3 2.4 2.1 2.5

Question for overall problem
1. If the company does not change its current distributionstrategy,
what will its manufacturing and distribution costs be for thefollowing
quarter?
2. Suppose that the company is willing to consider dropping the
distribution center limitations; that is, customer could be servedby any of
the distributon centers for which costs are available. Can costsbe
reduced? By how much?
3. The company wants to explore the possibility of satisfying somefo
the customer demand directly from the production plants. In
particular, the shipping cost is $.30 per unit from San bernardionto Los Angeles
and $.70 from San Bernardion to San Diego. The cost for direct
shipments from El Paso to San Antonio is $3.50 per unit. Candistribution
costs be frther reduced by considering these direct plantcustomer
shipments?
4. Over the next five years. Darby is anticipating moderategrowth
(5000 meters) to the North and West. Would you recommend thatthey
consdier plant expansion at this time?

Explanation / Answer

Part 3 concept

Update the values in the equation with the question details. Solve the LP in a similar way to previous parts.(Note there will new decision variables to be added)

Answer

Manufacturing Shipping Total

$423,230 $130,304 $553,534

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