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    CASE ON DISTRIBUTIONSYSTEM DESIGN

    Presented By: Aakanksha Jain 211001

    Amit Arora 211016

    Farhan Aqeel 211045

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    CASE DESCRIPTION

    DARBY COMPANY

    Manufactures and distributes meters used to measureelectric power consumption.

    Started with a production plant in El Paso anddistribution center in Ft. Worth, Texas.

    With expansion of business to north, new distributioncenter opened in Santa Fe, New Mexico.

    With growth of business in the West Coast, newdistribution center opened in Las Vegas and a

    production plant in San Bernardino, California.

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    PRODUCTION PLANT COST OF PRODUCTION

    El Paso 10.50

    San Bernardino 10

    PRODUCTION PLANT PRODUCTION CAPACITY

    El Paso 30000San Bernardino 20000

    Cost of production per meter at each production plant:

    Quarterly production capacity at each production plant:

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    El Paso

    SanBernardino

    2 PRODUCTIONPLANTS

    Ft. Worth Santa Fe

    Las Vegas

    3 DISTRIBUTIONCENTERS Dallas

    San Antonio

    Wichita

    Kansas City Denver

    Salt Lake City

    Phoenix

    Los Angeles

    San Diego

    9 CUSTOMERZONES

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    CU

    RRENT

    DI

    STRIBUTION

    SY

    STEM

    El Paso

    Ft. Worth

    Dallas

    San

    Antonio

    Wichita

    KansasCity

    San

    Bernardino

    Santa Fe

    Denver

    Salt LakeCity

    Phoenix

    Las Vegas

    LosAngeles

    San Diego

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    PART I

    If the company does not change its current

    distribution strategy, what will its manufacturingand distribution costs be for the following quarter?

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    MODEL DESCRIPTION

    To calculate the distribution cost from Production plants to the distribution centers

    we use a transportation model with production plants as sources and distribution

    centers as destinations.

    The demand of the distribution centers is calculated by adding the individualdemands of the customer zones catered by them.

    For Ft. Worth, demand = demand from Dallas+ San Antonio + Wichita +

    Kansas City

    =6300 + 4880 + 2130 + 1210

    =14520

    For Santa Fe, demand = demand from Denver + Salt lake city + Phoenix=6120 + 4830 + 2750

    =13700

    For Las Vegas, demand = demand from Los Angeles + San Diego

    =8580 + 4460

    =13040

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    Applying Vogels Approximation Method (VAM)

    FT.

    WORTH

    SANTA FE LAS

    VEGAS

    D1 SUPPLY

    EL PASO3.214520 2.26740 4.2 08740 30000

    15480

    6740

    (2.2)

    (2.2)

    SAN

    BERNARDI

    NO

    3.96960 1.213040 0 200006960

    (1.2)

    (3.9)

    DEMAND 14520 13700

    6740

    13040 8740 50000

    () (1.7) (3) (0)

    Initial Basic Feasible Solution:

    FT. WORTH SANTA FE LAS VEGAS D1

    EL PASO 14520 6740 -- 8740

    SAN

    BERNARDINO-- 6960 13040 --

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    FT.

    WORTH

    SANTA FE LAS

    VEGAS

    D1 Ui

    EL PASO -- -- 4.20 -- 0

    SAN BERNARDINO -- -- 0 1.7

    Vj 3.2 2.2 -0.5 0

    Cost for unoccupied cells:

    FT.

    WORTH

    SANTA FE LAS VEGAS D1

    EL PASO -- -- 4.70 --

    SAN BERNARDINO -- -- -1.70

    Net Evaluation:

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    Now to check for optimality, we again apply MODI method.

    Cost for occupied cells:

    FT.WORTH SANTA FE LASVEGAS D1 Ui

    EL PASO 3.2 2.2 -- 0 0

    SAN BERNARDINO -- -- 1.2 0 0

    Vj 3.2 2.2 1.2 0

    Cost for unoccupied cells:

    FT.

    WORTH

    SANTA FE LAS

    VEGAS

    D1 Ui

    EL PASO -- -- 4.20 -- 0

    SAN BERNARDINO 3.9 -- -- 0

    Vj 3.2 2.2 1.2 0

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    As we are given fixed distribution pattern from distribution center to customer zones, to

    calculate Distribution Cost from distribution centers to the customer zones we multiply

    the per meter cost of transportation with the demand at each customer zone.=6300*0.3+4880*2.1+2130*3.1+1210*4.4+6120*2.7+4830*4.7+2750*3.4+858

    0*2.1+4460*2.5

    =1890+10248+6603+5324+16524+22701+9350+18018+11150

    =$101808

    Thus, Total distribution cost =92252+101808

    =$194060

    For manufacturing cost, we multiply the quantity supplied to each distribution center

    from a production plant with the production cost at that production plant.

    Thus, manufacturing cost = 14520*10.50+13700*10.50+13040*10

    = $426710

    Therefore, Total Cost = 194060+426710

    =$620770

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    PART IISuppose that the company is willing to consider droppingthe distribution center limitations; that is, customers

    could be served by any of the distribution centers forwhich costs are available. Can costs be reduced? By howmuch?

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    Initial Basic Feasible Solution:

    DALL

    AS

    SAN

    ANTO

    NIO

    WICH

    ITA

    KANS

    AS

    CITY

    DENV

    ER

    SALT

    LAKE

    CITY

    PHOE

    NIX

    LOS

    ANGEL

    ES

    SAN

    DIEG

    O

    D1 FT.

    WORT

    H

    SANTA

    FE

    LAS

    VEGAS

    EL

    PASO-- -- -- -- -- -- -- -- -- -- 11180 18820 --

    SAN

    BERN

    ARDIN

    O

    -- -- -- -- -- -- -- -- -- -- -- -- 20000

    FT.

    WORT

    H

    6300 4880 -- -- -- -- -- -- -- -- 38820 -- --

    SANTA

    FE-- -- 2130 1210 6120 -- -- -- 620 8740 -- 31180 --

    LAS

    VEGAS-- -- -- -- -- 4830 2750 8580 3840 -- -- -- 30000

    Check for non-degeneracy:

    m+n-1 = 5+13-1=17 which is equal to the number of basic variables.

    Thus, solution is non-degenerate.

    Now, to check for optimality, we apply MODI method.

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    Cost for occupied cells:

    DALL

    AS

    SAN

    ANTO

    NIO

    WICH

    ITA

    KANS

    AS

    CITY

    DENV

    ER

    SALT

    LAKE

    CITY

    PHOE

    NIX

    LOS

    ANGEL

    ES

    SAN

    DIEG

    O

    D1 FT.

    WORT

    H

    SANTA

    FE

    LAS

    VEGAS

    Ui

    EL

    PASO-- -- -- --- -- -- -- -- -- -- 3.2 2.2 -- 2.4

    SAN

    BERN

    ARDIN

    O

    -- -- -- -- -- -- -- -- -- -- -- -- 1.2 1.2

    FT.

    WORT

    H

    0.3 2.1 -- -- -- -- -- -- -- -- 0 -- -- -0.8

    SANTA

    FE-- -- 4.5 6.0 2.7 -- -- -- 2.7 0 -- 0 -- 0.2

    LAS

    VEGAS-- -- -- -- -- 3.3 2.4 2.1 2.5 -- -- -- 0 0

    Vj 1.1 2.9 4.3 5.8 2.5 3.3 2.4 2.1 2.5 -0.2 0.8 -0.2 0

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    DALLAS SANANTO

    NIO

    WICHITA KANSAS

    CITY

    DENVER SALTLAKE

    CITY

    PHOENIX LOSANGEL

    ES

    SANDIEG

    O

    D1 FT.WORT

    H

    SANTAFE LASVEGAS Ui

    EL

    PASO -- -- 4.2 2.4

    SAN

    BERN

    ARDIN

    O

    3.9 -- 1.2

    FT.WORT

    H

    -- -- 3.1 4.4 6.0 0 -- -0.8

    SANTA

    FE5.2 5.4 -- -- -- 4.7 3.4 3.3 -- -- -- 0.2

    LAS

    VEGAS 5.4 -- -- -- -- 0 -- 0

    Vj 1.1 2.9 4.3 5.8 2.5 3.3 2.4 2.1 2.5 -0.2 0.8 -0.2 0

    Cost for unoccupied cells:

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    Net Evaluation:

    DALL

    AS

    SAN

    ANTO

    NIO

    WICH

    ITA

    KANS

    AS

    CITY

    DENV

    ER

    SALT

    LAKE

    CITY

    PHOE

    NIX

    LOS

    ANGEL

    ES

    SAN

    DIEG

    O

    D1 FT.

    WORT

    H

    SANTA

    FE

    LAS

    VEGAS

    EL

    PASO -- -- 1.8

    SAN

    BERN

    ARDIN

    O

    2.9 --

    FT.WORT

    H

    -- -- -0.4 -0.6 4.3 1 --

    SANTA

    FE3.9 2.3 -- -- -- 1.2 0.8 1 -- -- --

    LAS

    VEGAS 2.9 -- -- -- -- 0.2 --

    As all Cij is not equal to or greater than zero, thus solution is not optimal. To obtainan optimal solution, we insert in the solution and form a loop.

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    DALL

    AS

    SAN

    ANTONIO

    WICH

    ITA

    KANS

    ASCITY

    DENV

    ER

    SALT

    LAKECITY

    PHOE

    NIX

    LOS

    ANGELES

    SAN

    DIEGO

    D1 FT.

    WORTH

    SANTA

    FE

    LAS

    VEGAS

    EL

    PASO-- -- -- -- -- -- -- -- -- -- 11180

    +

    18820

    -

    --

    SAN

    BERN

    ARDIN

    O

    -- -- -- -- -- -- -- -- -- -- -- -- 20000

    FT.WORT

    H

    6300 4880 -- -- -- -- -- -- -- 38820-

    -- --

    SANTA

    FE-- -- 2130 1210

    -

    6120 -- -- -- 620 8740 -- 31180

    +

    --

    LAS

    VEGAS-- -- -- -- -- 4830 2750 8580