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MGT613 - Production / Operations Management

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    zareenZ

    Solution idea
    D=Demand= 24000
    S=Ordering/Setup cost= 2400
    H=Holding/Carrying Cost= 3
    U= Usage rate=24000/240= 100
    P= Production rate= 600

    Optimal Run Size:
    Q0= √2DS/H√p/(p-u)
    Q0= √(2240002400)/3√600/(600-100)
    Q0= √115200000/3√600/500
    Q0= √38400000* √1.20
    Q0= 6196.77*1.0954
    Q0= 6787.94 ≅6788

    Minimum total annual cost for carrying and setup cost.
    = Carrying Cost + Set up Cost
    =( I max/2)H+ ( D/Q0)S
    Where,
    I max= Q0/p ((p-u))
    I max= 6788/600 (600-100)
    I max= 11.31 (500)
    I max= 5655
    TC min= Carrying Cost+ Setup Cost
    TC min= (I max/2) H+ (D/Q0) S
    TC min= (5655/2) 3 + (24000/6788) 2400
    TC min= (2827.5) (3) + (3.53) (2400)
    TC min= 8482.5 + 8472
    TC min= 16954.5

    Cycle time for the Optimal Run Size.
    Q0/U=6788/100
    = 67.88 ≅ 68 days

    Run time
    Q0/p=6788/600
    = 11.31 days