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Consider the inventory model with the following information:
Demand, β = 5 unit/day
Setup cost, K = 10 Tk/order
Holding cost, h = 1 Tk/unit/day
C1 = 2, 0 < q < 15
C2 = 1, q ≥ 15
Answer,
We know,
First compute, Ym = √ 2Kβh = √ 2 x10 x 51 = 10 unit
Since ym < q, it’s necessary to check whether q is less than q1. The value of q1 is computed from
TCU 1 (Ym) = TCU 2 (q1)
β C1 + Kβym
+ h2
ym = β C2 + Kβq1
+ h2
q1
5 x 2 + 10x 510
+ 12
x 10 = 5 x 1 + 10x 5q1
+ 12
q1
q12 – 30 q1 + 100 = 0
q1 = 30±√900−4002
q1 = 26.18 or 3.82
By definition, q1 is selected as the larger value.
Since q1 > q, it follows that y* = q = 15
Total cost per unit, TCU (y*) = TCU2 (q), ym < q < q1 = 5 x 1 + 10x 515
+ 12
x 15 = 15.83