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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 C 1 = 2, 0 < q < 15 C 2 = 1, q 15 Answer, We know, First compute, Y m = 2 h = 2 x 10 x 5 1 = 10 unit Since y m < q, it’s necessary to check whether q is less than q 1 . The value of q 1 is computed from TCU 1 (Y m ) = TCU 2 (q 1 ) β C1 + ym + h 2 ym = β C2 + q 1 + h 2 q 1 5 x 2 + 10 x 5 10 + 1 2 x 10 = 5 x 1 + 10 x 5 q 1 + 1 2 q 1 q1 2 – 30 q1 + 100 = 0 q 1 = 30 ± 900400 2 q 1 = 26.18 or 3.82 By definition, q 1 is selected as the larger value. Since q 1 > q, it follows that y* = q = 15 Total cost per unit, TCU (y*) = TCU 2 (q), y m < q < q 1 = 5 x 1 + 10 x 5 15 + 1 2 x 15 = 15.83

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Page 1: Inventory

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