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