The assumptions of the production order quantity model are met in a situation where annual demand is 5000 units, setup cost is $40, holding cost is $1 per unit per month, the daily demand rate is 20 and the daily production rate is 100. How long is the cycle length (from the moment that production of a new batch starts until the moment all units are consumed)? A. 10.2 days.
B. 15.5 days.
C. 11.2 days.
D. 16.5 days.
E. 14.6 days.

A. 10.2 days.

Explanation:

Production rate(p) = 100 per day

Demand rate(d) = 20 per day

Annual demand(D) = 5000 units

Set up cost(S) = $40

Monthly Holding cost = $1 . So annual holding cost (H) = $1*12 = $12 per unit

Optimum run size(Q) = √{2DS / H [1-(d/p)]}

= √{(2*5000*40) / 12*[1 - (20/100)]}

= √[400000/12*(1-0.20)]

= √ [400000/(12*0.80)]

= √(400000/9.6)

= √41666.66666

= 204.12

Cycle length = Q/d

Cycle length = 204/20

Cycle length = 10.2 days

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