Question

14%) A company begins a review of ordering policies for a sample of items. The company operates 52 weeks a year. The following are the characteristics of one item: Demand = 3,380 units/year Ordering cost = $50/order Holding cost = $13/unit/year Lead time = 3 weeks Standard deviation of weekly demand = 16 units Desired cycle service level = 98% a) Calculate EOQ and use it to find the order interval (OI). Round the number to the nearest integer week. Hint: D/Q will give you the # of orders to place in a year; order interval = review interval. b) Suppose the company just finished a periodic review and found 20 units of on-hand inventory, how many units should be ordered (i.e. amount to order)?

Answer 1

Demand, D = 3,380 units/year

Working weeks per year = 52

Average weekly demand, d = 3380/52 = 65 units

Ordering cost, S = $50/order

Holding cost, H = $13/unit/year

Lead time, L = 3 weeks

Standard deviation of weekly demand, s = 16 units

Desired cycle service level = 98%

z value = NORMSINV(0.98) = 2.05

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a)

EOQ = sqrt(2DS/H)

= sqrt(2*3380*50/13)

= 161

# of orders to place in a year = D/Q = 3380/161 = 21

Review interval, P = Q/d = 161/65 = 2.5 ~ 3  (rounded to the nearest integer week)

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b)

Suppose the company just finished a periodic review and found 20 units of on-hand inventory, how many units should be ordered (i.e. amount to order)?

Order upto level = d*(L+P)+z*s*sqrt(L+P)

= 65*(3+3)+2.05*16*sqrt(3+3)

= 470

Current On hand inventory = 20 units

Amount to order = Order up to level - current on hand inventory

= 470 - 20

= 450 units

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