Tune Football Helmets Company is considering changing its current inventory cont

Question

Tune Football Helmets Company is considering changing its current inventory control system for football helmets. The information regarding the helmets is given below.

            Demand = 200 units/week

            Lead time = 2 weeks

            Order cost = $60/order

            Unit cost = $20

            Carrying charge rate = 0.075

            Desired service level = 90%

            Inventory Position (IP) = 450

            Standard deviation of weekly demand = 40

            Number of weeks per year = 52

            Compute T and M for a fixed period inventory system model with and without safety stock. Explain how this system would operate.

Explanation / Answer

D = Annual demand (units)=52week*200unit/week =10400

S = Cost per order ($) =$60

C = Cost per unit ($) =$20

I = Holding cost (%)=0.075

H = Holding cost ($) = I*C = 0.075*20=$1.50

LT = Lead Time = 2 week

Std Dev = Sigma = 40

Desired service Level 90%.

SO Z Value for 90% Confidence level from z-table is =NORMSINV(90%) = 1.2816

Inventory Position(IP)= 450

So EOQ = Sqrt(2*D*S/H)

= Sqrt(2*10400*60/1.5)

= 912.14 say 913 units

M = %u03BC + z*%u03C3

where %u03BC = the mean demand during the review period plus the lead-time period = 200+2*200 = 600 units

%u03C3 = the standard deviation of demand = 40 unit

z = the number of standard deviations necessary to obtain the acceptable stockout probability = 1.2816

SO M = 600+1.2816*40 = 651.26 or 651 units

Review period (T):Ordering decision rule : Place an order every (T) period where Order Qty at time t is Q= M-IP where IP is inv position at time t

SO Q = M-IP = 651-450 = 251 units

So No of order = 10400/251 = 41.4 say 42

So One order is placed every 52/42 = 1.25 weeks=T

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