Question

Tune Football Helmets Company is considering changing its current inventory control system for football helmets to a fixed-period inventory system. The information regarding the helmets is a follows: Demand = 200 units/week Lead time = 3 weeks Order cost = $60 /order Unit cost = $80 Carrying charge rate = 0.075 Desired service level = 90% Standard deviation of weekly demand = 40 Number of weeks per year = 52 a. Assuming no-safety stock is required, what is the economic time interval (T) and optimal replenishment level (M)? (Round your answers). b. What should be the safety stock be to have a 90% service level? c. What is the revised replenishment level to have 90% service level? d. At the beginning of the current week, the materials manager, checked the inventory level of helmets and found, for example, 450 units. There were no scheduled receipts and no back orders. How many units should be ordered if an order should be placed now? (assume 90% service level is required).

Answer 1

Demand= 200 units/week

Number of weeks per year = 52

Year;y Demand(R) = 200*52= 10400 units

Lead time(L) = 3 weeks

Order cost(C) = $60/order

Unit cost = $80

Carrying charge rate = 0.075

Desired service level = 90%

Standard deviation of weekly demand = 40

EOQ= == 456 units

T= EOQ/D= 456/(200*52)= 0.0438 years (Time interval between orders)= 0.0438*52=2.28 weeks

Optimal Replenishment without saftey stock(M) = RL/N= 10400*3/52= 600

b) With service level 90%

z= NORM.S.INV(0.90)=1.28

Safety stock= z*standard deviation*Sqrt(L) = 1.28*40*sqrt(3)= 88.68= 89 units

c) Revised replenish ment level = DL+SS= 200*3+ 89= 689 units

d) Inventiry on hand = 450

Order = 689-450 - 239 units

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