A Mexican company is considering changing the current inventory control system for sombreros. The information regarding the sombreros is given below:

Demand = 1,092 sombreros/week

Lead time = 4 weeks

Cost (price) of a sombrero = $820

Annual inventory holding cost rate = 2.5%

Order cost =$1,937.25 per order

Service level required = 90% (Z=1.29)

Standard deviation of weekly demand = 59 (L = t*L = 59*4 = 118)

Number of weeks per year = 52

The company has decided to use a fixed period systemto control the inventory.

1. Calculate T and M for a fixed period inventory system model with and without safety stock.

EOQ = 2DC(o)/C(h)

C(o) = $1,937.25 per order

C(h) = $820*2.5% = $21

D = 1092*52 = 56,784

EOQ = 2*56,784*1,937.25/21 = 3,276 sombreros

T = EOQ/D = (3,276 / 56,784)*52 = 3 weeks

M = D*(T+L) = 56,784*(3+4) = 397,488 SKUs

a . How would you calculate the safety stock?

b. Can you please explain how the system will operate with safety stock,i.e. the ordering decision rule

2.The COO says with the new inventory control system it's time to place an order at the beginning of the current week. The materials manager checked the inventory level and counted 2444 available sombreros. There were no scheduled receipts and no back orders, and the COO wants to operate with the safety stock. How many sombreros should be ordered?