Problem $2$

An important part is used in the assembly process of a plant, and this part is delivered by a

supplier. The demand of this part has normal distribution. The expected value of the yearly

demand is $1200$ units. The expected value of the demand during the lead time is $100$ units and

the standard deviation is $20$ units. The purchase cost of this part is $50$ THUF per unit and the

yearly inventory holding rate is $20$ percent. The order cost $240$ THUF. The lead time of delivery

is $30$ days. A continuous review system is applied in the warehouse of the plant

a$)$ Calculate the economic order quantity?

b$)$ Calculate the inventory reorder level, assuming that less than $3$ stock outs are allowed in a

year?

c$)$ Calculate the safety stock level and the inventory holding cost of the safety stock!

d$)$ How much is the total cost of the optimal order policy?

e$)$ Management assume that $3$ stock outs are not acceptable. How much the inventory holding

cost would increase if only maximum $1$ stock outs were allowed?