Question

1. Crestview sells a particularly popular Christmas card once a year and distributes the cards to gift shops. It costs Crestview $1 per card to order from a printing company, and Crestview receives $2 for each card sold. Each card that is not sold is discarded, and Crestview receives $0.1 for each. Crestview has estimated that the demand for the coming Christmas season follows a normal distribution with a mean of 100,000 and standard deviation of 30,000.

a) Determine the optimal number of cards Crestview should order for the coming Christmas season.

b) Suppose Crestview has purchased a printing machine and will print cards themselves. The cost to print each card is $0.75. Determine the optimal number of cards Crestview should print for the coming Christmas season.

c) Interpret the difference between the results in a) and b).

2. Consider the following information on an inventory management system:

​​Item Cost:​​​$10

​​Order Cost:​​​$300

​​Annual Holding Cost:​​30% of item cost

​​Annual Demand:​​15,000 units based on 300 working days

​​Average Demand:​​50 units

​​Std. Dev. of Demand:​​12 units per day

​​Leadtime:​​​16 days​

a) Ignoring the uncertainty in the demand (i.e. looking only at average values), find the optimal order quantity and the reorder point. What is the annual inventory holding and ordering cost for this policy?

b) Consider now the uncertainty. The order quantity remains the same. If the target is to have a 99% fill rate, what should be the reorder point? What is the safety stock? How much additional inventory cost is incurred due to the safety stock? What should be the reorder point?

Answer 1