Question

MARGI sells different types of wine. Customers place orders to the most popular “Summer Wine” at a rate of 125 bottles a month on the average. The store buys this wine from WSCo at $5 a bottle, and a required lead-time of 1.5 weeks. Ordering cost per order for MARGI is $14, and annual holding rate is 22%. Management is worried about daily variations of the demand, thus has decided to increase the EOQ order size by a lot.

1. Would management improve the cycle service level by doing so?
   1. Yes. The average inventory increases.
   2. Yes. If the order size increases, the safety stock also increases.
   3. Yes. The ratio of [Order size]/[Demand] increases.
   4. No. Order size does not affect the service level.
      
2. MARGI used to work with 50% service level before. How much safety stock MARGI held?
   1. I need to know the standard deviation, in order to answer.
   2. No safety stock at all
   3. 50% of the order size
   4. None of the above

To apply the cycle-service-level policy MARGI estimated the monthly standard deviation of demand at 53.5 bottles, where one month is considered 4 weeks.

3. Which statement is correct about the re-order point.
   1. The re-order point can be calculated by (1.5/4)*52)*125+sqrt((1.5/4)*52)*53.5
   2. Please provide the service level required SL, and then I will follow with norm.inv(SL,125,53.5)
   3. Please provide the service level required SL, and then I will follow with norm.inv(SL,125*(4/1.5),53.5*sqrt(4/1.5))
   4. Please provide the service level required SL, and then I will follow with
      norm.inv(SL,125(1.5/4),53.5*sqrt(1.5/4))
      

Management allows holding cost of safety stock to amount to 25% of the annual holding cost of the EOQ policy. What cycle service level can MARGI achieve with this amount of money? Calculate and show your work.

Answer 1

Mean Demand per month = 125

Annual Demand (D) = 125*12 = 1500

Cost of order (S) = $14

Holding Cost (H) = 22% of unit cost = 0.22*5 = $ 1.10

Lead time (L) = 1.5 weeks

As per EOQ policy

Question 1: Would management improve the cycle service level by doing so?

Answer: No. Order size does not affect the service level.

To improve the cycle service level, we need to increase the safety stock. Increase in EOQ has no impact on the service level.

Question 2: MARGI used to work with 50% service level before. How much safety stock MARGI held?

Answer: No safety stock at all

For a 50% service level, Z =0 so Safety stock (SS) will be zero

To apply the cycle-service-level policy MARGI estimated the monthly standard deviation of demand at 53.5 bottles, where one month is considered 4 weeks.

Lead time = 1.5 weeks = 1.5/4 = 0.375 month

ROP = Average demand during lead time + Safety Stock

Question: Which statement is correct about the re-order point.

Answer: Please provide the service level required SL, and then I will follow with norm.inv(SL,125(1.5/4),53.5*sqrt(1.5/4))

norm.inv(SL, average demand during lead time, standard deviation during a lead time)

Average demand during lead time = 125 * 1.5/4

standard deviation during a lead time = 53.5 * sqrt(1.5/4)

Question: Management allows holding cost of safety stock to amount to 25% of the annual holding cost of the EOQ policy. What cycle service level can MARGI achieve with this amount of money? Calculate and show your work.

As per EOQ policy,

Q = 195

Annual Holding Cost = Average Inventory * Holding Cost = (Q/2)*H = (195/2)*1.1 = $107.25

Holding cost of Safety stock = 25% of annual holding cost of the EOQ policy = 0.25 *107.25 = $26.8125

Safety Stock = Holding Cost of Safety stock/ Holding cost per unit = 26.8125/1.1 = 24.375 units

From Standard Normal Distribution Table, for Z = 0.74, the value of p = 0.7673

Service Level = 0.7673 = 76.73%