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))
      
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

Following information are provided in the question:-

1. Monthly Demand = 125 bottles

2. Yearly demand = 125 *12= 1500 bottles ( D)

3.Price per bottle = 5 $

4. Lead time = 1.5 weeks

5. Ordering cost per order = 14 $ ( S)

6. Inventory holding cost per year = 22 % of total demand = ( 1500 *5) 22/100 = 1650

7. Inventory holding cost per unit per year = 1650/1500 = 1.1 (H)

Economic Order Quantity ; EOQ = SQ ROOT ( 2 * S*D)/H = SQ ROOT ( ( 2 *14*1500)/1.1 ) = 195.4 I,e 195 bottles

(195 is the order quantity at which total inventory cost of the company will be minimum .)

Reorder level = Average usages * lead time = 31.25 * 1.5 = 46.8 I,e 47 bottles

(Monthly uses = 125 ; Weekly uses = 31.25 Lead Time = 1.5 Week )

This means that the company is giving the order for bottles when it has a stock of 47 bottles in its store .

The cycle service level stands for the probability of stock out due to variation in demand. If EQO is increased, the order quantity will increase , hence the cycle service level will improve.

Now :

(a) Average inventory will increase because the order quantity is increasing

(b) safety stock will also increase since order size is increasing

(c) Monthly demand is 125 bottles and order size in a month will be 523 ( 196 bottles are ordered in 1.5 weeks ,therefore monthly order will be 4/1.5 * 196 = 522.6) .

Therefore ORDER SIZE/ DEMAND will increase with the increase in EOQ

(d) Order size definitely affects the cycle service level because as soon as we reduce  Order size and at the same time demand increases there is a chance of Stock out situation .