Question

1. Scary Clowns, Inc., supplies special makeup cases to a major circus. The circus orders its EOQ of 1200 cases every two months from Scary Clowns. Scary Clowns incurs setup costs of $1800 every time it produces these cases, and its annual holding cost per case is $3.

a. How many units should Scary Clowns produce in each batch?

b. What is the total annual setup and holding cost for Scary Clowns using this policy?

2. Suzy’s Candy Distributors has an annual demand for its boxes of “Chocolate Heaven Candies” of 250,000 units, an ordering cost of $85 per order, and an annual holding cost percentage of 16%. The current purchase price for each box is $28, but the supplier has notified Suzy that starting next week, the purchase price will rise to $40. Suzy’s inventory of boxes is about to be depleted. How many boxes should Suzy purchase?

3. Consider a periodic review system, where orders are placed every 14 days. The firm strives to provide a 96.5% cycle service level. Demand averages 400 units per day, and the standard deviation of demand per day is 84 units. Lead time is 10 days.

a. How many units of safety stock should be held?

   b. What should the target inventory level (order-up-to level) be?

   c. Suppose that it is time to review the item. There are 170 units in inventory, and there is an outstanding backorder for 300 units. An order for 88 units is on the way. How many units should be ordered now?

4.   Consider a continuous review inventory system. Demand is normally distributed with an average of 64,000 per month and a monthly standard deviation of 8020 units. Lead time is two weeks (assume four weeks per month). If the firm desires only a 67% cycle service level, how many units of safety stock should be held?

SHOW YOUR WORK PLEASE

Answer 1

Answer to question1:

1. Annual demand for scary clowns = D = 1200 cases/ 2 months x 12 months = 7200 cases

Set up cost = Cs = $1800

Holding cost per case = Ch = $3

Units to be produced in each batch ( EOQ ) = square root ( 2 x Cs x D / Ch ) = square root ( 2 x 1800 x 7200 / 3 ) = 2939.38 ( 2939 rounded to nearest whole number )

1. Annual set up cost = Cs x Number of set ups = Cs x annual demand/ EOQ = $1800 x 7200 / 2939 = $4409.66

Annual holding cost = Ch x average inventory = Ch x EOQ /2 = $3 x 2939/2 = $4408.5

Total annual set up and holding cost = $4409.60 + $4408.50 = $8818.10

Answer to question 2 :

Annual demand for candies = D = 250,000 boxes

Ordering cost = Co = $ 85

Annual unit holding cost = Ch = 16% of $40 = $6.4

Number of boxes Suzy to purchase ( EOQ )

= square root ( 2 x Co x D / Ch )

= 2576.94 ( 2577 rounded to nearest whole number )

SUZY SHOULD PURCHASE = 2577 BOXES

                             Answer to question 3 :

                              Z value for 96.5% service level = NORMSINV ( 0.965 ) = 1.811

                             

Given are following data :

Review period = 14 days

Lead time = 10 days

Therefore , Protection period = review period + Lead time = 14 + 10 = 24 days

Standard deviation of demand during protection period

= Standard deviation of daily demand x square root ( Protection period )

= 84 x Square root ( 24 )

= 84 x 4.898

= 411.43

Therefore, safety stock = Z value x standard deviation of demand during protection period= 1.811 x 411.43 = 745.099 ( 745 rounded to nearest whole number )

745 UNITS OF SAFETY STOCK SHOULD BE HELD

Order upto level = Daily demand x Protection period + Safety stock = 400 x 24 + 745 = 9600 + 745 = 10345

ORDER UPTO LEVEL = 10345 UNITS

Number of units to be ordered now

= Order upto level – Inventory + Outstanding back order – Number of units on the way

= 10345 – 170 + 300 – 88

= 10387

NUMBER OF UNITS TO BE ORDERED NOW = 10387 UNITS

Answer to question 4 :

Z value of cycle service level = NORMSINV ( 0.67 ) = 0.44

Standard deviation of demand for 4 weeks = 8020 units

Therefore, standard deviation of demand during lead time of 2 weeks

= 8020 x Square root ( 2/4)

= 8020 x 0.707

= 5670.14

Amount of safety stock to be held

= Z value x standard deviation of demand during lead time

= 0.44 x 5670.14

= 2494.86 ( 2495 rounded to nearest whole number )

2495 UNITS OF SAFETY STOCK TO BE HELD