[Compatibility Mode]- Microsoft Word Wk5 (Summerwk4)A N PAGE LAYOUT REFERENCES M
ID: 421835 • Letter: #
Question
[Compatibility Mode]- Microsoft Word Wk5 (Summerwk4)A N PAGE LAYOUT REFERENCES MAILINGS REVE VIEW ACROBAT Inventory Assignment Part A A small hospital purchases units of red blood from a local blood collection agency. The hospital uses 2.,000 units monthly and pays $252.72 per unit. The cost per order is S150.00. The cost of capital is 11 and the handling, insurance, and spoilage costs are 8% of the item cost. 1. Determine the EOQ and the total annual inventory holding cost 2. The blood collection agency provides a $2,000 rebate/year for customers that order a minimum o 3. The hospital operates 365 days per year and the lead time to order blood is 10 days. Determine th 4. The bospital is concerned with fluctuating demand and would like to maintain safety stock with a 750 units for each order. Determine how much the hospital would save or lose each year if it accepted the suppliers offer reorder point and the average time between orders 95% service level Ifthe historical standard deviation of daily demand is 36 units, what should the new reorder point be? Part B Complete Problem No. 12 on page 286 of the Textbook.Explanation / Answer
Answer to question 1 :
Economic order Quantity ( EOQ )
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 150 x 24000 /48.01 )
= 387.25 ( 388 rounded to nearest whole number)
If we define, total annual inventory holding cost as
= Total ordering cost + Total annual inventory carrying cost
Then,
Annual ordering cost
= Ordering cost x Number of orders
= Ordering cost x Annual demand / EOQ
= Co x D/EOQ
= $150 x 24000/388
= $9278.35
Annual inventory carrying cost
= Annual unit inventory cost x average inventory
= Ch x EOQ/2
= $48.01 x 388/ 2
= $9313.94
Therefore, total annual inventory holding cost = $9278.35 + $9313.94 = $18592.29
Answer to question 2 :
Order quantity =750 units
Annual ordering cost
= Ordering cost x Number of orders
= Ordering cost x annual demand / order quantity
= $150 x 24000/ 750
= $4800
Annual inventory carrying cost
= Annual unit inventory carrying cost x Average inventory
= Ch x Order quantity / 2
= $48.01 x 750 /2
= $18003.75
Total annual inventory holding cost
= $4800 + $18003.75
= $22803.75
Therefore ,
Increase in annual inventory holding cost
= $22803.75 - $18592.29
= $4211.46
Increase in annual inventory holding cost ( i.e. increase of $4211.46 ) is more than $2000 rebate obtained for order quantity of 750 making net increase in total cost as =$4211.46 - $2000 = $2211.46
Therefore,
HOSPITAL WILL LOSE EVERY YEAR $2211.46 IF IT ACCEPTED THE SUPPLIER OFFER
Answer to question 3 :
Daily demand = 24000 / 365
Lead time to order blood = 10 days
Therefore , reorder point = Daily demand x Lead time ( days) = ( 24000/365 ) x 10 = 657.53 ( 658 units rounded to nearest whole number )
Average time between orders = EOQ/ annual demand x 365 days = 388/24000 x 365 = 5.90 days
Answer to question 4 :
Z value corresponding to service level of 95 % = NORMSINV ( 0.95 ) = 1.6448
Standard deviation of daily demand = 36 units
Lead time = 10 days
Therefore, standard deviation of demand during lead time = 36 x Square root ( 10 ) = 36x3.162=113.832
Safety stock
= Z value x standard deviation of demand during lead time
= 1.6448 x 113.832
= 187.23 ( 187 rounded to nearest whole number )
New reorder point = Old reorder point ( as derived in question #3 ) + Safety stock = 658+187=845
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