Question

Problem 2

The ER would like to add Tegaderm (a semi-occlusive dressing) to the pharmacy’s inventory, as it currently stocks none and it would be helpful for patients to be able to apply at home after discharge. It has been assigned SKU-2319. You are in charge of ordering the correct amount of inventory. We know demand will be 80 dressings per day. Tegaderm is pricey, at about $1.50 per dressing with a fixed ordering and shipping cost of $12 per order. The annual cost of holding Tegaderm is fairly modest at only 10% of the unit cost. Assume a calendar year of 365 days, and the ER is (thankfully) open every day of the year.  Please round to the nearest whole unit (for units, dollars can remain in dollar/cents) for this entire problem.

1. Determine the Economic Order Quantity (EOQ) for Tegaderm. Please round to the nearest whole unit.
   1. EOQ = Sqrt((2*D*S)/h) Where D = Annual demand = 365*80 = 29200, h = 10% of $1.5 = $0.15 and S = ordering cost = $12
   2. = Sqrt((2*29200*12)/0.15) = 2161.480974 = 2161 (Rounded to nearest whole number)
      
2. Determine the time between orders (in days) and the total annual relevant inventory cost (i.e., sum of holding and ordering costs). Assume all orders are full orders.
   1. Time between orders = number of working days in year/no of orders in a year = 365/(29800/2161) = 26.46862416 days
   2. Total annual relevant inventory cost using EOQ = (29800/2161)*12+(2161/2)*0.15 = $327.56
      
3. Calculate the reorder point assuming the replenishment lead time is 7 days. Also, assume that demand is constant.
   1. Reorder point = Daily usage*lead time = 80*7 = 560 units

4. The supplier of Tegaderm (3M) has announced that Tegaderm must be ordered in packages of 100. What order quantity would you now use to meet 3M’s specification while still minimizing total annual relevant inventory costs? What is the increase in the total annual relevant inventory cost by using this new order quantity compared to the EOQ from your answer in part (a)?
   1. Total annual relevant inventory cost using packages of 100 = (29800/100)*12+(100/2)*0.15 = 3583.5
   2. Increase in cost by ordering in using packages of 100 = 3583.5-327.56 = 3255.94
   3. So, ordering quantity 2161 should be used to meet 3M’s specification while still minimizing total annual relevant inventory costs

Problem 3

Although your initial calculations were quite precise, you learn that Tegaderm experiences multiple stock-outs in the pharmacy. You have also learned that demand is actually variable; it has a mean of 80 dressings per day, with a daily standard deviation of 10. Additionally, 3M takes longer to ship than expected: it actually takes 10 days to receive an order. Please round to the nearest whole unit (for units, dollars can remain in dollar/cents) for this entire problem. You may ignore the quantity restriction from Problem 2.d in this problem, i.e., Tegaderm can be ordered in any integer number of units.

Note the unit cost of $1.50 per dressing, annual holding cost per unit inventory at 10% of unit cost, and fixed ordering cost of $12 remain the same. The ER also remains open for 365 days per year.

1. Assume the pharmacy uses a continuous review policy. How many units of Tegaderm should each order consist of?
2. Compute the safety stock needed to provide a 95% service level. What is the annual holding cost for holding this safety stock?
3. What should the re-order point be to provide a 95% service level?
4. How much additional safety stockis needed if the service level is increased from 95% to 98%?  By how much does the total annualrelevant inventory cost rise when the service level is increased from 95% to 98%?

(Note: z-values corresponding to standard normal probabilities can be calculated using Excel by using ‘norm.s.inv()’ function orcan be found in the table provided at the end of the problem)

Table of z-values

Probability	z-value	Probability	z-value
0.99	2.326	0.89	1.227
0.98	2.054	0.88	1.175
0.97	1.881	0.87	1.126
0.96	1.751	0.86	1.080
0.95	1.645	0.85	1.036
0.94	1.555	0.84	0.994
0.93	1.476	0.83	0.954
0.92	1.405	0.82	0.915
0.91	1.341	0.81	0.878
0.90	1.282	0.80	0.842

Question 2 is answered. I need Question 3/Part 3 Answered.

Answer 1

Economic Order Quantity refers to the number of unit the company should add to the inventory and the order is made to minimize the total inventory cost. It maintain a balance between ordering costs and carrying costs. Reorder point is the level of inventory which the firm holds in stock and when the inventory level reach this point, the firm must reorder the item.