Question

A community hospital in Southeast Ohio consumes 1,000 boxes of bandages per week. The price of bandages is $35 per box, and the hospital operates 52 weeks per year. The ordering cost is $15, and the cost of holding one box is 15% of the price of the material. The lead time to receive materials is 2 weeks. CERTAIN DEMAND (SET STANDARD DEVIATION TO 0)

a) Currently, the hospital orders bandages in lot sizes of 900 boxes for total costs of $3,229.16.

i. Calculate the EOQ quantity using OM explorer. Enter 50% for cycle-service level on Inputs tab. What is the EOQ quantity? (see Inputs tab)

ii. What are the costs for this EOQ quantity? (see Results tab)

iii. How much money could the hospital save by using the EOQ quantity instead of the lot size of 900?

b) What happens to the EOQ quantity when the unit price doubles? How does that change the ordering behavior of the manager? Why does that make economic sense?

c) What happens to the EOQ quantity if the ordering costs go down by 20% - to $12 per order (use original unit price, $35/box)?

d) The EOQ is the optimal lot size that minimizes the sum of holding & ordering costs. Is there any reason a company wouldn’t want to use the EOQ?

UNCERTAIN DEMAND (STANDARD DEVIATION ≠ 0)

e) Demand is still 1000 boxes per week and is normally distributed, with a standard deviation of weekly demand of 100 boxes. Use cost information from original problem statement.

i. What safety stock is necessary if the hospital uses a continuous review system and a 97% cycle-service level is desired?

ii. What is the reorder point? (HINT: Use weekly demand numbers for this calculation)

iii. What is the cost of using the continuous review system?

iv. How does the safety stock change if lead time is reduced from 2 weeks to 1 week?

v. What happens to overall costs if cycle-service level is reduced to 80% (use original lead time = 2 weeks)? Which industries/business might use a lower cycle-service level?

f) If the hospital uses a periodic review system, with the review period (P) equal to 2 weeks and cycle-service level of 97%: i. What would be the target inventory level, T? (Use the original information from part e)

ii. What is the cost of using the periodic review system?

iii. Compare/Contrast the continuous review system and periodic review system in terms of safety stock and costs. What are the managerial implications of each?

Answer 1

a.

(A) Annual consumption of bandages =1000*52 boxes= 52000 boxes

(P)price per box= $35

(O)Ordering cost = $15

(S)holding cost =$35*15% = $5.25

Lead time = 2 weeks

(i) EOQ=√ 2*A*O/ S

=√ 2*52000*15/5.25

= 545 UNITS

(ii) cost of placing EOQ order =

ordering cost = no. of orders * cost per order

= 96 * 15

= $1440

+ holding cost = 545/2*5.25 = $1430.63

Total cost per EOQ order =$2870.63

No. of orders = 52000/545 =96 orders

(iii) Total cost of purchasing 900units = $ 3229.16

Total cost of purchasing 545 units = $ 2870.63

Cost can be save by the hospital = $358.53

b. If unit price gets double

Holding cost will be = 70*15% =$10.5

new EOQ=√ 2*52000*15/10.5= 386 units

The EOQ will be reduced i.e. because the carrying and holding costwill increase due to change in unit price .

The ordering behaviour of manager will definately be changed he will prefer to buy less quantity at a time as it will cost him more to store more quantity.

c. If Ordering cost  goes down by 20% =$ 12

Then, EOQ=√ 2* 52000*12 / 5.25  

= 488 units

If ordering cost decrease by 20% EOQ will also gets decrease by 10%

d. Yes there is a reason that some companies didnot use the EOQ as in some companies there is unusual demand as some months have high demand of the product while others have less  demand . so, they prefer to buy as per the consumption of the product.