Question

13.26 County Hospital orders syringes from a hospital supply firm. The hospital expects to use 40,000 per year. The cost to order and have the syringes delivered is $800. The annual carrying cost is $1.90 per syringe because of security and theft. The hospital supply firm offers the following quantity discount pricing schedule.

QUANTITY	PRICE
????0–9,999	$3.40
10,000–19,999	?3.20
20,000–29,999	?3.00
30,000–39,999	?2.80
40,000–49,999	?2.60
50,000+	?2.40

1. What is the order quantity and total cost at each price point.

2. How would you advise the hospital?

3. Would your recommendation change if yearly demand went up to 45,000?

4. What is the reorder point for both demand levels if it takes 4 days for supplies to arrive.

5. Realistically demand for syringes is variable, and the daily demand is normally distributed at 105 a day with a standard deviation of 10. The lead time for restocking is still 4 days. If the hospital wants a service level of 99%, what is the reorder point? How much safety stock does this include?

Answer 1

1. The order quantity and total cost at each price point is calculated as below :

2. ADVISE : I will advise the Hospital to place order of 20,000 syringes per order as it minimises the Total Annual Cost for the hospital.

3. If yearly demand increased to 45,000, the revised calculations are below :

My recommendation will change to 30,000 syringes per order as with revised demand, this is the level at which the total annual cost is minimum.

4) The reorder points for both the demand points are as below :

5) For daily demand of 105, we calculate the safety stock and reorder point as below :