Wood County Hospital consumes 1,000 boxes of bandages per week. The price of ban

Question

Wood County Hospital 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 cost of processing an order is $15 and the cost of holding one box for a year is 15 percent of the value of the material.

a. The hospital orders bandages in lot sizes of 900 boxes. What extra cost does the hospital incur, which it could save by using the EOQ method?

b. Demand is normally distributed, with a standard deviation of weekly demand of 100 boxes. The lead time is 2 weeks. What safety stock is necessary if the hospital uses a continuous review system and a 97 percent cycle-service level is desired? What should be the reorder point?

c. If the hospital uses a periodic review system, with P = 2 weeks, what should be the target inventory level, T?

Explanation / Answer

a. Annual Demand (1000 * 52) 52000 Ordering Cost $        15.00 Holding Cost ( 35 * 15%) $          5.25 EOQ = 2AO / H where A = Annual Demand O = Ordering Cost per order H = Holding Cost per unit per annum EOQ = 2AO / H = (2 * 52000 * 15) / 5.25 = 545.1081 units or, 545 units Order Size (A) 545 900 Average Inventory = EOQ/2 (B) 272.5 450 Ordering Cost per order ( C) $15 $15 # orders per year = Annual Demand / EOQ (D) 95 58 Holding Cost (E = B * $5.25) $ 1,430.63 $ 2,362.50 Ordering Cost (F = D * $10) $ 1,431.19 $     866.67 Total Cost (E+F) $ 2,861.82 $ 3,229.17 Savings in Cost = $3229.17 - 2861.82 = $367.35 b. Mean Demand 1000 Standard Deviation of Daily Demand (SDd) 100 Lead Time (weeks) 2 Standard Deviation of Lead Time (SDl) = SDd * Lead Time = 100*2 = 225 141.42 Service Level Desired 97% Z Value at 97% 1.881 Safety Stock for 97% service level Z value * Standard Deviation (Demand Lead Time) (141.42 * 1.881) 266 Z Value = 1.881 Lead Time Demand ( Lead Time * Avg Demand) 2000 Reorder Point = Lead Time Demand + Safety Stock 2266 c. In a periodic review system, find target inventory T, given: P = 2 weeks L = 2 weeks Safety stock = z * std Dev (P,L) Std Dev (P,L) = Std Dev Demand * P+L = 100 * 2+2 = 200 units Safety stock = 1.881* (200) = 376 units T = Average demand during the protection interval + Safety stock T = 1000(2 + 2) + 376 T = 4,376 units

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