Question

Wood County Hospital consumes 1000 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% of the value of the material.

1. The hospital orders bandages in lot sizes of 900 boxes, what extra cost does the hospital incur, which it could save by using EOQ method?
2. 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% cycle-service is desired? What should be the reorder point?    When the cycle-service level is 97%, z = 1.88.

Answer 1

DEMAND = 52000
ORDERING COST = 15
HOLDING COST = 5.25
COST PER UNIT = 35

WORKING = 52

EOQ = SQRT(2 * ANNUAL DEMAND * ORDERING COST / HOLDING COST PER UNIT) = SQRT(2 * 52000 * 15 / 5.25) = 545
ANNUAL HOLDING COST = (EOQ / 2) * HOLDING COST PER UNIT = (545 / 2) * 5.25 = 1431

ANNUAL ORDERING COST = (DEMAND / EOQ) * ORDERING COST = (52000 / 545) * 15 = 1431

TOTAL COST OF MANAGING INVENTORY = ANNUAL HOLDING COST + ANNUAL ORDERING COST = 1431 + 1431 = 2862

USING 900 UNITS

FOR VALUE OF 900 UNITS:
ANNUAL HOLDING COST = (900 / 2) * 5.25 = 2363
ANNUAL ORDERING COST = (52000 / 900) * 15 = 867
TOTAL COST OF MANAGING = 2363 + 867 = 3230
SAVINGS = 3230 - 2862 = 368

2. DEMAND = 1000
STDEV DEMAND = 100
SERVICE LEVEL = 97, CORRESPONDING Z VALUE 1.88
LEAD TIME = 2

REORDER POINT = (DEMAND * LT) + SAFETY STOCK
SAFETY STOCK = Z * STANDARD DEVIATION OF DEMAND * SQRT(LEAD TIME)

SAFETY STOCK = 1.88 * 100 * SQRT(2) = 265.87

ROP = (1000 * 2) + 265.87 = 2266

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