1. Grant County Hospital consumes 2,000 boxes of 45 clamps per week. The price of clamps is $76 per box, and the hospital operates 52 weeks per year. The cost of processing an order is $62, and the cost of holding one box of clamps for a year is 28 percent of the value of the clamp. a. The hospital orders the 45 clamps in lot sizes of 1,000 boxes. What extra cost does the hospital incur that 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 two weeks. What safety stock is necessary if the hospital uses a continuous-review system and a 99-percent cycle-service level is desired? What should be the reorder point? a. If the hospital uses a periodic-review system, with P = two weeks, what should be the target inventory level, T?

Annual demand (D) = 2000 boxes

Ordering cost (S) = $62

Price = $76 per box

Holding cost (H) = 28% of price = 28% of $76 = $21.28

Average weekly demand (d) = D/Number of weeks per year

= 2000/52

= 38.46 boxes

a) Economic order quantity (Q*) = sqrt of (2DS / H)

= sqrt of [(2 x 2000 x 62) / 21.28)]

= 107.95 or rounded to 108 boxes

Total cost with EOQ = Holding cost + ordering cost

= [(Q/2)H] + [(D/Q) S]

= [(108/2)21.28] + [(2000/108)62]

= $1149.12 + $1148.15

= $2297.27

If with the current policy order quantity (Q) = 1000 boxes

Total cost = Ordering cost + Holding cost

= [(D/Q) S] + [(Q/2)H]

= [(2000/1000)62] + [(1000/2)21.28]

= $124 + $10640

= $10764

Extra cost = Total cost with current policy – Total cost with EOQ

= $10764 – $2297.27

= $8466.73

b) Standard deviation of weekly demand (sigmad) = 100 boxes

Lead time (L) = 2 weeks

At 99% service level value of Z = 2.33

Reorder point = d x L + (Z x sigma d x sqrt of L)

= 38.46 x 2 + (2.33 x 100 x sqrt of 2)

= 76.92 + (2.33 x 100 x 1.41)

= 76.92 + 328.53

= 405.45 boxes

a) with a periodic review system,

Review period (P) = 2 weeks

Target inventory level = d(P+L) + [Z x sigma d x sqrt of (P+L)]

= 38.46(2+2) + [2.33 x 100 x sqrt of (2+2)]

= (38.46 x 4) + (2.33 x 100 x sqrt of 4)

= 153.84 + (2.33 x 100 x 2)

= 153.84 + 466

= 619.84 boxes

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