1. Solved Problems Chapter 12: Inventory 1

2. Solved Problem The data shows projected annual dollar usage for 20 items. Exhibit 12.3 shows the data sorted, and indicates that about 70% of total dollar usage is accounted for by the first 5 items. Exhibit 12.2 Usage-Cost Data for 20 Inventoried Items 2

3. Exhibit 12.3 ABC Analysis Calculations 3

4. Exhibit 12.4 ABC Histogram for the Results from Exhibit 12.3 4

5. Solved Problem: Merkle Pharmacies, P. 245 D = 24,000 cases per year. C o = $38.00 per order. I = 18 percent. C = $12.00 per case. C h = IC = $2.16. TC = Q ($2.16) + ($38.00) 1212 24,000 Q EOQ = = 919 cases rounded to a whole number. 2(24,000)(38) 2.16 √ 5

6. Ordering costs are $45.00 per order. One ream of paper costs $3.80. Annual inventory-holding cost rate is 20%. The average annual demand is 15,000 reams, or about 15,000/52 = 288.5 per week. The standard deviation of weekly demand is about 71. The lead time from the manufacturer is two weeks. Solved Problem: Southern Office, p. 247 Southern Office Supplies, Inc. distributes laser printer paper. Inventory-holding cost is C h = IC = 0.20($3.80) = $0.76 per ream per year. 6

7. Solved Problem The average demand during the lead time is (288.5)(2) = 577 reams. The standard deviation of demand during the lead time is approximately 71√2 = 100 reams. The EOQ model results in an order quantity of 1333, reorder point of 577, and total annual cost of $1,012.92. 7

8. r =  L + z  L = 577 + 1.645(100) = 742 reams Solved Problem Desired service level of 95%, which results in a stockout of roughly once every 2 years. For a normal distribution, this corresponds to a standard normal z-value of 1.645. This policy increases the reorder point by 742 – 577 = 165 reams, which represents the safety stock. The cost of the additional safety stock is C h times the amount of safety stock, or ($0.76/ream)(165 reams) = $125.40. 8

9. Managing Fixed Period Inventory Systems Economic time interval: T = Q*/D [12.12] Optimal replenishment level without safety stock: M = d (T + L) [12.13] Where: d = Average demand per time period. L = Lead time in the same time units. M = Demand during the lead time plus review period. Solved Problem: Southern Office, p. 249, Fixed Period Inventory Systems 9

10. Managing Fixed Period Inventory Systems Uncertain Demand Compute safety stock over the period T + L. The replenishment level is computed as: M =  T+L + zσ T+L  T+L =  t (T + L) σ T+L = σ t √T + L [12.14] [12.15] [12.16] 10

11. Solved Problem: p. 250 A buyer orders fashion swimwear about six months before the summer season. Each piece costs $40 and sells for $60. At the sale price of $30, it is expected that any remaining stock can be sold during the August sale. The cost per item of overestimating demand is equal to the purchase cost per item minus the August sale price per item: c s = $40 – $30 = $10. The per-item cost of underestimating demand is the difference between the regular selling price per item and the purchase cost per item; that is, c u = $60 – $40 = $20. 11

12. Solved Problem Assume that a uniform probability distribution ranging from 350 to 650 items describes the demand. Exhibit 12.12 Probability Distribution for Single Period Model 12

13. Solved Problem The optimal order size Q must satisfy: P (demand ≤ Q*) = c u /(c u + c s ) = 20/(20+10) = 2/3 Because the demand distribution is uniform, the value of Q* is two-thirds of the way from 350 to 650. This results in Q* = 550. 13