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Solved Problems

Solved Problems. Chapter 12: Inventory. 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

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Solved Problems

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  1. Solved Problems Chapter 12: Inventory

  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

  3. Exhibit 12.3 ABC Analysis Calculations

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

  5. Solved Problem: Merkle Pharmacies, P. 245 D = 24,000 cases per year. Co = $38.00 per order. I = 18 percent. C = $12.00 per case. Ch = IC = $2.16. 24,000 Q 1 2 TC = Q ($2.16) + ($38.00) √ 2(24,000)(38) 2.16 EOQ = = 919 cases rounded to a whole number.

  6. Solved Problem: Southern Office, p. 247 Southern Office Supplies, Inc. distributes laser printer paper. • Inventory-holding cost is Ch= IC = 0.20($3.80) = $0.76 per ream per year. • 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.

  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.

  8. 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 Ch times the amount of safety stock, or ($0.76/ream)(165 reams) = $125.40. r = mL+ zsL= 577 + 1.645(100) = 742 reams

  9. Solved Problem: Southern Office, p. 249, Fixed Period Inventory Systems 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.

  10. Managing Fixed Period Inventory Systems • Uncertain Demand • Compute safety stock over the period T + L. • The replenishment level is computed as: [12.14] [12.15] [12.16] M = mT+L + zσT+L mT+L = mt (T + L) σT+L= σt √T + L

  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: cs = $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, cu = $60 – $40 = $20.

  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

  13. Solved Problem The optimal order size Q must satisfy: P (demand ≤ Q*) = cu /(cu + cs) = 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.

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