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Inventory Models

Inventory Models. Quantity Discount Models. TYPES OF QUANTITY DISCOUNT MODELS. Quantity Discount Models are of two types All Units Discounts Above a certain order level, Q 1 , all units in the order are discounted (Usual Case) Incremental Discounts (Not Discussed Here)

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Inventory Models

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  1. Inventory Models Quantity Discount Models

  2. TYPES OF QUANTITY DISCOUNT MODELS • Quantity Discount Models are of two types • All Units Discounts • Above a certain order level, Q1, all units in the order are discounted (Usual Case) • Incremental Discounts (Not Discussed Here) • Above a certain order level, Q1, all items above Q1 are discounted – the first Q1 items are sold at a non-discounted price

  3. ALL UNIT QUANTITY DISCOUNTS Reconsider the juicer example where: H = .14, CO = 12, D = 6240/yr Suppose the following all-unit discount pricing plan applies: Quantity Unit Ordered Cost <300 $10.00 300- 600 $ 9.75 600-1000 $ 9.50 1000-5000 $ 9.40 ≥5000 $ 9.00

  4. PIECEWISE APPROACH • Consider each quantity discount for Ci as if it were valid everywhere from 0 -  • STEP 1: For each value of Ci, calculate the corresponding value of Qi* -- it will change slightly since Ch = HCi and Ci changes slightly. • STEP 2: For each quantity discount for Ci, consider the interval (from a lower limit QL to an upper limit QU) over which the price Ci is valid and determine the value of Q that gives the lowest cost for the interval. (See next slide.) • STEP 3: Compare the lowest costs for each interval, and choose the lowest of these interval lowest costs.

  5. DETERMINIG THE BEST VALUE OF Q FOR EACH INTERVAL AND OVERALL • BEST VALUE OF Q FOR AN INTERVAL BETWEEN QL AND QU • If Q* >QU, ignore this interval • if Qi* is in interval, Qopt = Qi* • If Q* < QL, Qopt = QL

  6. QOPT for the interval in which Qi* > QU Lowest point occurs at QU.Qopt = QU But we can see that Q* (which will have an even deeper discount) gives alower total cost, TC. QL QU Qi* TC Q

  7. QOPT When Qi* Is In the Interval Q* is the lowest point in the interval.Qopt = Q* QU QL Q* TC Q

  8. QOPT for the interval in which Qi* < QL Lowest point occurs at QL.Qopt. = QL Q* QL QU TC Q

  9. Calculations for C = $10Interval (0,300) Since Q* > 300, the optimal solution for the model cannot come from this interval.

  10. Calculations for C = $9.75Interval (300,600) Since Q* = 331 is in the interval (300,600), for this interval: Qopt = Q* = 331

  11. Calculations for C = $9.50Interval (600,1000) Since Q* = 336 < 600,for this interval: Qopt = 600

  12. Calculations for C = $9.40Interval (1000,5000) Since Q* = 337 < 1000,for this interval: Qopt = 1000

  13. Calculations for C = $9.00Interval (5000,) Since Q* = 345 < 5000,for this interval: Qopt = 5000

  14. QUANTITY DISCOUNT APPROACH FOR ALLEN Quantity Unit Cost Ch Q* Qopt TC < 300 $10.00 $1.40 327 ---- ---- 300-600 $ 9.75 $1.365 331 331 $61,292 600-1000 $ 9.50 $1.33 336 600 $59,804 1000-5000 $ 9.40 $1.316 337 1000 $59,389 5000 $ 9.00 $1.26 345 5000 $59,325 • ORDER 5000 Note: This is over a 9 month supply -- is this OK?

  15. REORDER POINT ANALYSIS • Reorder point and safety stock determination are not affected by quantity discounts. • They are found in the same way as before: • r* = LD + SS if demand is constant over lead time • r* is found using service levels if demand varies during lead time

  16. Using the Template Optimal Values Enter Values Enter Discount Breaks and Discount Prices All-Units Worksheet

  17. Review • Types of Discount Models: • All-unit and Incremental • All-Units Quantity Discount Model • Qi* is found for each interval from QL to QU • Best point for interval is Qi* if Qi* is in interval • If Q* < QL, QL is best point for interval • Best value of Q is found by finding the lowest cost for each interval and taking the Q with the lowest total cost. • Reorder point analysis is not affected. • Use of template

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