1 / 17

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)

abel
Download Presentation

Inventory Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 VALUE BEST VALUE OF Q OF Qi* FOR INTERVAL > QU QU (Ignore – can get better discount) in interval Qi* < QL 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

More Related