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The Total-Cost Curve is U-Shaped

Ordering and Carrying Costs. The Total-Cost Curve is U-Shaped. Annual Cost. Ordering Costs. Order Quantity (Q). Q O. ( optimal order quantity). Total Cost. Adding Purchasing cost doesn’t change EOQ. PD. Cost. TC with PD. TC without PD. 0. Quantity. EOQ. Quantity Discount.

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The Total-Cost Curve is U-Shaped

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  1. Ordering and Carrying Costs The Total-Cost Curve is U-Shaped Annual Cost Ordering Costs Order Quantity (Q) QO (optimal order quantity)

  2. Total Cost Adding Purchasing costdoesn’t change EOQ PD Cost TC with PD TC without PD 0 Quantity EOQ

  3. Quantity Discount By quantity discount, we mean the price per unit decreases as order quantity increases. When quantity discounts are offered, there is a separate, U-shaped, total cost curve for each unit price. When unit price decreases, the total cost curve drops. A different total cost curve is applied to each price. If we have quantity discount, then we should weigh the benefit of price discount against the increase in inventory cost.

  4. Example Demand for a product is 816 units / year ==> D = 816 Ordering cost is $12 / order ==> S = 12 Carrying cost is $4 / unit / year ==> H = 4 Price schedule is as follows Quantity (Q) Price (P) 1-49 20 50-79 18 80-99 17 100 or more 16 What is the best quantity that we could order to minimize our total annual cost?

  5. Total Cost Including Purchasing Cost p1 p2 p3 p4 EOQ Cost 0 Quantity

  6. Total Cost with different Purchase Price Smaller unit prices will raise total cost curve less than larger unit prices. For each price, there is a separate U-shaped total cost curve for total cost. Note that no single curve is applied to the entire range of quantities. Each curve is applied to a portion of the range.

  7. Quantity Discount Large quantity purchases Price Discount - purchasing cost Fewer orders - Ordering costs More inventory - inventory cost Our objective is to minimize the total annual costs TC = SD/Q + HQ/2 + PD In our initial model we assumed price is fixed. Therefore we did not include PD in the model.

  8. Total Cost With Price Discount p1 p2 p3 p4 EOQ Cost 0 Quantity

  9. Total Cost Including Purchasing Cost p1 Cost p2 p3 p4 0 Quantity EOQ

  10. Total Cost Including Purchasing Cost The applicable or feasible total cost is initially on the curve with the highest unit price and then drops down curve by curve at the price breaks. Price breaks are the minimum quantities needed to obtain the discounts. If carrying cost is stated in terms of cost / unit of product / year, there is a single EOQ which is the same for all cost curves.

  11. Solution Procedure 1- Compute EOQ without price considerations. This EOQ is the same for all prices. 2- But this EOQ is feasible for only one price. Identify the corresponding price and quantity. 3-If EOQ is feasible for the lowest price ==>it is the solution. If it is not, then calculate: a) TC for EOQ and corresponding feasible price. Note that TC is… TC = HQ/2 + SD/Q +PD b) calculate TC for all Qs of price break after the above prices. Compare their TC to find the best Q ==>it is the solution.

  12. Total Cost Including Purchasing Cost Q p1 Cost p2 p4 p3 0 Quantity EOQ

  13. Total Cost Including Purchasing Cost Q p1 Cost p4 p2 p3 0 EOQ Quantity

  14. Total Cost Including Purchasing Cost EOQ p1 Cost p4 p3 p2 0 Quantity

  15. Example Demand for a product is 816 units / year ==> D = 816 Ordering cost is $12 / order ==> S = 12 Carrying cost is $4 / unit / year ==> H = 4 Price schedule is as follows Quantity (Q) Price (P) 1-49 20 50-79 18 80-99 17 100 or more 16 What is the best quantity that we could order to minimize our total annual cost?

  16. Example (Q) (P) 1-49 20 50-79 18 80-99 17 100 or more 16 Q=70 is in the 50-79 range. Therefore, the corresponding price is $18. Obviously, we do not consider P=20, but what about P=17 or P=16?

  17. Total Cost Including Purchasing Cost p1 Cost p2 p3 p4 0 Quantity EOQ

  18. Example Is Q = 70 and P = 18 better or Q = 80 and P = 17 or Q = 100 and P = 16 TC = HQ/2 + SD/Q + PD TC ( Q = 70 , P = 18) = 4(70)/2 +12(816)/70 + 18(816) TC = 14968 TC ( Q = 80 , P = 17) = 4(80)/2 +12(816)/80+ 17(816) TC = 14154 TC ( Q = 100 , P = 16) = 4(100)/2 +12(816)/100 + 16(816) TC = 13354

  19. Example • Demand for a product is 25 tones / day and there are 200 • working days / year. ==> D = 25(200) = 5000. • Ordering cost is $48 / order ==> S = 48 • Carrying cost is $2 / unit / year ==> H = 2 • Price schedule is as follows: • Quantity (Q) Price (P) • 600-... 8 • 400-599 9 • 0-399 10 • What is the best quantity that we could order to minimize our total annual cost?

  20. Example Q P 600-... 8 400-599 9 0-399 10 Q=490 is in the 400-599 range. Therefore, the corresponding price is $9. Obviously, we do not consider P=10 but what about P=8?

  21. Example Is Q = 490 and P = 9 better or Q = 600 and P = 8 We should compare their TC TC = HQ/2 + SD/Q + PD TC ( Q = 490 , P = 9) = 2(490)/2 + 48(5000)/490+ 9(5000) TC = 490 + 489.8 + 45000 = 45979.8 TC ( Q = 600 , P = 8) = 2(600)/2 + 48(5000)/600 + 8(5000) TC = 41000

  22. Assignment 12b • Problem 2: A small manufacturing firm uses approximately 3400 pounds of chemical dye per year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The supplier has just announced that orders of 1000 pounds and more will be filled at a price of $2 per pound. The ordering cost is $100 and inventory carrying cost is 51 cents per unit per year. • Determine the order size that will minimizes the total cost. • If the supplier offered a discount at 1500 pounds instead of 1000 pounds, what order size will minimize total cost?

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