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Outline EOQ Model with Price Break (All Units) The model The cost function and feasibility The procedure An example

LESSON 13 INVENTORY MODELS (DETERMINISTIC) EOQ MODEL WITH PRICE BREAKS. Outline EOQ Model with Price Break (All Units) The model The cost function and feasibility The procedure An example. EOQ Model with Price Breaks (All Units).

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Outline EOQ Model with Price Break (All Units) The model The cost function and feasibility The procedure An example

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  1. LESSON 13INVENTORY MODELS (DETERMINISTIC) EOQ MODEL WITH PRICE BREAKS Outline • EOQ Model with Price Break (All Units) • The model • The cost function and feasibility • The procedure • An example

  2. EOQ Model with Price Breaks (All Units) • So far, we have assumed that the unit cost is independent of the order quantity. • Often, the supplier encourages larger order sizes by providing price discounts. Such quantity discounts are common for many consumer products. • The text discusses two types of discounts. In each case, there are one or more breakpoints defining changes in the unit cost. • All units: discount is applied to all units. • Incremental units: discount is applied to the additional units beyond the breakpoint.

  3. EOQ Model with Price Breaks (All Units) • The difference between the two types of discounting can be discussed with an example. Suppose that the charge for photocopying is $0.10 per copy for 0-9 copies and $0.08 per copy for 10-49 copies. If 12 copies are made the total charge is computed as follows: • All units: each of the 12 units is charged $0.08. So, the total charge = $0.08  12 = $0.96 • Incremental units: the first 9 copies is charged $0.10 each and the remaining 3 units are charged $0.08 each. So, the total charge = $0.10  9 + $0.08  3 = $1.14.

  4. EOQ Model with Price Breaks (All Units) • With all units discount schedule, the total charge may be less if a larger quantity is ordered. See the previous example again. If 9 units are ordered, the total charge = $0.10  9 = $0.90. But, if 10 units are, the total charge = $0.08  10 = $0.80. So, even if you need 9 units, order 10 units, throw away the 10th unit and save $0.10. See the figure on the next slide. • Despite the above drawback, all units discount is often used because it is much simpler than the incremental units schedule. This course covers only the all units discount schedule.

  5. EOQ Model with Price Breaks (All Units)

  6. EOQ Model with Price Breaks (All Units) • Assumptions • Demand occurs at a constant rate of items per year. • Ordering Cost is per order. • Purchase Cost is per item if the quantity ordered is between 0 and , if the order quantity is between and , etc. • Holding Cost is per item in inventory per year (note holding cost is based on the cost of the item, ). • Delivery time (lead time) is constant.

  7. EOQ Model with Price Breaks (All Units)The Cost Function and Feasibility • Some Formulae • Optimal order quantity: the procedure for determining optimal order quantity will be demonstrated • Number of orders per year: • Time between orders (cycle time): years • Total annual cost: (holding + ordering + purchase)

  8. EOQ Model with Price Breaks (All Units) The Cost Function and Feasibility • The total annual cost function is different at different price level

  9. EOQ Model with Price Breaks (All Units) The Cost Function and Feasibility • The total annual cost function function is computed and plotted in the next slide for the following example:

  10. EOQ Model with Price Breaks (All Units)The Procedure Steps 1. Determine the largest (cheapest) feasible EOQ value and list all the candidates: The most efficient way to do this is to compute the EOQ for the lowest price first, and continue with the next higher price. Stop when the first EOQ value is feasible (that is, within the correct interval). At each price level choose the candidate for optimal order quantity as follows: • if the EOQ is feasible, the EOQ (the largest feasible EOQ) is a candidate for the optimal order quantity. • if the EOQ is not feasible, a candidate for the optimal order quantity is the minimum order quantity (a breakpoint) available at that price range.

  11. EOQ Model with Price Breaks (All Units)The Procedure Steps 2. Find cost given by each candidate and choose the best candidate: Compare the total annual cost given by the candidates. The optimal order quantity is the candidate for which the total annual cost is the minimum. Note carefully that this means comparing costs at the largest feasible EOQ and at all the price breakpoints that are greater than the largest feasible EOQ.

  12. Example 3: Nick's Camera Shop carries Zodiac instant print film. The film normally costs Nick $3.20 per roll, and he sells it for $5.25. Nick's average sales are 21 rolls per week. His annual inventory holding cost rate is 25% and it costs Nick $20 to place an order with Zodiac. If Zodiac offers a 7% discount on orders of 400 rolls or more and a 10% discount for 900 rolls or more, determine Nick's optimal order quantity.

  13. Step 1: Determine the largest (cheapest) feasible EOQ and list all the candidates

  14. Step 2: Find cost given by each candidate and choose the best candidate

  15. READING AND EXERCISES Lesson 13 Reading: Section 4.7 , pp. 214-217 (4th Ed.), pp. 205-208 (5th Ed.) Exercise: 22, 24, pp. 220-221(4th Ed.), p. 211 (5th Ed.)

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