<ul><li>Cover some realistic situations which relax one or more of the EOQ assumptions </li></ul><ul><ul><li>Non-Instantan...
<ul><li>Item used or sold as they are completed, without waiting for a full lot to be completed </li></ul><ul><li>Usual ca...
<ul><li>Recall … </li></ul><ul><li>TC  =  annual holding costs plus annual setup costs </li></ul><ul><li>  =  </li></ul><u...
<ul><li>Buildup at a rate of (  p-d ) (units/day) during  production phase until a lot size of  Q  is produced </li></ul><...
<ul><li>Total Cost =  Annual holding costs + annual ordering costs </li></ul><ul><li>Setting up the total cost equation,  ...
<ul><li>Differentiation of this equation with respect to  Q , setting the result equal to zero,  and solving for  Q  resul...
Demand = 30 barrels/day  Setup cost = $200 Production rate = 190 barrels/day  Annual holding cost = $0.21/barrel Annual de...
Demand = 30 barrels/day  Setup cost = $200 Production rate = 190 barrels/day  Annual holding cost = $0.21/barrel Annual de...
Demand = 30 barrels/day  Setup cost = $200 Production rate = 190 barrels/day  Annual holding cost = $0.21/barrel Annual de...
Demand = 30 barrels/day  Setup cost = $200 Production rate = 190 barrels/day  Annual holding cost = $0.21/barrel Annual de...
<ul><li>Quantity discounts are price incentives to purchase large quantities </li></ul><ul><li>Price break is the minimum ...
<ul><li>There are cost curves for each price level </li></ul><ul><li>The feasible total cost begins at the top curve, then...
C for P = $4.00 C for P = $3.50 C for P = $3.00 Total annual cost, $ Purchase quantity,  Q 0   100   200   (a) Total cost ...
<ul><li>Step 1: </li></ul><ul><li>Beginning with the lowest price, calculate the EOQ for each price level until a feasible...
Purchase Discounts     Example Annual demand = 936 units Ordering cost = $100.00 Holding cost = 25% of unit price Order Qu...
Purchase Discounts     Example Price = $60.00 Price = $59.00 Price = $58.00
<ul><li>Step 2: </li></ul><ul><li>If the first feasible EOQ found is for the lowest price level, this quantity is the best...
Purchase Discounts     Example Price = $60.00 Price = $59.00 Price = $58.00
Purchase Discounts     Example Annual demand = 936 units Ordering cost = $100.00 Holding cost = 25% of unit price Order Qu...
<ul><li>The best purchase quantity is 250 units, which does not correspond to the deepest discount price. </li></ul><ul><l...
<ul><li>Single-Period Inventory Model </li></ul><ul><ul><li>One time purchasing decision (Example: vendor selling t-shirts...
<ul><li>Problem for seasonal and high fashion goods. </li></ul><ul><li>Only allowed to order one time. </li></ul><ul><li>S...
<ul><li>List different demand levels and probabilities </li></ul><ul><li>Develop a payoff table, where each new row repres...
<ul><li>The payoff is: </li></ul><ul><li>where:  p  =  profit per unit sold during the season   l  =  loss per unit dispos...
<ul><li>Calculate the  expected  payoff of each  Q . For a specific  Q , first multiply each payoff by its demand probabil...
<ul><li>For one item,  p  = $10 and  l = $5.  The probability distribution for the season’s demand is: </li></ul><ul><li> ...
<ul><li>Complete the following payoff matrix, as well as the column on the right showing expected payoff.  </li></ul><ul><...
<ul><li>Payoff if  Q  = 30 and  D  = 20: </li></ul><ul><li>Payoff if  Q  = 30 and  D  = 40: </li></ul><ul><li>Expected pay...
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Cover Some Realistic Situations Which Relax One Or More Of The Eoq Assumptions

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  • Cover Some Realistic Situations Which Relax One Or More Of The Eoq Assumptions

    1. 1. <ul><li>Cover some realistic situations which relax one or more of the EOQ assumptions </li></ul><ul><ul><li>Non-Instantaneous Replenishment </li></ul></ul><ul><ul><li>Quantity Discounts </li></ul></ul><ul><ul><li>One-Period Decisions </li></ul></ul>Operations Management Special Inventory Models
    2. 2. <ul><li>Item used or sold as they are completed, without waiting for a full lot to be completed </li></ul><ul><li>Usual case is where production rate, p , exceeds the demand rate, d , so there is a buildup rate of ( p – d ) units during time when both production and demand occur. </li></ul><ul><li>Both p and d expressed in same time interval. </li></ul>Special Inventory Models Non-Instantaneous Replenishment
    3. 3. <ul><li>Recall … </li></ul><ul><li>TC = annual holding costs plus annual setup costs </li></ul><ul><li> = </li></ul><ul><li>Ave. Inv. Level = </li></ul><ul><li>Now ... </li></ul><ul><li>Avg. Inv. Level = </li></ul>Non-Instantaneous Replenishment Economic Lot Size (ELS)
    4. 4. <ul><li>Buildup at a rate of ( p-d ) (units/day) during production phase until a lot size of Q is produced </li></ul><ul><li>Buildup continues for Q / p days (units/units/day) </li></ul><ul><li>I max = units per day, ( p-d ), x number of days ( Q / p ) </li></ul><ul><li>where: p = production rate d = demand rate Q = lot size </li></ul>Non-Instantaneous Replenishment Economic Lot Size (ELS)
    5. 5. <ul><li>Total Cost = Annual holding costs + annual ordering costs </li></ul><ul><li>Setting up the total cost equation, where D is the annual demand: </li></ul>Non-Instantaneous Replenishment Economic Lot Size (ELS)
    6. 6. <ul><li>Differentiation of this equation with respect to Q , setting the result equal to zero, and solving for Q results in the Economic Production Lot Size, ELS : </li></ul><ul><li>Since p > d , the second term is greater than 1, </li></ul><ul><ul><li>so the ELS is __________ than the EOQ </li></ul></ul>Non-Instantaneous Replenishment Economic Lot Size (ELS)
    7. 7. Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Non-Instantaneous Replenishment Example ELS = p p - d 2 DS H
    8. 8. Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Non-Instantaneous Replenishment Example
    9. 9. Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Non-Instantaneous Replenishment Example TBO ELS = (350 days/year) ELS D
    10. 10. Demand = 30 barrels/day Setup cost = $200 Production rate = 190 barrels/day Annual holding cost = $0.21/barrel Annual demand = 10,500 barrels Plant operates 350 days/year Non-Instantaneous Replenishment Example Production time = ELS p
    11. 11. <ul><li>Quantity discounts are price incentives to purchase large quantities </li></ul><ul><li>Price break is the minimum purchase quantity to get a certain discount price </li></ul><ul><li>The item’s price is no longer fixed so there are three relevant cost components </li></ul><ul><ul><li>annual purchase costs in addition to annual holding costs and annual ordering (setup) costs </li></ul></ul>Special Inventory Models Quantity Discounts
    12. 12. <ul><li>There are cost curves for each price level </li></ul><ul><li>The feasible total cost begins at the top curve, then drops down, curve by curve, at the price breaks. </li></ul><ul><li>The EOQs do not necessarily produce the best (“minimum total annual cost”) lot size. </li></ul>Quantity Discounts Feasible Price-Quantity Combinations
    13. 13. C for P = $4.00 C for P = $3.50 C for P = $3.00 Total annual cost, $ Purchase quantity, Q 0 100 200 (a) Total cost curves with purchased materials added Purchase Discounts Total Cost Curves First price break Second price break
    14. 14. <ul><li>Step 1: </li></ul><ul><li>Beginning with the lowest price, calculate the EOQ for each price level until a feasible EOQ is found. </li></ul><ul><ul><li>it is feasible if the quantity lies in the range corresponding to its price. </li></ul></ul><ul><li>As subsequent prices are larger than the previous one, the holding cost, H , ( H = i·P ) gets larger. </li></ul><ul><li>Since H is in the denominator of the EOQ formula, the EOQ gets smaller . </li></ul>Purchase Discounts Solution Procedure
    15. 15. Purchase Discounts Example Annual demand = 936 units Ordering cost = $100.00 Holding cost = 25% of unit price Order Quantity Price per Unit 0 - 249 $60.00 250 - 499 $59.00 500 or more $58.00
    16. 16. Purchase Discounts Example Price = $60.00 Price = $59.00 Price = $58.00
    17. 17. <ul><li>Step 2: </li></ul><ul><li>If the first feasible EOQ found is for the lowest price level, this quantity is the best lot size. </li></ul><ul><li>Otherwise, calculate the total cost for the first feasible EOQ and for the most economical, feasible order quantity at each lower price level. </li></ul><ul><li>The quantity with the lowest total cost is optimal. </li></ul>Purchase Discounts Solution Procedure
    18. 18. Purchase Discounts Example Price = $60.00 Price = $59.00 Price = $58.00
    19. 19. Purchase Discounts Example Annual demand = 936 units Ordering cost = $100.00 Holding cost = 25% of unit price Order Quantity Price per Unit 0 - 249 $60.00 250 - 499 $59.00 500 or more $58.00
    20. 20. <ul><li>The best purchase quantity is 250 units, which does not correspond to the deepest discount price. </li></ul><ul><li>This is not always true - EOQ is affected by: </li></ul><ul><ul><li>small discounts, quantity break points, </li></ul></ul><ul><ul><li>large holding cost, and </li></ul></ul><ul><ul><li>small demand. </li></ul></ul><ul><li>Small lot sizes may be better even though the price is not the lowest </li></ul>Quantity Discounts Example
    21. 21. <ul><li>Single-Period Inventory Model </li></ul><ul><ul><li>One time purchasing decision (Example: vendor selling t-shirts at a football game) </li></ul></ul><ul><ul><li>Seeks to balance the costs of inventory overstock and under stock </li></ul></ul><ul><li>Multi-Period Inventory Models </li></ul><ul><ul><li>Fixed-Order Quantity Models </li></ul></ul><ul><ul><ul><li>Event triggered (Example: running out of stock) </li></ul></ul></ul><ul><ul><li>Fixed-Time Period Models </li></ul></ul><ul><ul><ul><li>Time triggered (Example: Monthly sales call by sales representative) </li></ul></ul></ul>Special Inventory Models Inventory Models
    22. 22. <ul><li>Problem for seasonal and high fashion goods. </li></ul><ul><li>Only allowed to order one time. </li></ul><ul><li>Short selling seasons and long lead times prohibit the possibility of placing a second order. </li></ul><ul><li>A balance between ordering enough to meet demand and not having any left over at the end of the season. </li></ul><ul><li>Sometimes referred to as the ”Newsvendor” problem </li></ul>Special Inventory Models One-Period Decisions
    23. 23. <ul><li>List different demand levels and probabilities </li></ul><ul><li>Develop a payoff table, where each new row represents a different order quantity and each column represents a different demand. </li></ul>One-Period Decisions Selecting the Purchase Quantity
    24. 24. <ul><li>The payoff is: </li></ul><ul><li>where: p = profit per unit sold during the season l = loss per unit disposed of after the season Q = purchase quantity D = demand level </li></ul>One-Period Decisions Selecting the Purchase Quantity
    25. 25. <ul><li>Calculate the expected payoff of each Q . For a specific Q , first multiply each payoff by its demand probability, and then add the products. </li></ul><ul><li>Choose the order quantity Q with the highest expected payoff. </li></ul>One-Period Decisions Selecting the Purchase Quantity
    26. 26. <ul><li>For one item, p = $10 and l = $5. The probability distribution for the season’s demand is: </li></ul><ul><li> Demand Demand ( D ) Probability 10 0.2 20 0.3 30 0.3 40 0.1 50 0.1 </li></ul>One-Period Decisions Example
    27. 27. <ul><li>Complete the following payoff matrix, as well as the column on the right showing expected payoff. </li></ul><ul><li>D Expected Q 10 20 30 40 50 Payoff --- (.2) (.3) (.3) (.1) (.1) --- </li></ul><ul><li>10 $100 $100 $100 $100 $100 $100 20 50 200 200 200 200 170 30 0 ____ 300 ____ 300 ____ 40 –50 100 250 400 400 175 50 –100 50 200 350 500 140 </li></ul>One-Period Decisions Example
    28. 28. <ul><li>Payoff if Q = 30 and D = 20: </li></ul><ul><li>Payoff if Q = 30 and D = 40: </li></ul><ul><li>Expected payoff if Q = 30: </li></ul><ul><li>What is the best choice for Q ? </li></ul>One-Period Decisions Example

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