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

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

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