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Inventory models

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INVENTORY MODELS

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Inventory models

  1. 1. 12 Inventory Management
  2. 2. Independent Demand A B(4) C(2) D(2) E(1) D(3) F(2) Dependent Demand Independent demand is uncertain. Dependent demand is certain. Inventory
  3. 3. Inventory Models  Independent demand – finished goods, items that are ready to be sold  E.g. a computer  Dependent demand – components of finished products  E.g. parts that make up the computer
  4. 4. Types of Inventories  Raw materials & purchased parts  Partially completed goods called work in progress  Finished-goods inventories  (manufacturing firms) or merchandise (retail stores)
  5. 5. Types of Inventories (Cont’d)  Replacement parts, tools, & supplies  Goods-in-transit to warehouses or customers
  6. 6. Functions of Inventory  To meet anticipated demand  To smooth production requirements  To protect against stock-outs
  7. 7. Functions of Inventory (Cont’d)  To help hedge against price increases  To permit operations  To take advantage of quantity discounts
  8. 8. Objective of Inventory Control  To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds  Level of customer service  Costs of ordering and carrying inventory
  9. 9.  A system to keep track of inventory  A reliable forecast of demand  Knowledge of lead times  Reasonable estimates of  Holding costs  Ordering costs  Shortage costs  A classification system Effective Inventory Management
  10. 10. Inventory Counting Systems  Periodic System Physical count of items made at periodic intervals  Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item
  11. 11. Inventory Counting Systems (Cont’d)  Two-Bin System - Two containers of inventory; reorder when the first is empty  Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached 0 214800 232087768
  12. 12.  Lead time: time interval between ordering and receiving the order  Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year  Ordering costs: costs of ordering and receiving inventory  Shortage costs: costs when demand exceeds supply Key Inventory Terms
  13. 13. ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. AA - very important BB - mod. important CC - least important Annual $ value of items AA BB CC High Low Low High Percentage of Items
  14. 14.  Economic order quantity (EOQ) model  The order size that minimizes total annual cost  Economic production model  Quantity discount model Economic Order Quantity Models
  15. 15.  Only one product is involved  Annual demand requirements known  Demand is even throughout the year  Lead time does not vary  Each order is received in a single delivery  Inventory Level = 0 when new order just arrived  There are no quantity discounts Assumptions of EOQ Model
  16. 16. The Inventory Cycle Profile of Inventory Level Over Time Quantity on hand Q Receive order Place order Receive order Place order Receive order Lead time Reorder point Usage rate Time
  17. 17. Total Cost Annual carrying cost Annual ordering cost Total cost = + TC = Q 2 H D Q S+
  18. 18. Cost Minimization Goal Order Quantity (Q) Ordering Costs QO AnnualCost (optimal order quantity) TC Q H D Q S= + 2
  19. 19. Minimum Total Cost The total cost curve reaches its minimum where the Carrying Cost = Ordering Cost Q 2 H D Q S=
  20. 20. Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. Q = 2DS H = 2(Annual Demand)(Order or Setup Cost) Annual Holding Cost OPT
  21. 21. Economic Production Quantity (EPQ)  Assumptions  Only one product is involved  Annual demand requirements are known  Usage rate is constant  Usage occurs continually, but production occurs periodically  The production rate is constant  Lead time does not vary  There are no quantity discounts 12-21
  22. 22. Quantity Discount Model  Quantity discount  Price reduction offered to customers for placing large orders priceUnit where 2 CostPurchasingCostOrderingCostCarryingCostTotal = ++= ++= P PDS Q D H Q 12-22
  23. 23. Quantity Discounts 12-23
  24. 24. Quantity Discounts 12-24
  25. 25. EPQ: Inventory Profile Q Q* Imax Production and usage Production and usage Production and usage Usage only Usage only Cumulative production Amount on hand Time 12-25
  26. 26. EPQ (Economic Production Quantity) Assumptions  Same as the EOQ except: inventory arrives in increments & is drawn down as it arrives
  27. 27. EPQ Equations  Adjusted total cost:  Maximum inventory:  Adjusted order quantity:       +      = H I S Q D TC MAX EPQ 2       −= p d QIMAX 1       − = p d H DS EPQ 1 2
  28. 28. EPQ Example  Annual demand = 18,000 units  Production rate = 2500 units/month  Setup cost = $800  Annual holding cost = $18 per unit  Lead time = 5 days  No. of operating days per month = 20
  29. 29. EPQ Example Solution monthunitspmonthunitsd /2500;/1500 12 000,18 === units p d H DS Q 2000 2500 1500 118 800000,182 1 2 =       −× ×× =       − = units p d QIMAX 800 2500 1500 120001 =      −×=      −= 400,14200,7200,7 18 2 800 800 2000 000,18 2 =+=       ×+      ×=      +      = H I S Q D TC MAX
  30. 30. EPQ Example Solution (cont.)  The reorder point:  With safety stock of 200 units: unitsSSdLR 5752005 20 1500 =+×=+= unitsdLR 3755 20 1500 =×==
  31. 31. When to Reorder with EOQ Ordering  Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered  Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.  Service Level - Probability that demand will not exceed supply during lead time.
  32. 32. Determinants of the Reorder Point  The rate of demand  The lead time  Demand and/or lead time variability  Stockout risk (safety stock)
  33. 33. Safety Stock reduce risk of stockout during lead time
  34. 34. Reorder Point ROP Risk of a stockout Service level Probability of no stockout Expected demand Safety stock 0 z Quantity z-scale The ROP based on a normal Distribution of lead time demand
  35. 35. Fixed Quantity Fixed time
  36. 36.  Single period model: model for ordering of perishables and other items with limited useful lives  Shortage cost: generally the unrealized profits per unit  Excess cost: difference between purchase cost and salvage value of items left over at the end of a period Single Period Model
  37. 37.  Continuous stocking levels  Identifies optimal stocking levels  Optimal stocking level balances unit shortage and excess cost  Discrete stocking levels  Service levels are discrete rather than continuous  Desired service level is equaled or exceeded Single Period Model
  38. 38. Optimal Stocking Level Service Level So Quantity Ce Cs Balance point Service level = Cs Cs + Ce Cs = Shortage cost per unit Ce = Excess cost per unit
  39. 39. Example 15  Ce = $0.20 per unit  Cs = $0.60 per unit  Service level = Cs/(Cs+Ce) = .6/(.6+.2)  Service level = .75 Service Level = 75% Quantity C e Cs Stockout risk = 1.00 – 0.75 = 0.25
  40. 40.  Too much inventory  Tends to hide problems  Easier to live with problems than to eliminate them  Costly to maintain  Wise strategy  Reduce lot sizes  Reduce safety stock Operations Strategy

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