Inventory models
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INVENTORY MODELS
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Inventory models
- 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. 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. Types of Inventories Raw materials & purchased parts Partially completed goods called work in progress Finished-goods inventories (manufacturing firms) or merchandise (retail stores)
- 5. Types of Inventories (Cont’d) Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers
- 6. Functions of Inventory To meet anticipated demand To smooth production requirements To protect against stock-outs
- 7. Functions of Inventory (Cont’d) To help hedge against price increases To permit operations To take advantage of quantity discounts
- 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. 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. 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. 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. 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. 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. Economic order quantity (EOQ) model The order size that minimizes total annual cost Economic production model Quantity discount model Economic Order Quantity Models
- 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. 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. Total Cost Annual carrying cost Annual ordering cost Total cost = + TC = Q 2 H D Q S+
- 18. Cost Minimization Goal Order Quantity (Q) Ordering Costs QO AnnualCost (optimal order quantity) TC Q H D Q S= + 2
- 19. Minimum Total Cost The total cost curve reaches its minimum where the Carrying Cost = Ordering Cost Q 2 H D Q S=
- 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. 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. 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
- 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. EPQ (Economic Production Quantity) Assumptions Same as the EOQ except: inventory arrives in increments & is drawn down as it arrives
- 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. 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
- 30. 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
- 31. EPQ Example Solution (cont.) The reorder point: With safety stock of 200 units: unitsSSdLR 5752005 20 1500 =+×=+= unitsdLR 3755 20 1500 =×==
- 32. 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.
- 37. Determinants of the Reorder Point The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock)
- 39. Safety Stock reduce risk of stockout during lead time
- 40. 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
- 42. 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
- 43. 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
- 44. 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
- 45. 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
- 46. 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