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Inventory Control

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Published in: Mechanical
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Presentation on Inventory Control.

Trinity A / Chandigarh

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Teaches: Indian National Mathematical Olympiad (INMO), Mental Maths, Olympiad Exam Preparation, Regional Mathematical Olympiad (RMO), Advanced Excel, Basic Computer, MS Office, School Level Computer, Mathematics, Statistics, Science, Social Studies, B.Tech Tuition, Drawing, Mechanical, AutoCAD Training, French, German, Study in Germany

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  1. Chapter 6: Inventory Control
  2. Inventory Any stored resource used to satisfy a current or future need (raw materials, work-in-process, finished goods, etc.) Represents as much as 50% of invested capitol at some companies Excessive inventory levels are costly Insufficient inventory levels lead to stockouts
  3. Inventory Planning and Control For maintaining the right balance between high and low inventory to minimize cost Planning on What Inventory to Stock and How to Acquire It Forecasting Parts/Product Demand Controlling Inventory Levels Feedback Measurements to Revise Plans and Forecasts
  4. 1. 2. 3. 4. 5. Main Uses of Inventory The decoupling function Storing resources Irregular supply and demand Quantity discounts Avoiding stockouts and shortages
  5. Inventory Control Decisions Objective: Minimize total inventory cost Decisions: How much to order? When to order?
  6. 1. 2. 3. 4. 5. Components of Total Cost Cost of items Cost of ordering Cost of carrying or holding inventory Cost of stockouts Cost of safety stock (extra inventory held to help avoid stockouts)
  7. Economic Order Quantity (EOQ): Determining How Much to Order One of the oldest and most well known inventory control techniques Easy to use Based on a number of assumptions
  8. 1. 2. 3. 4. 5. 6. Assumptions of the EOQ Model Demand is known and constant Lead time is known and constant Receipt of inventory is instantaneous Quantity discounts are not available Variable costs are limited to: ordering cost and carrying (or holding) cost If orders are placed at the right time, stockouts can be avoided
  9. Inventory Level Over Time Based on EOQ Assumptions Inventory Level Order Quantity = Q = 7----------------------------=--------------------------------7 Maximum Inventory Level Q Minimum Inventory 0 Time
  10. Minimizing EOQ Model Costs ' Only ordering and carrying costs need to be minimized (all other costs are assumed constant) As Q (order quantity) increases: — Carry cost increases — Ordering cost decreases (since the number of orders per year decreases)
  11. EO Cost Minimum Total Cost Model Total Cost Curve for Total Cost of Carrying and Ordering Optimal Order Quantity (Q*) Carrying Cost Curve Ordering Cost Curve Order Quantity in Units At optimal order quantity (Q*): Carrying cost = Ordering cost
  12. Finding the Optimal Order Quantity Parameters : Q* = Optimal order quantity (the EOQ) = Annual demand D = Ordering cost per order Co Ch = Carrying (or holding) cost per unit per yr = Purchase cost per unit P
  13. Two Methods for Carrying Cost Carry cost (Ch) can be expressed either: 1. As a fixed cost, such as Ch = $0.50 per unit per year 2. As a percentage of the item's purchase cost (P) I = a percentage of the purchase cost
  14. EOQ Total Cost Total ordering cost Total carrying cost Total purchase cost = Total cost Note: = (D/Q) x co (Q/2) is the average inventory level Purchase cost does not depend on Q
  15. Finding Q* Recall that at the optimal order quantity (Q*): Carry cost = Ordering cost (D/Q*) x co = (Q*/2) x Rearranging to solve for Q* (2DC0/Ch)
  16. EOQ Example: Sumco Pump co. Buys pump housing from a manufacturer and sells to retailers = 1000 pumps annually D = $10 per order Co Ch = $0.50 per pump per year
  17. Using ExcelModules for Inventory ' Worksheet for inventory models in ExcelModules are color coded — Input cells are yellow — Output cells are green ' Select "Inventory Models" from the ExcelModules menu, then select "EOQ"
  18. Average Inventory Value After Q* is found we can calculate the average value of inventory on hand Average inventory value = P x (Q*/2)
  19. Calculating Ordering and Carrying Costs for a Given Q_ ' Sometimes Co and Ch are difficult to estimate We can use the EOQ formula to calculate the value of Co or Ch that would make a given Q optimal: co = Q2 x Ch/(2D) = 2DC0/Q2
  20. Sensitivity of the EOQ_ Formula The EOQ formula assumes all inputs are know with certainty ' In reality these values are often estimates ' Determining the effect of input value changes on Q* is called sensitivity analysis
  21. Sensitivity Analysis for Sumco ' Suppose Co = $15 (instead of $10), which is a 50% increase Assume all other values are unchanged The new Q* = 245 (instead of 200), which is a 22.5% increase This shows the nonlinear nature of the formula
  22. Reorder Point: Determining When to Order After Q* is determined, the second decision is when to order Orders must usually be placed before inventory reaches 0 due to order lead time ' Lead time is the time from placing the order until it is received The reorder point (ROP) depends on the lead time (L)
  23. Inventory Level (Units) Q* ROP (Units) Reorder Point ROP ROP = L Slope = Units/Day = d Time Lead Time = L (Days)
  24. Sumco Example Revisited Assume lead time, L = 3 business days Assume 250 business days per year Then daily demand, d = 1000 pumps/ 250 days = 4 pumps per day ROP = (4 pumps per day) x (3 days) = 12 pumps
  25. Economic Production Quantity: Determining How Much to Produce The EOQ model assumes inventory arrives instantaneously ' In many cases inventory arrives gradually The economic production quantity (EPQ) model assumes inventory is being produced at a rate of p units per day There is a setup cost each time production begins
  26. Inventory Control With Production Inventory Level Maximum Inventory Part of Inventory Cycle During Which Production Is Taking Place There Is No Production During This Part of the Inventory Cycle Time
  27. Determining Lot Size or EPQ Parameters Q* = Optimal production quantity (or EPQ) Cs = Setup cost = annual demand D = daily demand rate d = daily production rate
  28. Average Inventory Level We will need the average inventory level for finding carrying cost Average inventory level is h the maximum Max inventory = Q x (1- d/p) Ave inventory = h Q x (1- d/p)
  29. Total Cost Setup cost Carrying cost Production cost = Total cost As in the EOQ model: = [h Q x (1- d/p)] x Ch The production cost does not depend on Q The function is nonlinear
  30. Finding Q* As in the EOQ model, at the optimal quantity Q* we should have: Setup cost = Carrying cost (D/Q*) x = [1/2 Q* x (1- dip)] x Rearranging to solve for Q*
  31. EPQ for Brown Manufacturing Produces mini refrigerators (has 167 business days per year) = 10,000 units annually D d = 1000/ 167 = —60 units per day = 80 units per day (when producing) p Ch = $0.50 per unit per year Cs = $100 per setup = $5 to produce each unit P
  32. Length of the Production Cycle The production cycle will last until Q* units have been produced ' Producing at a rate of p units per day means that it will last (Q*/p) days ' For Brown this is: Q* = 4000 units p = 80 units per day 4000 / 80 = 50 days
  33. Quantity Discount Models A quantity discount is a reduced unit price based on purchasing a large quantity Example discount schedule: TABLE 12.2 Quantity Discount Schedule DISCOUNT NUMBER 1 2 3 DISCOUNT QUANTITY O to 999 1,000 to 1,999 2,000 and over DISCOUNT 00/0 40/0 50/0 DISCOUNT COST $5.00 $4.80 $4.75
  34. 1. 2. 3. 4. Four Steps to Analyze Quantity Discount Models Calculate Q* for each discount price If Q* is too small to qualify for that price, adjust Q* upward Calculate total cost for each Q* Select the Q* with the lowest total cost
  35. Brass Department Store Example Sells toy cars D = 5000 cars annually Co = $49 per order Ch = $0.20 per car per year Quantity Discount Schedule TABLE 12.2 Quantity Discount Schedule DISCOUNT NUMBER 1 2 3 DISCOUNT QUANTITY O to 999 1,000 to 1,999 2,000 and over DISCOUNT 00/0 40/0 50/0 DISCOUNT COST $5.00 $4.80 $4.75
  36. Use of Safety Stock ' Safety stock (SS) is extra inventory held to help prevent stockouts ' Frequently demand is subject to random variability (uncertainty) ' If demand is unusually high during lead time, a stockout will occur if there is no safety stock
  37. Use of Safety Stock Inventory on Hand Time Stockout Inventory on Hand Q+SS Safety Stock, SS stockout Is Avoided O Units Time
  38. Determining Safety Stock Level Need to know: ' Probability of demand during lead time (DDLT) ' Cost of a stockout (includes all costs directly or indirectly associated, such as cost of a lost sale and future lost sales)
  39. ABCO safety Stock Example ROP = 50 units (from previous EOQ) Place 6 orders per year Stockout cost per unit = $40 Ch = $5 per unit per year DDLT has a discrete distribution TABLE 12.3 Probability of Demand During Lead Time for ABCO, Inc. NUMBER OF UNITS 30 50 60 70 PROBABILITY 0.2 0.2 0.3 0.2 0.1 1.0
  40. Analyzing the Alternatives With uncertain DDLT this becomes a "decision making under risk" problem ' Each of the five possible values of DDLT represents a decision alternative for ROP ' Need to determine the economic payoff for each combination of decision alternative (ROP) and outcome (DDLT)
  41. Stockout and Additional Carrying Costs Additional Stockout Cost Carrying Cost ROP = DDLT ROP < DDLT ROP > DDLT $40 per unit Short per year $5 per unit per year
  42. safety Stock With Unknown Stockout Costs ' Determining stockout costs may be difficult or impossible ' Customer dissatisfaction and possible future lost sales are difficult to estimate Can use service level instead Service level = 1 — probability of a stockout
  43. Hinsdale co. Example DDLT follows a normal distribution (g = 350, 0 = 10) They want a 95% service level (i.e. 5% probability of a stockout) SS = ?
  44. Safety Stock and the Normal Distribution 5% Area of Normal Curve = 350 = Mean Demand = 350 = Standard Deviation = 10 = Mean Demand + Safety Stock X SS = Safety Stock = X—
  45. Calculating SS From the standard Normal Table, z = 1.645 = x- 350 so 366.45 10 and, SS = 16.45 (which could be rounded t017)
  46. ABC Analysis ' Recognizes that some inventory items are more important than others A group items are considered critical (often about 70% of dollar value and 10% of items) B group items are important but not critical (often about 20% of dollar value and 20% of items) C group items are not as important (often about 10% of dollar value and 70% of items)
  47. VED Analysis - VED stands for vital, essential and desirable. - relates to the classification of maintenance spare parts and denotes the essentiality of stocking spares. spares are split into three categories in order of importance. From the view-points of functional utility, the effects of non-availability at the time of requirement or the operation, process, production, plant or equipment and the urgency of replacement in case of breakdown. spares are so important that their non-availability renders the equipment or a number of equipment in a process line completely inoperative, or even causes extreme damage to plant, equipment or human life.
  48. SDE Analysis S: Refers to scarce items, items which are in short supply. Usually these are raw materials, spare parts and imported items. D: Stands for difficult items, items which are not readily available in local markets and have to be procured from faraway places, or items for which there are a limited number of suppliers; or items for which quality suppliers are difficult to get. E: Refer to items which are easily available in the local markets.
  49. FSN Analysis Here the items are classified into fast-moving (F), slow- moving (S) and Non-moving (N) items on the basis of quantity and rate of consumption. The non-moving items (usually, not consumed over a period of two years) are of great importance. It is found that many companies maintain huge stocks of non-moving items blocking quite a lot of capital. Moreover, there are thousands of such items. Scrutiny of these items is made to determine whether they could be used or to be disposed off. The classification of fast and slow moving items helps in arrangement of stocks in stores and their distribution and handling methods.

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