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Inventory management

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Inventory management Inventory management Presentation Transcript

  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 1 Omer MaroofOmer Maroof MBA 4MBA 4thth SemesterSemester Enrollment no:110130Enrollment no:110130 Inventory managementInventory management decisionsdecisions
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 2  Inventory System Defined  Inventory Costs  Independent vs. Dependent Demand  Single-Period Inventory Model  Multi-Period Inventory Models: Basic Fixed-Order Quantity Models  Multi-Period Inventory Models: Basic Fixed-Time Period Model  Miscellaneous Systems and Issues OBJECTIVES
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 3 Inventory Management 1. DEFINITION  Inventory in business refers to merchandize held for sale in ordinary course of business.  It includes materials and supplies that are consumed in production .  It refers to Current Assets.  It is different from Fixed Assets. 2. Contents of Inventory  Raw materials.  Components  Work in process  Finished goods  Consumable  Machine spares  Tools, Jigs & Fixtures
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 4 Inventory System  Inventory is the stock of any item or resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process  An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 5 Purposes of Inventory  To ”decouple” or separate various parts of the production process  To provide a stock of goods that will provide a “selection” for customers  To take advantage of quantity discounts  To hedge against inflation and upward price changes
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 6 Purposes of Inventory 1. To maintain independence of operations 2. To meet variation in product demand 3. To allow flexibility in production scheduling 4. To provide a safeguard for variation in raw material delivery time
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 7 Inventory Process stage Demand Type Number & Value Other Raw Material WIP & Finished Goods Independent Dependent A Items B Items C Items Maintenance Dependent Operating Inventory Classifications
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 9 SELECTIVE INVENTORY CONTROL Selective inventory control is defined as process of classifying items into different categories and thereby directing appropriate attention to the materials. It is based on the principle of ‘Vital few and trivial many’ made by Pareto. CLASSIFICATION 1. A-B-C technique 2. V-E-D classification 3. H-M-L ’’ 4. F-S-N ’’ 5. S-D-E ’’ 6. S-O-S ’’ 7. G-O-L-F ’’ 8. X-Y-Z ’’ 9
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 10 Inventory Costs  Holding (or carrying) costs – Costs for storage, handling, insurance, etc  Setup (or production change) costs – Costs for arranging specific equipment setups, etc  Ordering costs – Costs of someone placing an order, etc  Shortage costs – Costs of canceling an order, etc
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 11 E(1 ) Independent vs. Dependent Demand Independent Demand (Demand for the final end- product or demand not related to other items) Dependent Demand (Derived demand items for component parts, subassemblies, raw materials, etc) Finished product Component parts
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 12 Inventory Systems  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)
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 13 Single-Period Inventory Model uo u CC C P + ≤ soldbeunit willy that theProbabilit estimatedunderdemandofunitperCostC estimatedoverdemandofunitperCostC :Where u o = = = P This model states that we should continue to increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of: Cu/Co+Cu This model states that we should continue to increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of: Cu/Co+Cu
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 14 Single Period Model Example  Our college basketball team is playing in a tournament game this weekend. Based on our past experience we sell on average 2,400 shirts with a standard deviation of 350. We make $10 on every shirt we sell at the game, but lose $5 on every shirt not sold. How many shirts should we make for the game? Cu = $10 and Co = $5; P ≤ $10 / ($10 + $5) = .667 Z.667 = .432 (use NORMSDIST(.667) or Appendix E) therefore we need 2,400 + .432(350) = 2,551 shirts
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 15 Multi-Period Models: Fixed-Order Quantity Model Model Assumptions (Part 1)  Demand for the product is constant and uniform throughout the period  Lead time (time from ordering to receipt) is constant  Price per unit of product is constant
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 16 Multi-Period Models: Fixed-Order Quantity Model Model Assumptions (Part 2)  Inventory holding cost is based on average inventory  Ordering or setup costs are constant  All demands for the product will be satisfied (No back orders are allowed)
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 17 Basic Fixed-Order Quantity Model and Reorder Point Behavior R = Reorder point Q = Economic order quantity L = Lead time L L Q QQ R Time Number of units on hand 1. You receive an order quantity Q. 2. Your start using them up over time. 3. When you reach down to a level of inventory of R, you place your next Q sized order. 4. The cycle then repeats.
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 18 Cost Minimization Goal Ordering Costs Holding Costs Order Quantity (Q) C O S T Annual Cost of Items (DC) Total Cost QOPT By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 19 Basic Fixed-Order Quantity (EOQ) Model Formula H 2 Q +S Q D +DC=TC Total Annual = Cost Annual Purchase Cost Annual Ordering Cost Annual Holding Cost + + TC=Total annual cost D =Demand C =Cost per unit Q =Order quantity S =Cost of placing an order or setup cost R =Reorder point L =Lead time H=Annual holding and storage cost per unit of inventory TC=Total annual cost D =Demand C =Cost per unit Q =Order quantity S =Cost of placing an order or setup cost R =Reorder point L =Lead time H=Annual holding and storage cost per unit of inventory
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 20 Deriving the EOQ Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt Q = 2DS H = 2(Annual Demand)(Order or Setup Cost) Annual Holding CostOPT Reorder point, R = d L _ d = average daily demand (constant) L = Lead time (constant) _ We also need a reorder point to tell us when to place an order We also need a reorder point to tell us when to place an order
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 21 EOQ Example (1) Problem Data Annual Demand = 1,000 units Days per year considered in average daily demand = 365 Cost to place an order = $10 Holding cost per unit per year = $2.50 Lead time = 7 days Cost per unit = $15 Given the information below, what are the EOQ and reorder point? Given the information below, what are the EOQ and reorder point?
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 22 EOQ Example (1) Solution Q = 2DS H = 2(1,000 )(10) 2.50 = 89.443 units orOPT 90 units d = 1,000 units / year 365 days / year = 2.74 units / day Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _ 20 units In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units. In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units.
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 23 EOQ Example (2) Problem Data Annual Demand = 10,000 units Days per year considered in average daily demand = 365 Cost to place an order = $10 Holding cost per unit per year = 10% of cost per unit Lead time = 10 days Cost per unit = $15 Determine the economic order quantity and the reorder point given the following… Determine the economic order quantity and the reorder point given the following…
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 24 EOQ Example (2) Solution Q = 2DS H = 2(10,000 )(10) 1.50 = 365.148 units, orOPT 366 units d = 10,000 units / year 365 days / year = 27.397 units / day R = d L = 27.397 units / day (10 days) = 273.97 or _ 274 units Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units. Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units.
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 25 Fixed-Time Period Model with Safety Stock Formula order)onitems(includeslevelinventorycurrent=I timeleadandreviewover thedemandofdeviationstandard= yprobabilitservicespecifiedafordeviationsstandardofnumberthe=z demanddailyaverageforecast=d daysintimelead=L reviewsbetweendaysofnumberthe=T orderedbetoquantitiy=q :Where I-Z+L)+(Td=q L+T L+T σ σ q = Average demand + Safety stock – Inventory currently on handq = Average demand + Safety stock – Inventory currently on hand
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 26 Multi-Period Models: Fixed-Time Period Model: Determining the Value of σT+L ( )σ σ σ σ σ T+L d i 1 T+L d T+L d 2 = Since each day is independent and is constant, = (T+ L) i 2 = ∑  The standard deviation of a sequence of random events equals the square root of the sum of the variances
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 27 Example of the Fixed-Time Period Model Average daily demand for a product is 20 units. The review period is 30 days, and lead time is 10 days. Management has set a policy of satisfying 96 percent of demand from items in stock. At the beginning of the review period there are 200 units in inventory. The daily demand standard deviation is 4 units. Given the information below, how many units should be ordered? Given the information below, how many units should be ordered?
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 28 Example of the Fixed-Time Period Model: Solution (Part 1) ( )( )σ σT+L d 2 2 = (T + L) = 30 +10 4 = 25.298( )( )σ σT+L d 2 2 = (T + L) = 30 +10 4 = 25.298 The value for “z” is found by using the Excel NORMSINV function, or as we will do here, using Appendix D. By adding 0.5 to all the values in Appendix D and finding the value in the table that comes closest to the service probability, the “z” value can be read by adding the column heading label to the row label. The value for “z” is found by using the Excel NORMSINV function, or as we will do here, using Appendix D. By adding 0.5 to all the values in Appendix D and finding the value in the table that comes closest to the service probability, the “z” value can be read by adding the column heading label to the row label. So, by adding 0.5 to the value from Appendix D of 0.4599, we have a probability of 0.9599, which is given by a z = 1.75 So, by adding 0.5 to the value from Appendix D of 0.4599, we have a probability of 0.9599, which is given by a z = 1.75
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 29 Example of the Fixed-Time Period Model: Solution (Part 2) or644.272,=200-44.272800=q 200-298)(1.75)(25.+10)+20(30=q I-Z+L)+(Td=q L+T units645+ σ So, to satisfy 96 percent of the demand, you should place an order of 645 units at this review period So, to satisfy 96 percent of the demand, you should place an order of 645 units at this review period
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 30 Price-Break Model Formula CostHoldingAnnual Cost)SetuporderDemand)(Or2(Annual = iC 2DS =QOPT Based on the same assumptions as the EOQ model, the price-break model has a similar Qopt formula: i = percentage of unit cost attributed to carrying inventory C = cost per unit Since “C” changes for each price-break, the formula above will have to be used with each price-break cost value
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 31 Price-Break Example Problem Data (Part 1) A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of $4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units? A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of $4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units? Order Quantity(units) Price/unit($) 0 to 2,499 $1.20 2,500 to 3,999 1.00 4,000 or more .98
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 32 Price-Break Example Solution (Part 2) units1,826= 0.02(1.20) 4)2(10,000)( = iC 2DS =QOPT Annual Demand (D)= 10,000 units Cost to place an order (S)= $4 First, plug data into formula for each price-break value of “C” units2,000= 0.02(1.00) 4)2(10,000)( = iC 2DS =QOPT units2,020= 0.02(0.98) 4)2(10,000)( = iC 2DS =QOPT Carrying cost % of total cost (i)= 2% Cost per unit (C) = $1.20, $1.00, $0.98 Interval from 0 to 2499, the Qopt value is feasible Interval from 2500-3999, the Qopt value is not feasible Interval from 4000 & more, the Qopt value is not feasible Next, determine if the computed Qopt values are feasible or not
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 33 Price-Break Example Solution (Part 3) Since the feasible solution occurred in the first price- break, it means that all the other true Qopt values occur at the beginnings of each price-break interval. Why? Since the feasible solution occurred in the first price- break, it means that all the other true Qopt values occur at the beginnings of each price-break interval. Why? 0 1826 2500 4000 Order Quantity Total annual costs So the candidates for the price- breaks are 1826, 2500, and 4000 units So the candidates for the price- breaks are 1826, 2500, and 4000 units Because the total annual cost function is a “u” shaped function Because the total annual cost function is a “u” shaped function
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 34 Price-Break Example Solution (Part 4) iC 2 Q +S Q D +DC=TC Next, we plug the true Qopt values into the total cost annual cost function to determine the total cost under each price-break Next, we plug the true Qopt values into the total cost annual cost function to determine the total cost under each price-break TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = $12,043.82 TC(2500-3999)= $10,041 TC(4000&more)= $9,949.20 TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = $12,043.82 TC(2500-3999)= $10,041 TC(4000&more)= $9,949.20 Finally, we select the least costly Qopt, which is this problem occurs in the 4000 & more interval. In summary, our optimal order quantity is 4000 units Finally, we select the least costly Qopt, which is this problem occurs in the 4000 & more interval. In summary, our optimal order quantity is 4000 units
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 35 Maximum Inventory Level, M Miscellaneous Systems: Optional Replenishment System M Actual Inventory Level, I q = M - I I Q = minimum acceptable order quantity If q > Q, order q, otherwise do not order any.
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 36 Miscellaneous Systems: Bin Systems Two-Bin System Full Empty Order One Bin of Inventory One-Bin System Periodic Check Order Enough to Refill Bin
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 37 ABC Classification System  Items kept in inventory are not of equal importance in terms of: – dollars invested – profit potential – sales or usage volume – stock-out penalties 0 30 60 30 60 A B C % of $ Value % of Use So, identify inventory items based on percentage of total dollar value, where “A” items are roughly top 15 %, “B” items as next 35 %, and the lower 65% are the “C” items
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 38 Inventory Accuracy and Cycle Counting  Inventory accuracy refers to how well the inventory records agree with physical count  Cycle Counting is a physical inventory-taking technique in which inventory is counted on a frequent basis rather than once or twice a year
  • McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 39