3 Inventory Definitions BA 3393/31/2017Inventory DefinitionsInventory vs. Inventory systemDependent vs. Independent environmentsTypesSafety StockAnticipation InventoryHedge inventory (unusual events)Transportation or Pipeline Inventory3
4 Purposes of Inventory 1. Independence of operations. 2. Variation BA 3393/31/2017Purposes of Inventory1. Independence of operations.2. VariationProduct demandMaterial Delivery Time3. Scheduling flexibility4. Volume Discounts5. Material price fluctuations4
5 Inventory Costs Holding (or carrying) costs BA 3393/31/2017Inventory CostsHolding (or carrying) costsSetup (or production change) costsOrdering costs.Shortage costs.5
6 Inventory Systems Rules to manage inventory, specifically: BA 3393/31/2017Inventory SystemsRules to manage inventory, specifically:timing (when to order)sizing (how much to order)Continuous Review or Fixed-Order Quantity Models (Q)Event triggered (Example: running out of stock)Periodic Review or Fixed-Time Period Models (P)Time triggered (Example: Monthly sales call by sales representative)7
7 Comparison of Periodic and Continuous Review Systems BA 3393/31/2017Comparison of Periodic and Continuous Review SystemsPeriodic ReviewFixed order intervalsVariable order sizesConvenient to administerInventory position only required at reviewContinuous ReviewVarying order intervalsFixed order sizes (Q)Allows individual review frequenciesPossible quantity discountsLower, less-expensive safety stocks
8 BA 3393/31/2017Inventory costsC = Unit cost or production cost: the additional cost for each unit purchased or produced.H = Holding costs: cost of keeping items in inventory(cost of lost capital, taxes and insurance for storage, breakage, etc., handling and storing)S = Setup or ordering costs: a fixed cost incurred every time you place an order or a batch is produced.
9 Total costs of carrying inventory BA 3393/31/2017Total costs of carrying inventoryAssumptionsdemand is constant and uniform throughout the period for your products (5 cases per day)Price per unit is constant for the period ($16/case)Inventory holding cost is based on an average cost.Total Inventory Policy Cost annually = annual purchase cost + annual order cost + annual holding cost
11 Total cost of Inventory Policy = annual purchase cost (annual demand * Cost/item) + annual order cost (annual # orders * Cost to order) + annual holding cost (average units held*cost to carry one unit)
12 Total Inventory Cost Equation BA 3393/31/2017Total Inventory Cost EquationD = yearly demand of unitsC = cost of each unitQ = quantity orderedS = cost to place orderH = average yearly holding cost for each unit= storage+interest*CD/Q = number of orders per yearQ/2 = average inventory held during a given periodassuming with start with Q and drop to zerobefore next order arrives (cycle inventory).
13 Deriving the EOQ : Economic Order Quantity BA 3393/31/2017Deriving the EOQ : Economic Order QuantityUsing calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero
14 EOQ Model--Basic Fixed-Order Quantity Model (Q) 3/31/2017EOQ Model--Basic Fixed-Order Quantity Model (Q)R = Reorder pointQ = Economic order quantityL = Lead timeLQRTimeNumberof unitson hand
15 BA 3393/31/2017The Reorder PointReorder point = (average period demand)*Lead Time periods= d * L
16 Another EOQ Example Annual Demand = 1,000 units BA 3393/31/2017Another EOQ ExampleAnnual Demand = 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.50Lead time = 7 daysCost per unit = $15Determine the economic order quantity & reorder point.
17 BA 3393/31/2017Minor Deviations HereWhat causes minor deviations from the ideal order size?Assumptions behind the regular EOQ Model?
18 Variations in lead time BA 3393/31/2017Variations in lead timeIf we have variations in lead time, how should we change the reorder point so we rarely run out? Reorder Point = Average demand during lead time(d*L) + safety stock (Z* sL)where: d = average daily (or weekly) demand L = Lead time (matching days or weeks) sL = standard deviation of demand during lead time. sD = standard deviation of demand (days or weeks).
19 Service Level or % of time inventory will meet demand during lead time BA 339Service Level or % of time inventory will meet demand during lead time3/31/2017Z ValueResulting Service Level1.2890%1.6595%2.3399%3.0899.9%
20 Example Annual Demand = 1000 units BA 3393/31/2017ExampleAnnual Demand = 1000 units250 work days in the year d=1000/250 = 4 units/dayQ= 200 units L=9 days sL = 3 unitsz=2 (97.7% likelihood that we won’t run out during lead time) Reorder point= d*L +z*sL = (4*9) + (2*3) = 42 units
21 P Method (periodic review) BA 3393/31/2017P Method (periodic review)You have a predetermined time (P) between orders (sales rep comes by every 10 days) or the average time between orders from EOQ = Q/DHow much should you order to bring inventory level up to some predetermined level, R where:R = restocking levelCurrent Inventory position = IPOrder Quantity= R-IP
22 Restocking Level Needs to meet most demand situations BA 3393/31/2017Restocking LevelNeeds to meet most demand situationsR= Restocking level = Average demand during lead time & review period+ safety stock = mP+L + z* sP+L where: mP+L = average demand during lead time and review period z = # of standard dev from mean above the average demand (higher z is lower probability of running out). sRP+L = standard deviation of demand during lead time + review period
23 ABC Inventory Management Based on “Pareto” concept (80/20 rule) and total usage in dollars of each item.Classification of items as A, B, or C based on usage.Purpose is to set priorities on effort used to manage different SKUs, i.e. to allocate scarce management resources.SKU: Stock Keeping Unit
24 ABC Inventory Management ‘A’ items: 20% of SKUs, 80% of dollars‘B’ items: 30 % of SKUs, 15% of dollars‘C’ items: 50 % of SKUs, 5% of dollarsThree classes is arbitrary; could be any number.Percents are approximate.Danger: dollar use may not reflect importance of any given SKU!
25 Example of SKU list for 10 items Annual Usage in UnitsUnit CostDollar UsagePercentage of Total Dollar Usage15,000$$ ,5002.9%21,5008.0012,0004.7%310,00010.50105,00041.2%46,0002.0057,5000.503,7501.5%613.6081,60032.0%70.7584,5001.255,6252.2%97,0002.5017,5006.9%103,0002.4%Total$ 254,725100.0%