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Inventory Systems Rules 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) 6
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Comparison of Periodic andContinuous Review Systems Periodic Review Continuous Review Fixed order intervals Varying order intervals Variable order sizes Fixed order sizes (Q) Allows individual review Convenient to frequencies administer Possible quantity discounts Inventory position only Lower, less-expensive required at review safety stocks 7
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Inventory 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. 8
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Total costs of carrying inventory Assumptions demand 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. TotalInventory Policy Cost annually = annual purchase cost + annual order cost + annual holding cost 9
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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) 11
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Total Inventory Cost Equation D Q TC = D * C + S + H Q 2D = 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 period assuming with start with Q and drop to zero before next order arrives (cycle inventory). 12
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Deriving the EOQ :Economic Order Quantity Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero 2DS 2(Annual Demand)(Order or Setup Cost) Q = EOQ = = H Annual Holding Cost 13
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EOQ Model--Basic Fixed-Order Quantity Model (Q)Numberof unitson hand Q Q Q R L L Time R = Reorder point Q = Economic order quantity L = Lead time 14
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The Reorder PointReorder point = (average period demand)*Lead Time periods = d*L 15
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Another EOQ ExampleAnnual Demand = 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.50 ead time = 7 daysCost per unit = $15 Determine the economic order quantity & reorder point. 16
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Minor Deviations Here What causes minor deviations from the ideal order size? Assumptions behind the regular EOQ Model? 17
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Variations in lead time If 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* σL) σL =σD L where: d = average daily (or weekly) demand L = Lead time (matching days or weeks) σL = standard deviation of demand during lead time. σD = standard deviation of demand (days or weeks). 18
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Service Level or % of time inventory willmeet demand during lead time Z Value Resulting Service Level 1.28 90% 1.65 95% 2.33 99% 3.08 99.9% 19
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Example Annual Demand = 1000 units 250 work days in the year d=1000/250 = 4 units/day Q= 200 units L=9 days σL = 3 units z=2 (97.7% likelihood that we won’t run out during lead time) Reorder point= d*L +z*σL = (4*9) + (2*3) = 42 units 20
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P 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/D How much should you order to bring inventory level up to some predetermined level, R where: R = restocking level Current Inventory position = IP Order Quantity= R-IP 21
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Restocking Level Needs to meet most demand situations R= Restocking level = Average demand during lead time & review period+ safety stock = µP+L + z* σP+L where: µP+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). σRP+L = standard deviation of demand during lead time + review period 22
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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 23
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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 dollars Three classes is arbitrary; could be any number. Percents are approximate. Danger: dollar use may not reflect importance of any given SKU! 24
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Example of SKU list for 10 items Percentage of Annual Usage Total Dollar Item in Units Unit Cost Dollar Usage Usage 1 5,000 $ 1.50 $ 7,500 2.9% 2 1,500 8.00 12,000 4.7% 3 10,000 10.50 105,000 41.2% 4 6,000 2.00 12,000 4.7% 5 7,500 0.50 3,750 1.5% 6 6,000 13.60 81,600 32.0% 7 5,000 0.75 3,750 1.5% 8 4,500 1.25 5,625 2.2% 9 7,000 2.50 17,500 6.9% 10 3,000 2.00 6,000 2.4% Total $ 254,725 100.0% 25
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ABC Chart for SKU List 45.0% 120.0% 40.0% 100.0% Cumulative % Usage 35.0% A B C Percent Usage 30.0% 80.0% 25.0% 60.0% 20.0% 15.0% 40.0% 10.0% 20.0% 5.0% 0.0% 0.0% 3 6 9 2 4 1 10 8 5 7 Item No. Percentage of Total Dollar Usage Cumulative Percentage 26
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ABC Application Jewelry Store Fine Dining Restaurant Outdoor Retailer Large Department Store 27
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