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Irwin/McGraw-Hill 1 What is Inventory? Definition--The stock of any item or resource used in an organization Raw materials Finished products Component parts Supplies Work in process

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Irwin/McGraw-Hill 2 Inventory System Purpose The set of policies and controls that determine what inventory levels should be maintained, when stock should be replenished, and how large orders should be

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Irwin/McGraw-Hill 3 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 5. To take advantage of economic purchase- order size

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Irwin/McGraw-Hill 4 Inventory Costs Holding (or carrying) costs Setup (or production change) costs Ordering costs Shortage (or backlog) costs

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Irwin/McGraw-Hill 5 Independent vs. Dependent Demand Independent Demand (Demand not related to other items) Dependent Demand (Derived/Calculated)

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Irwin/McGraw-Hill 6 Classifying Inventory Models Fixed-Order Quantity Models Event triggered Make exactly the same amount Use re-order point to determine timing Fixed-Time Period Models Time triggered Count the number needed to re-order

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Inventory Control Inventory Inventory Models Fixed Time Period Models Fixed Order Quantity Models Uncertainty in Demand Find the EOQ and R Simple EOQ w/usage EOQ w/ Quantity Discounts Select Q and find R Find the EOQ and R Determine p and d Calculate Total costs Constant Demand Single Period Models

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Irwin/McGraw-Hill 8 Fixed-Order Quantity Models Assumptions 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 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)

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Irwin/McGraw-Hill 9 EOQ Model--Basic Fixed-Order Quantity Model R = Reorder point Q = Economic order quantity L = Lead time L L QQQ R Time Inventory Level

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Irwin/McGraw-Hill 10 Basic Fixed-Order Quantity Model Total Annual Cost = Annual Purchase Cost Annual Ordering Cost Annual Holding Cost ++ Derive the Total annual Cost Equation, where: TC - Total annual cost D - Annual demand (and d-bar = average daily demand = D/365) 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

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Irwin/McGraw-Hill 11 Cost Minimization Goal Ordering Costs Holding Costs Q OPT Order Quantity (Q) COSTCOST Annual Cost of Items (DC) Total Cost

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Irwin/McGraw-Hill 12 Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero L= Lead time (constant) d= average demand per time unit _ Reorder Point, R = dL

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Irwin/McGraw-Hill 13 EOQ Example Annual Demand (D) = 1,000 units Days per year considered in average daily demand = 365 Cost to place an order (S) = $10 Holding cost per unit per year (H) = $2.40 Lead time (L) = 7 days Cost per unit (C) = $15 Determine the economic order quantity and the reorder point.

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Irwin/McGraw-Hill 14 Solution When the inventory level reaches 20, order 91 units. 91 or 92 units??? Why do we round up?

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Irwin/McGraw-Hill 15 Problem Retailer of Satellite Dishes D = 1000 units S = $ 25 H = $ 100 How much should we order? What are the Total Annual Stocking Costs?

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Irwin/McGraw-Hill 16 EOQ with Quantity Discounts What if we get a price break for buying a larger quantity? To find the lowest cost order quantity: Since C changes for each price-break, H=iC Where, i = percentage of unit cost attributed to carrying inventory and, C = cost (or price) per unit Find the EOQ at each price break. Identify relevant and feasible order quantities. Compare total annual costs The lowest cost wins.

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Irwin/McGraw-Hill 17 EOQ with Quantity Discounts Example Copper may be purchased for $.82 per pound for up to 2,499 pounds $.81 per pound for 2,500 to 5,000 pounds $.80 per pound for orders greater than 5,000 pounds Demand (D) = 50,000 pounds per year Holding costs (H) are 20% of the purchase price per unit Ordering costs (S) = $30 How much should the company order to minimize total costs?

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Problem (Order Quantity 100's of units) (Costs in $,000) <2500 < >5000 Feasible

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Inventory Control Inventory Inventory Models Fixed Time Period Models Fixed Order Quantity Models Uncertainty in Demand Find the EOQ and R Find the L Find Z Safety Stock Constant Demand Single Period Models

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Irwin/McGraw-Hill 20 What if demand is not Certain? Use safety stock to cover uncertainty in demand. Given: service probability which is the probability demand will NOT exceed some amount. The safety stock level is set by increasing the reorder point by the amount of safety stock. The safety stock equals z L where, L = the standard deviation of demand during the lead time. For example for a 5% chance of running out z 1.65

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Irwin/McGraw-Hill 21 Problem Annual Demand = 25,750 or 50 wks/year Annual Holding costs = 33% of item cost ($10/unit) Ordering costs are $ d = 25 per week Leadtime = 1 week Service Probability = 95% Find: a.) the EOQ and R b.) annual holding costs and annual setup costs c.) Would you accept a price break of $50 per order for lot sizes that are larger than 2000?

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Inventory Control Inventory Inventory Models Fixed Time Period Models Fixed Order Quantity Models Current Inventory Find the T+L Find Z Find order quantity (q) Single Period Models

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Irwin/McGraw-Hill 23 Fixed-Time Period Models Check the inventory every review period and then order a quantity that is large enough to cover demand until the next order will come in. The model assumes uncertainty in demand with safety stock added to the order quantity. More exposure to variability than fixed-order models

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Irwin/McGraw-Hill 24 Fixed-Time Period Model with Safety Stock Formula q = Average demand + Safety stock - Inventory currently on hand

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Irwin/McGraw-Hill 25 Determining the Value of T+L The standard deviation of a sequence of random events equals the square root of the sum of the variances.

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Irwin/McGraw-Hill 26 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?

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Irwin/McGraw-Hill 27 Example of the Fixed-Time Period Model: Solution So, to satisfy 96 percent of the demand, you should place an order of 645 units at this review period.

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Irwin/McGraw-Hill 28 Problem A pharmacy orders antibiotics every two weeks (14 days). the daily demand equals 2000 the daily standard deviation of demand = 800 lead time is 5 days service level is 99 % present inventory level is 25,000 units What is the correct quantity to order to minimize costs?

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Inventory Control Inventory Inventory Models Fixed Time Period Models Fixed Order Quantity Models Uncertainty in Demand Constant Demand Single Period Models

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Irwin/McGraw-Hill 30 Single – Period Model for items w/obsolescence (newsboy problem) For a single purchase Amount to order is when marginal profit (MP) is equal to marginal loss (ML). Adding probabilities (P = probability of that unit being sold) for the last unit ordered we want P(MP) (1-P)ML or P ML /(MP+ML) Increase order quantity as long as this holds.

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Irwin/McGraw-Hill 31 Single–Period Model (Text Prob. #21) Famous Alberts Cookie King Demand (dozen) Probability of Demand 1, , , , , , , How many cookies should he bake? Each dozen sells for $0.69 and costs $0.49 with a salvage value of $0.29.

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Irwin/McGraw-Hill 32 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 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 50% are the C items.

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Irwin/McGraw-Hill 33 Inventory Accuracy and Cycle Counting Inventory accuracy Do inventory records agree with physical count? Cycle Counting Frequent counts When? (zero balance, backorder, specified level of activity, level of important item, etc.)

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