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1 Chapter 13 Inventory Systems for Independent Demand u This section explores: –The definition and purpose of inventory –Inventory costs –Independent vs. dependent demand –Types of inventory systems

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2 What is Inventory? u Inventory is the stock of any item or resource used in an organization, such as: –Raw materials –Finished products –Component parts –Supplies –Work in process (or progress)

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3 Why Carry Inventory? (Pros) 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 large purchase discounts

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4 Inventory Carrying and Changing Costs (Cons) u Carrying costs (most significant) –Interest (capital opportunity cost) u Setup (or production change) costs –Tooling u Ordering costs u Shortage costs –Difficult to evaluate e.g. loss of goodwill.

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5 E(1) Independent vs. Dependent Demand Independent Demand (Demand not related to other items) Dependent Demand (Derived from other higher level items)....

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6 Inventory Systems and Models u Inventory systems provide the organizational structure and the operating policies for controlling materials to be stocked u Two general types of system models: –Fixed-Order Quantity (or Economic Order Quantity, EOQ or Q) Models: Event triggered –Fixed-Time Period (or periodic system fixed-order interval or P) Models: Time triggered

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7 Comparison of Q and P Inventory Systems Feature Order quantity When to order Recordkeeping Inventory size Labor to maintain Types of items Fixed-Order Quantity (Q) Constant: same amount order- ed each time. When quantity on hand drops to reorder level Each time items removed or added Less than fixed-time period Higher due to continuous record- keeping High-priced and critical items Fixed-Time Period (P) Variable: different each time order is made When the review period arrives Inventory counted only at review period Larger than fixed-order quantity

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8 Fixed-Order Quantity (Q) System Idle state Waiting for demand Demand occurs Unit withdrawn from inventory or back ordered Compute inventory status Status = On hand + On order - Back order Is status < Reorder point? Issue order for Exactly Q units Yes No

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9 Fixed-Time Period Quantity (P) System Idle state Waiting for demand Demand occurs Unit withdrawn from inventory or back ordered Compute inventory status Status = On hand + On order - Back order Has review time arrived? Issue order for quantity needed Yes No Compute order quantity to bring inventory to desired level

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10 Some Comments on Inventory Systems u The cost to carry inventory is 25-35% of the inventory’s worth annually. Therefore, inventory reduction is one strategy for reducing cost. u It is important to match the system used to the operational results desired. It is not wise to focus only on reducing inventory costs or a particular element of the cost. u The inventory control systems discussed apply to manufacturers. Service and retail firms usually use simpler control methods.

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11 Fixed-Order Quantity Models Assumptions u Demand for the product is constant and uniform throughout the period u Lead time (time from ordering to receipt) is constant u Inventory holding cost is based on average inventory u Ordering and setup costs are constant u All demand for product are satisfied i.e. backorders are not allowed u Price per unit of product is constant....

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12 EOQ Model--Basic Fixed-Order Quantity Model R = Reorder point Q = Economic order quantity L = Lead time L L QQQ R Time Number of units on hand....

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13 Cost Minimization Goal Ordering Costs Holding Costs Q OPT Order Quantity (Q) COSTCOST Annual Cost of Items (DC) Total Cost....

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14 Basic Fixed-Order Quantity Model Total Annual Cost = Annual Purchase Cost Annual Ordering Cost Annual Holding Cost ++ TC Total annual cost D Demand CCost per unit Q Order quantity SCost of placing an order or setup cost RReorder point LLead time HAnnual holding and storage cost per unit of inventory....

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15 Deriving the EOQ u Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero....

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16 EOQ Example 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 Determine the economic order quantity and the reorder point.....

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17 Solution....

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18 In-Class Exercise 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. Note: (Tag hidden-slide icon to project solution)....

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19 Solution....

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20 Fixed-Time Period Model Issue an order for the number of units needed Compute order quantity to bring inventory up to required level Compute inventory status Status = On hand + On order - Back order Idle state Waiting for demand Demand occurs Unit withdrawn from inventory or back ordered Is status < Reorder point? Yes No....

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21 Fixed-Time Period Model....

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22 Determining the Value of Z....

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23 Determining the Value of T+L u The standard deviation of a sequence of random events equals the square root of the sum of the variances....

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24 Example--Fixed-Time Period Model 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. How many units should be ordered?....

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25 Solution (continued) To satisfy 96 percent of demand order 779 units at this review period..... Z-value for 96% probability of satisfying demand is 1.76 see normal curve probability table.

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26 Miscellaneous Systems Optional Replenishment System Q = minimum acceptable order quantity If q > Q, order q. Maximum Inventory Level, M Actual Inventory Level, I q = M - I M I....

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27 Miscellaneous Systems Bin Systems Two-Bin System FullEmpty Order One Bin of Inventory One-Bin System Periodic Check Order Enough to Refill Bin....

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28 ABC Classification System u Items kept in inventory are not of equal importance in terms of: –dollars invested –profit potential –sales or usage volume –stock-out penalties A C % of $ Value % of Use B

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29 Inventory Accuracy and Cycle Counting u Inventory accuracy –Do inventory records agree with physical count? u Cycle Counting –Frequent counts »Which items? »When? »By whom?.... Last Slide

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