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Continuous Review Systems in Inventory Management Talia Gruber Marriott School November 2011

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Agenda Continuous review systems defined Inventory positions and reorder points Reorder points with constant demand and lead time Reorder points with variable demand and constant lead time Reorder points with variable demand and lead time Two-Bin System

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What are Continuous Review Systems? Systems that determine whether it is time to reorder a product by tracking the remaining inventory levels of the product each time a withdrawal is made.

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Alternate Names The Continuous Review System may also be called: –Reorder Point (ROP) System –Fixed Order-quantity System –Quantity and Reorder Point (QR) System –Q System

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Inventory Position Inventory Position (IP) measures the level of the current product’s ability to fulfill future orders. IP = OH + SR - BO

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Reorder Point A predetermined minimum level that triggers the order of a fixed quantity of the product.

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Selecting the Reorder Point with Constant Demand and Lead Time On-hand Inventory Time Order Received Order Placed Inventory Position R LLL

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Practice Problem with Constant Demand and Lead Time Demand for water bottles from a particular concession stand is always 30 per day and the lead time is always 2 days. The on hand inventory is currently 15 bottles, and there is is an incoming order of 50 water bottles. If there are currently no backorders, what is the inventory position? Should a new order be placed?

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Solution R = Total demand during lead time = 30*2 = 60 bottles IP = OH + SR – BO = 15 + 50 – 0 = 65 bottles 65 > 60 so a new order is NOT needed

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Selecting Reorder Point with Variable Demand and Constant Lead Time Demand is not usually constant and predictable To guard against stock-outs, reorders that include safety stock should be selected Reorder Point = Avg. demand during lead time + Safety stock

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Selecting Reorder Point with Variable Demand and Constant Lead Time On-hand Inventory Time Order Placed Inventory Position R Order Received

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Selecting Reorder Point with Variable Demand and Constant Lead Time Three steps to selecting a reorder point: 1.Choose an appropriate service-level policy 2.Determine the demand during lead time probability distribution 3.Determine the safety stock and reorder point levels

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Step 1: Service Level Policy Service Level: The desired probability of not running out of stock during an order cycle An 80% service cycle = An 80% chance that the stock will not run out during the lead time.

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Step 2: Demand During Lead Time Distribution In order to calculate the specific safety stock level, you must determine the demand during lead time distribution by knowing the: –Mean –Standard Deviation

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Step 2 Continued Determine the demand during the lead time distribution by making the following assumptions: –Average demand is known –Standard deviation of demand is known –Probability distributions of demand are independent and identical over each time period.

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Step 2 Formulas Average demand during lead time: d + d + d + … = dL Variance of demand during lead time: σ 2 d + σ 2 d + σ 2 d + … = σ 2 d L Standard deviation of demand during lead time: σ dLT = √( σ 2 d L) = σ d √ (L)

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Step 2 Calculations + += Demand week 1Demand week 2Demand week 3 Demand for 3-week lead time σ d = 10 50 150 σdLT = 17.32

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Step 3: Safety Stock and Reorder Point Average demand during lead time 50% Service Level = 50% Service Level = 90% Average demand during lead time 90% =

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Step 3 Continued: Formulas Safety Stock = zσ dLT Z = The number of standard deviations needed to achieve the service level σ dLT = Standard deviation of demand during lead time Reorder Point = dL + safety stock

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Practice Problem with Variable Demand and Constant Lead Time The average weekly demand for water bottles from a particular concession stand is 80 bottles per week, and the constant lead time is 3 weeks. There is a standard deviation of 10 bottles. If a 95% service level is desired, what would the safety stock and reorder point be?

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Solution d = 80 bottles σ d = 10 bottles L = 3 weeks σ dLT = σ d √ (L) = 10√(3) = 17.32 z = 1.64 Safety stock = zσ dLT = (1.64)(17.32) = 28.40 or 28 bottles Reorder Point = dL + safety stock = (80)(3) + 28 = 268 bottles

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Selecting Reorder Point with Variable Demand and Lead Time Two assumptions: –Demand and lead time are measured in the same time units (i.e. days, weeks, etc.) –Demand and lead time are independent of one another

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Formulas for Variable Demand and Variable Lead Time Safety stock = zσ dLT R = (Avg. weekly demand x Avg. lead time in weeks) + safety stock = dL + safety stock

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Practice Problem with Variable Demand and Lead Time The average weekly demand for water bottles from a particular concession stand is 50 bottles per week, with a standard deviation of 10 bottles. The average lead time is 2 weeks, with a standard deviation of 1 week. If an 80% service level is desired, what would the reorder point be?

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Solution d = 50 bottles σ d = 10 bottles L = 2 weeks σ LT = 1 week σ dLT = √(Lσ 2 d + d 2 σ 2 LT ) = √[(2)(10) 2 + (50) 2 (1) 2 ] = 51.96 bottles z = 0.84 Safety stock = zσ dLT = (0.84)(51.96) = 43.64 or 44 bottles Reorder point = dL + safety stock = (50)(2) + 44 =144 bottles

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Two-Bin System The two-bin system is a type of continuous review visual system, used to help employees keep track of inventory levels without maintaining formal written records of the inventory’s current position.

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How it Works Divide inventory between bin 1 and bin 2 Bin 1: Use all the inventory in bin 1 first. Bin 2: Once the inventory in bin 1 runs out, place a new order and then begin using the inventory in bin 2 until the new order arrives.

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Summary Continuous review systems assist management by informing them when new inventory needs to be ordered and how much inventory to order. Reorder points and safety stock can be calculated under 3 circumstances: –Constant demand and lead time –Variable demand and constant lead time –Variable demand and lead time The two-bin system is a visual Q System

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Sources Chapman, S. N., Clive, L. M., Tony Arnold, J. R. (2008). Introduction to Materials Management. New Jersey: Pearson Prentice Hall. Dreckshage, B. J., Kerber B. (2011). Lean Supply Chain Management Essentials: A Framework for Materials Managers. Florida: Taylor and Francis Group, LLC Krajewski, Malhotra, Ritzman (2010). Operantions Management: Processes and Supply Chains. New Jersey: Pearson Prentice Hall. Tersine, R. J. (1994). Principles of Inventory Management. New Jersey: PTR Prentice-Hall Toomey, J. W. (2000). Inventory Management: Principles, Concepts and Techniques. Massachusetts: Kluwer Academic Publishers

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