FourRolesOfInventory6x

# FourRolesOfInventory6x - Four Roles of Inventory Four Roles...

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1/31/2007 Industrial Data and Systems Analysis 1 Four Roles of Inventory Peter L. Jackson Professor School of O.R. and I.E. 1/31/2007 Industrial Data and Systems Analysis 2 Pipeline Stock Cycle Stock Decoupling Stock Safety Stock 1/31/2007 Industrial Data and Systems Analysis 3 Pipeline Stock Value-added process time or transport time, T Output rate, r Input rate, r Little’s Law: Average pipeline stock = rT To reduce pipeline stock, reduce the duration of value-added activities 1/31/2007 Industrial Data and Systems Analysis 4 Decoupling Stock Decoupling stock: queues of work between workstations caused by variability in processing times 1/31/2007 Industrial Data and Systems Analysis 5 A Useful Queueing Model Focus on a single workstation Jobs arrive at rate λ Jobs can be completed at rate µ < so the workstation is sometimes idle 1 Workstation Jobs arriving Completed jobs departing Waiting queue 1/31/2007 Industrial Data and Systems Analysis 6 No Decoupling Stock in Deterministic Case If the time between arrivals is constant and the processing time is constant then there will never be a queue Utilization rate: fraction of time the workstation is busy; = busy/(busy+idle) busy idle arrival arrival arrival arrival

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1/31/2007 Industrial Data and Systems Analysis 7 Variability is the Enemy Queues develop when the arrival rate temporarily exceeds the processing rate Assume independent and identically distributed (i.i.d.) inter-arrival times, and i.i.d. process times busy idle 1/31/2007 Industrial Data and Systems Analysis 8 Interpreting the Utilization Rate Let ρ = λ / µ is the utilization rate, the average fraction of time the workstation is in use 1- is the probability you will find the queue empty and the workstation idle if you observe it at a random time - is the average rate at which queues decrease, once a queue has formed /(1- )= /( ) a unit-less measure of the ability of workstation to work off queues 1/31/2007 Industrial Data and Systems Analysis 9 How Shall We Measure Variability? m a = mean interarrival time (m = 1/ ) σ 2 = variance of interarrival time c / m , the coefficient of variation of interarrival time is a unit-less measure of variability a 1 corresponds to high variability = 1 is characteristic of the exponential distribution 1 for our examples 1/31/2007 Industrial Data and Systems Analysis 10 Variability is called the squared coefficient of variation (SCV) of the interarrival process Or, “the arrival SCV” Similarly, let e = mean effective processing time (m = variance of effective processing time Why “effective”? Recall our adjustments to the throughput rate (speed loss, breakdowns, etc.) 1/31/2007 Industrial Data and Systems Analysis 11 Variability of Effective Process Time Process times are usually not highly variable on their own Time to make a part if everything goes well
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## This note was uploaded on 01/09/2009 for the course ORIE 312 taught by Professor D.ruppert,p.jacks during the Spring '08 term at Cornell.

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FourRolesOfInventory6x - Four Roles of Inventory Four Roles...

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