Process Flow Analysis The Little’s Law The main source for preparing these slides is Managing Business Process Flow Anupindi, Chopra, Deshmoukh, Van Mieghem, and Zemel

Five Elements of the Process View Management Information structure Network of Activities and Buffers Inputs Outputs Goods Services Flow units (customers, data, material, cash, etc.) Labor & Capital Resources

How target improvement How target improvement? Identify and Monitor Operational Performance Measures Inventory Flow Rate Quality Cost Flexibility Time

Flow Time, Flow Rate, and Inventory Flow Time: The time required by a flow unit to move through all the processes from entry to exit. It is not the same for all flow units different types of flow units variability in the flow time of a flow unit Average flow time of a process is the average flow time of all flow units. Flow Rate: The number of flow units passing a specific point (entry, exit or any intermediate point) in the process per unit of time. It changes over time variability in the flow rate seasonality (e.g. tax season for a CPA) Average flow rate in a stable process  Throughput Inventory: The number of flow units within the boundaries of the process at any time.

The Essence of Process Flow Customer expectations Customer Value Proposition   Customer satisfaction   Process competencies Financial performance  Inventory Flow time Flow rate In any process our goal is to meet our customers’ expectations. Certain measures to help us accomplish that is to identify key attributes that are important to customers. We categorize these product attributes along the following 4 dimensions. Cost: Time: Variety: Quality: Quality Time Cost Flexibility  Essence of process flow 

Is the Security Checkpoint a stable Process? In a Stable Process Average inflow rate is the same as average outflow rate. Throughput (R) is the average flow rate Ideally, R should be equal to the customer demand. Is the Security Checkpoint a stable Process? Scanner can handle 12 passengers per minute It can handle inflow Average inflow rate is 600 passengers/hr, or 10 passengers/min Can we have 9 instead of 12? If we have 20 instead of 12, could we still have people waiting in the line? Average outflow capacity (process capacity) must be greater than average inflow rate, while average inventory is not zero.

There is a relationship between R, T, and I. The Little’s Law Inventory I [units] Flow rate/Throughput R [units/hr] ... Flow Time T [hrs] There is a relationship between R, T, and I. Throughput x Flow Time = Inventory RT=I Ardavan Asef-Vaziri June/2011 Process Flow Analysis-Basics 6

Little’s Law: Examples In Vancouver Airport: Average waiting line length = I = 17.5 passengers Throughput or R = 600/60 = 10 passengers/minute Compute the flow time at Flow time T  RT=I  T= I/R T= 17.5 /10 = 1.75 minutes / passenger (on average). 7

Little’s Law: Examples I=2000 garage doors, with no inventory buildup (i.e. stable process; always on average we have 2000) R=1000 garage doors/week. Each garage door costs $3,300 to produce. What is the Average Flow Time for $1? We can translate volumes into $ I = 2,000(3,300) = $6,600,000 tied up in inventory (average). R = 1,000(3,300) = $3,300,000/week. I=RT  T=I/R T = 6,600,000/3,300,000 = 2 weeks. 8

Little’s Law applied to different process flow examples Monetary Flow. For the new euro introduction in 2002, Wim Duisenberg had to decide how many new Euro coins to stamp by 2002. Euroland’s central banks’ cash-in-coins handling was estimated at €300 billion per year. The average cash-in-coins holding time by consumers and businesses was estimated at 2 months. How many Euro coins were to be made? Customer Flow. Taco Bell processes on average 1,500 customers per day (15 hours). On average there are 75 customers in the restaurant (waiting to place the order, waiting for the order to arrive, eating etc.). How long does an average customer spend at Taco Bell and what is the average customer turnover? Euro’s: NYT 2001: “As of Jan. 1, some 50 billion new coins and 14.5 billion euro notes are to be pumped into circulation.” Our number: I = 300/yr * 2mo = 300/yr * 1/6 yr = 50 9

Little’s Law applied to different process flow examples Job Flow. The Travelers Insurance Company processes 10,000 claims per year. The average processing time is 3 weeks. Assuming 50 weeks in a year, what is the average number of claims “in process”. Material Flow. Wendy’s processes an average of 5,000 lb. of hamburgers per week. The typical inventory of raw meat is 2,500 lb. What is the average hamburger’s cycle time and Wendy’s turnover? Cash Flow. Motorola sells $300 million worth of cellular equipment per year. The average accounts receivable in the cellular group is $45 million. What is the average billing to collection process cycle time? 10

Little’s Law: Cash Flow Steel Company: Processes $400M of iron ore per year. The cost of processing the ore is $200M per year. The average inventory is $100M. How long does a dollar spend in the process? The flow unit is a cost dollar. The process is the steel manufacturing operations The value of the inventory includes both ore and processing cost. I = $100M/year A Total of $400M + $200M = $600M flows through the process each year. Throughput R = $600M/year Average flow time T = I/R = 100/600 = 1/6 year = 2 months 11

Little’s Law: inventory Turns Question: A general manager at Baxter states that her inventory turns three times a year (Cost of Goods Sold is three times of average inventory). She also states that everything that Baxter buys gets processed and leaves the docks within six weeks. Are these statements consistent? Of the 3 operational measures of performance, inventory, throughput and average flow time – a process manager only needs to focus on 2 measures, as they directly determine the third measure via Little’s Law. Measuring which one is cheaper? For a given level of throughput in any process, the only way to reduce flow time is to reduce inventory and vice versa. 12