What is little's law in operations management

CH6

6.1 PROCESS THINKING Process thinking is the point of view that all work can be seen as a process. It begins by describing the process of interest as a system. A system is defined by its boundaries, inputs, outputs, suppliers, customers, and system flows. System definition is needed before detailed measurement and process flowcharting can begin. A system is a collection of interrelated elements whose whole is greater than the sum of its parts. The human body, for example, is a system. The heart, lungs, brain, and muscles cannot function without one another. They are interrelated, and the function of one part affects the others. The whole of the body is greater than any of its individual parts or components.

A business organization can also be viewed as a system. Its parts are the functions of marketing, operations, finance, accounting, human resources, and information systems. Each of these functions accomplishes nothing by itself. A business cannot sell what it cannot produce, and it does no good to produce a product or service that cannot be sold. The functions in an organization are highly interactive and have value as a system that they do not have separately. Within operations, the transformation or conversion system is made up of workers, equipment, customers (for services), and the activities that carry out the transformation. The transformation system can be analyzed by first specifying the system boundaries. The boundaries delineate the resources and activities in the system being analyzed from those that are outside of the analysis and decision area. Identification of the system boundaries is always difficult and somewhat arbitrary, but it must be done to separate the system being analyzed from the larger system or organization in which it operates. In this sense, the boundaries of a firm separate the firm from the larger supply chain in which it resides.

6.2 THE PROCESS VIEW OF BUSINESS One of the most important contributions of process thinking is that a business can be viewed as

a system that consists of a collection of interconnected processes. The process view of a

business is horizontal in nature; the functional view is vertical. This is shown graphically

in Figure 6.1.

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6.3 PROCESS FLOWCHARTING Process flowcharting refers to the creation of a visual diagram to describe a transformation process. Flowcharting is known by several names: process mapping, flow-process charting, and in a service operations context asservice blueprinting. Value stream mapping is yet another approach to process flowcharting popularized by firms that implement lean systems and lean thinking. Creating a visual diagram can be invaluable in documenting what happens within a transformation process. This pictorial documentation, when it includes process measurements, can help to identify how the transformation process can be improved by changing some or all of the following elements: 1. Raw materials 2. Product or service design 3. Job design 4. Processing steps or activities used 5. Management control information 6. Equipment or tools 7. Suppliers

1. Identify and select a relevant transformation process (or system) to study. This can be the entire supply chain for a product or a service, the entire firm, or a part of the firm, for example, the shipping department. Ideally, the selected transformation process is thought to affect performance.

2. Identify an individual or a team of individuals to be responsible for developing the flowchart and for subsequent analyses. This individual or team should have some familiarity with the transformation process and should have process ownership, that is, authority for initiating and/or implementing changes to the process. When a selected transformation process cuts across different functions, a cross-functional team should be involved. When a selected transformation process cuts across the supply chain, interfirm collaboration becomes critical. 3. Specify the boundaries of the transformation process. The boundaries denote where the selected transformation process begins and ends, identify the customer(s) and the supplier(s) of the transformation process, and determine how many processing steps or activities are to be evaluated. In some cases, a function or department within an organization is the customer or supplier; in other cases, another firm is the customer or supplier. 4. Identify and sequence the operational steps or the activities necessary to complete the output for the customer(s). It is important in process flowcharting to depict what is actually happening and not what one thinks is happening. Once the “as it is” flowchart has been created and the transformation process has been analyzed, creating a “to be” flowchart may help show what the transformation process should look like when improvement changes have been implemented. 5. Identify the performance metrics for the operational steps or the activities within the selected transformation process. These metrics should be tied to the performance of the

overall transformation process. For example, if delivery performance is of interest, it may be useful to track the processing times for each operational step or activity. Alternatively, if quality performance is of interest, it may be useful to track the defect rate for each operational step or activity. 6. Draw the flowchart, defining and using symbols in a consistent manner

FIGURE 6.4 Common flowcharting symbols.

6.4 PROCESS-FLOW ANALYSIS AS ASKING QUESTIONS

TABLE 6.1 Process-flow questions about performance

Question

Category Examples

1. Flow

 Is the transformation process balanced or unbalanced?

 Where is the bottleneck in the transformation process?

 Are all operational steps or activities necessary?

 How jumbled is the flow within the transformation process?

2. Time

 How long does it take to produce/deliver one unit of output?

 Can the length of this time be reduced?

 What is the time between successive units of output?

 Where is there excessive setup time?

 Where is there excessive waiting time?

3. Quantity

 How many units theoretically can be produced/delivered in a given

period (e.g., a week)?

 How easy is it to change this quantity?

 How many units are actually produced/delivered in a specified period

(e.g., a week)?

4. Quality

 What is the historical defect rate?

 Which operational step or activity contributes to the defect rate?

 Where do errors occur?

5. Cost

 How much does it cost to produce/deliver one unit of output?

 What are the cost buckets that make up the cost to produce/deliver one

unit of output?

 Can some cost buckets be reduced/eliminated?

6.5 MEASURING PROCESS FLOWS Let’s study the airport security process during check-in at a major airport. There is a line of passengers waiting to clear security and a number of security scanners for examining passengers and their carry-on luggage. We can measure the total time it takes from entering the security line until passengers are cleared to catch their flights. It turns out that these three observations are related: the average number of passengers in the line, the average rate at which security can process passengers, and the average time it takes passengers to get through the line. This relationship is called Little’s Law, named after the operations researcher who discovered it.

Average waiting time in line at airport security follows Little’s Law.

Little’s Law shows that the average number of items in a system (I) is the product of the average

arrival rate to the system (R) and the average time an item stays in the system (T).

In mathematical terms Little’s Law is stated as follows: I = T × R

Where I = average number of things in the system (or “inventory”) T = average throughput time (processing time + waiting time) R = average flow rate in the process In the case of airport security, if the security screeners can process an average of five passengers per minute (R = 5) and it takes an average of 20 minutes to get through the security line (T = 20), the average number of passengers in line will be 100 (R × T = 100). An assumption is that the process is in a steady state in which the average output rate equals the average input rate to the process. Little’s Law is very powerful and is widely used in practice. It applies to manufacturing and service transformation processes. Little’s Law can be used in a variety of settings and situations. Example Suppose a factory can produce an average of 100 units of product per day. The throughput time, including all processing and waiting time for the product, is an average of 10 days.

1. T = 10 days 2. R = 100 units per day

Then the average inventory (partly finished product) in the factory will be I = 10 × 100 = 1000 units For another example, the amount of money in accounts receivable can be considered as inventory, or the stock of money. Using Little’s Law, if there is $2 million in accounts receivable (I) and $20,000 per day is added to and subtracted from (flows through) accounts receivable (R), the throughput time is 100 days (T = I/R = 2,000,000/20,000) Therefore, accounts receivable has 100 days of outstanding receivables. Next, we extend process measurements to include capacity, supply, and demand. Capacity is the maximum rate of output from a transformation process or the maximum flow rate that can be sustained over a period of time. In the airport security example, the average flow rate was five passengers per minute, but the capacity of the security checkpoint may have been greater, say, eight passengers per minute. With random arrivals (such as passengers arriving to enter the line) it is necessary to have capacity that exceeds the average arrival rate. If the arrival rate is greater than the capacity, the line will build up to an infinite length. This occurs because there are periods when the arrivals are less than the average and the full capacity cannot be used during those times. Queuing (or waiting line) theory, which is covered in a technical chapter explains these phenomena in detail.

6.7 PROCESS REDESIGN Process redesign usually starts with identifying critical processes required to meet the customers’ needs. Then the critical processes, many of which cut across organization boundaries, are analyzed in detail using the methods described in this chapter. To pursue a successful radical redesign requires four principles:Page 107

1.Organize around outcomes, not tasks. The insurance company was originally organized according to tasks, using the classic division of labor. When the company reorganized around the outcome, which was customer service, dramatic improvements were made. A customer service representative handled all activities associated with the desired outcome. Although it is not always possible to have one person do everything, jobs can be broadened and handoffs between departments can be minimized. 2. Have the people who do the work process their own information. When bedside or portable information system access is available, nurses can update patient electronic medical records as they are dispensing medications to the patient. By doing so, nurses avoid delaying the record update and also do not “hand off” the information for input by someone else, thus reducing the likelihood of inadvertent errors. This principle can be applied in many situations in which information is passed from one department to another. 3. Put the decision point where the work is performed, and build control into the process. It is better to push decision making to the lowest possible level. This will eliminate layers of bureaucracy and speed up the decision-making process. In the insurance example, the customer service representative had greater latitude to make decisions directly for the customer rather than referring decisions to other departments. To accomplish this, however, information and controls must be built into the process itself. 4. Eliminate unnecessary steps in the process. Simplifying the processes frequently means that unnecessary steps and paperwork are eliminated. Every step is examined by using the flowcharting techniques discussed earlier, and only those that add value for the customer should be retained. Process redesign can be used to streamline and implify work flows. Process redesign is just one of many methods that can be used to improve operations. It uses a process view of the organization as a way of improving process flows. As a result of process redesign, processes will be simplified, process flows improved, and non- value-added work eliminated.

SOLVED PROBLEMS Problem 1. A ticket line for a Minnesota Vikings football game has an average of 100 fans

waiting to buy tickets and an average flow rate of 5 fans per minute. What is the average time that a ticket buyer can expect to wait in line?

Solution Using Little’s Law I = T × R, solve for T:

T = I ÷ R = 100 ÷ 5 = 20 A ticket buyer can expect to spend an average of 20 minutes in line.

Problem 2. Joe’s commercial laundry has contracts to wash bedsheets for hotels. Joe intakes

each batch of sheets, which takes 1 minute, and then the sheets are washed, taking 20 minutes, and dried, taking 30 minutes. The batch of sheets is ironed, taking 10 minutes for one Page 109 employee to complete each batch, and there are two

employees ironing sheets. Finally, Joe packages the sheets and bills the customer, taking 2 minutes. Joe has five washing machines and seven dryers that can process one batch of sheets each. a. What is the capacity of the laundry system, and what is the bottleneck? b. What is the average throughput time of a batch of sheets? c. If the flow rate is 10 batches per hour, what is the average number of batches of

sheets in the system (inventory)?

Solution a. The capacity of each resource is as follows:

 Joe takes 3 minutes for each batch and can thus handle 20 batches per hour.  Ironing takes 10 minutes, and so each employee can handle 6 batches per hour

and the total capacity for two employees is 12 batches per hour.  Washing machines take 20 minutes per batch or three loads per hour for each

machine, and there are five machines, for a total capacity of 15 batches per hour.  Dryers take 30 minutes per batch or two loads per hour from each machine ×

seven machines for a capacity of 14 batches per hour. The most constraining (minimum capacity) resource is the ironing, and so the system capacity is 12 batches per hour and ironing is the bottleneck.

b. The average throughput time (assuming no waiting time) of the system for each batch of sheets is:

T = 1 + 20 + 30 + 10 + 2 = 63 minutes c. I = T × R = (63 ÷ 60) × 10 = 10.5 batches (note, that the 63 minutes must be

converted to hours using 60 minutes in an hour)

Problem 3. A restaurant has 30 tables. When the guests arrive, the manager seats them, servers

serve them, and the cashier assists them when they pay the bill. The process is shown with processing times above the process steps and waiting times that occur between operations below the steps. One manager, one cashier, and four servers are available.

a. What is the capacity of the system and the bottleneck resource? b. What is the throughput time for each customer? c. If there are 20 arrivals per hour, what is the average number of tables filled?

Solution a. The capacity of each resource is as follows:

 The manager takes 1 minute each and can handle 60 customers (or tables) per hour.

 The cashier takes 2 minutes each and can handle 30 customers per hour.  Each server takes 10 minutes per table and can handle 6 tables per hour. There

are four servers, and so the total capacity for servers is 24 tables per hour.  There are 30 tables available. Page 110The resource with the minimum capacity is the servers, and so the system

capacity is 24 tables per hour and the bottleneck is the servers. b. The throughput time (including both processing time and waiting time) of the

system for each customer is 1 + 2 + 3 + 4 + 1 + 2 + 5 + 10 + 20 + 30 + 5 = 83 minutes

c. If there are 20 arrivals per hour, there will be an average of I = T × R = (83 ÷ 60) × 20 = 27.7 tables being used

Discussion Questions 1. In the following operations, isolate a system for analysis and define customers,

services produced, suppliers, and the primary process flows. a. A college b. A fast-food restaurant c. A library

2. Explain how the process view of an organization is likely to uncover the need for greater cross-functional cooperation.

3. Explain Little’s Law in your own words. How can it be used, and what are its limitations?

4. Provide a definition of a bottleneck. Why is it important to find the bottleneck? 5. Explain the differences between capacity, flow rate, and demand. 6. What kinds of problems are presented by the redesign of existing processes that are

not encountered in the design of a new process? 7. Why is it important to define the system of interest before embarking on

improvement? Give three reasons. 8. Find examples of flowcharts and study their details. Describe how the flowcharts

might be used to make improvements. 9. Describe service blueprinting in your own words, including examples of when it

should be used.