The number of workstations required is minimized

The precedence and cycle-time requirements are not violated

Finding a Solution

Line Balancing

Assignment of work to stations in a line so as to achieve the desired output rate with the smallest number of workstations

Achieving the goal is similar to the theory of constraints but it differs in how it addresses bottlenecks

Precedence Diagram

AON Diagram

A Line Process

The bottleneck schedule is the drum because it sets the beat or the production rate for the entire plant and is linked to market demand

The buffer is the time buffer that plans early flows into the bottleneck and thus protects it from disruption

The rope represents the tying of material release to the drum beat, which is the rate at which the bottleneck controls the throughput of the entire plant

Drum-Buffer-Rope Systems

Application 7.2

Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall.

O’Neill Enterprises manufactures three unique products (A, B, C) that are fabricated and assembled in four different workstations (W, X, Y, Z) using a small batch process.

Each of the products visits every one of the four workstations, though not necessarily in the same order.

Batch setup times are negligible.

O’Neill can make and sell up to the limit of its demand per week, and there are no penalties for not being able to meet all the demand.

Each workstation is staffed by a worker dedicated to work on that workstation alone, and is paid $12 per hour.

Variable overhead costs are $8000/week. The plant operates one 8-hour shift per day, or 40 hours/week.

Which of the four workstations W, X, Y, or Z has the highest total workload, and thus serves as the bottleneck for O’Neill Enterprises?

Application 7.2

Identify the bottleneck by computing aggregate workloads at each workstation.

The firm wants to satisfy as much of the product demand in a week as it can.

Each week consists of 2,400 minutes of available production time.

Multiplying the processing time at each station for a given product with the number of units demanded per week yields the workload represented by that product.

These loads are summed across all products going through a workstation to arrive at the total load for the workstation, which is then compared with the others and the existing capacity of 2,400 minutes.

Example 7.2

We define the bottleneck as step 2, which has the highest time per loan processed.

The throughput time to complete an approved loan application is 15 + 20 + max(15, 12) + 10 = 60 minutes.

The actual time taken for completing an approved loan will be longer than 60 minutes due to nonuniform arrival of applications, variations in actual processing times, and the related factors.

The capacity for loan completions is derived by translating the “minutes per customer” at the bottleneck step to “customer per hour.” At First Community Bank, it is 3 customers per hour because the bottleneck step 2 can process only 1 customer every 20 minutes (60/3).

Example 7.1

Work should be released into the system only as frequently as needed by the bottlenecks.

Bottleneck flows = market demand

Activating a nonbottleneck resources is not the same as utilizing a bottleneck.

It doesn’t increase throughput or promote better performance.

Every capital investment must be viewed from the perspective of the global impact on throughput, inventory and operating expense.

Key Principles of the TOC

Theory of Constraints and

Financial Measures

Using trial and error, one possible solution is shown below.

Application Problem 7.4

Finding a Solution

a. What should be the line’s cycle time?

b. What is the smallest number of workstations that she could hope for in designing the line for this cycle time?

c. Suppose that she finds a solution that requires only five stations. What would be the line’s efficiency?

Green Grass’s plant manager just received marketing’s latest forecasts of Big Broadcaster sales for the next year. She wants its production line to be designed to make 2,400 spreaders per week for at least the next 3 months. The plant will operate 40 hours per week.

Example 7.5

Example 7.4

SOLUTION

Identify the bottleneck by computing total workload at each workstation. The firm wants to satisfy as much of the product demand in a week as it can. Each week consists of 2400 minutes of available production time. Multiplying the processing time at each station for a given product with the number of units demanded per week yields the capacity load. These loads are summed across all products going through that workstation and then compared with the existing capacity of 2400 minutes.

Application Problem 7.2

Identifying the Bottleneck – 7.2

Diablo Electronics manufactures four unique products (A, B, C, and D) that are fabricated and assembled in five different workstations (V, W, X, Y, and Z) using a small batch process. Each workstation is staffed by a worker who is dedicated to work a single shift per day at an assigned workstation. Batch setup times have been reduced to such an extent that they can be considered negligible. Figure 7.2 is a flowchart of the manufacturing process. Diablo can make and sell up to the limit of its demand per week, and no penalties are incurred for not being able to meet all the demand.

Which of the five workstations (V, W, X, Y, or Z) has the highest utilization, and thus serves as the bottleneck for Diablo Electronics?

Identifying the Bottleneck

Example 7.2

Which single step is the bottleneck? The management is also interested in knowing the maximum number of approved loans this system can process in a 5-hour work day.

Identifying the Bottleneck

Example 7.1

Managers at the First Community Bank are attempting to shorten the time it takes customers with approved loan applications to get their paperwork processed. The flowchart for this process is shown in the next slide.

Approved loan applications first arrive at activity or step 1, where they are checked for completeness and put in order.

At step 2, the loans are categorized into different classes according to the loan amount and whether they are being requested for personal or commercial reasons.

While credit checking commences at step 3, loan application data are entered in parallel into the information system for record-keeping purposes at step 4.

Finally, all paperwork for setting up the new loan is finished at step 5. The time taken in minutes is given in parentheses.

Identifying the Bottleneck

Example 7.1

The focus should be on balancing flow, not on balancing capacity.

Maximizing the output and efficiency of every resource may not maximize the throughput of the entire system.

An hour lost at a bottleneck or constrained resource is an hour lost for the whole system.

An hour saved does not make the system more productive.

Inventory is only needed in front of bottlenecks and in front of assembly and shipping points.

Key Principles of the TOC

Identify the System Bottleneck(s)

Exploit the Bottleneck(s)

Subordinate All Other Decisions to Step 2

Elevate the Bottleneck(s)

Do Not Let Inertia Set In

Theory of Constraints

**07- 01**

**Constraint Management**

Chapter 7

Chapter 7

A plant manager needs a design for an assembly line to assembly a new product that is being introduced. The time requirements and immediate predecessors for the work elements are as

follows:

Application Problem 7.4

The theoretical minimum number of workstations is 5 and the cycle time is 60 seconds, so this represents an optimal solution to the problem.

Finding a Solution

where

n = number of stations

C = cycle time

t = total time required to assemble each unit

Idle time = nc – t

Idle time

A Line Process

Green Grass, Inc., a manufacturer of lawn and garden equipment, is designing an assembly line to produce a new fertilizer spreader, the Big Broadcaster. Using the following information on the production process, construct a precedence diagram for the Big Broadcaster.

Example 7.4

Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall.

Drum-Buffer-Rope

A planning and control system that regulates the flow of work-in-process materials at the bottleneck or the capacity constrained resource (CCR) in a productive system.

Drum-Buffer-Rope Systems

a. What is the capacity per hour of Type A customers?

b. If 30 percent of the customers are Type A customers and 70 percent are Type B customers, what is the average capacity?

c. When would Type A customers experience waiting lines, assuming there are no Type B customers in the shop? Where would Type B customers have to wait, assuming no Type A customers?

Two types of customers enter Barbara’s Boutique shop for customized dress alterations. After T1, Type A customers proceed to step T2 and then to any of the three workstations at T3, followed by steps T4 and T7. After step T1,Type B customers proceed to step T5 and then steps T6 and T7. The numbers in the parentheses are the minutes it takes that activity to process a customer.

Application Problem 7.1

Bottleneck

A capacity constraint resource whose available capacity limits the organization’s ability to meet the product volume or mix, or demand fluctuations.

Constraint

Any factor that limits the performance of a system and restricts its output.

What is a Constraint?

c =

where

c = cycle time in hours

r = desired output rate

Desired output rate – Ideally is matched to the staffing or production plan

Cycle time - Maximum time allowed for work at each station is

A Line Process

1

r

Balance delay (%) = 100 – Efficiency

Efficiency and Balance Delay

A Line Process

t

nc

Efficiency (%) =

where

t = total time required to assemble each unit

t

c

TM =

Theoretical minimum number of stations

A Line Process

c. Now calculate the efficiency of a five-station solution, assuming for now that one can be found:

Example 7.5

Suppose that we are fortunate enough to find a solution with just four stations. What is the idle time per unit, efficiency, and the balance delay for this solution?

Application Problem 7.4

1/60 (hr/unit) = 1 minute/unit = 60 seconds/unit

244 seconds

60 seconds

b. Now calculate the theoretical minimum for the number of stations by dividing the total time, t, by the cycle time, c = 60 seconds. Assuming perfect balance, we have

c = 1/r =

a. First convert the desired output rate (2,400 units per week) to an hourly rate by dividing the weekly output rate by 40 hours per week to get units per hour. Then the cycle time is

TM =

t

c

If the desired output rate is 30 units per hour, what are the cycle time and theoretical minimum?

Application Problem 7.4

For Type A customers

Step T2 can process (60/13) = 4.62 customers per hour.

Step T3 has three work stations and a capacity of (60/14) + (60/10) + (60/11) = 15.74 customer per hour.

Step T4 can process (60/18) = 3.33 customers per hour.

The bottleneck for type A customers is T4.

Application 7.1

For Type B customers

T6 is the bottleneck for Type B customers.

The capacity for Type B customers is (60/22) = 2.73 customers per hour.

The average capacity is 0.3(3.33) + 0.7(2.73) = 2.9 customers per hour.

Application 7.1

2750

(80x10)=800

(70x13)=910

(65x16)=1040

2075

(80x5)=400

(70x10)=700

(65x15)=975

2225

(80x10)=800

(70x12)=840

(65x9)=585

2310

(80x12)=960

(70x10)=700

(65x10)=650

These calculations show that workstation Z is the bottleneck, because the aggregate work load at Z exceeds the available capacity of 2400 minutes per week.

Application 7.2

Type B customers would wait before steps T5 and T6 for the same reason. This assumes there are always new customers entering the shop.

Application 7.1

c. Type A customers would wait before steps T2 and T4 because the activities immediately preceding them have a higher rate of output.

1,400

100 x 10 = 1,000

0

0

2,300

100 x 5 = 500

80 x 5 = 400

80 x 5 = 400

80 x 10 = 800

60 10 = 600

2,600

0

80 x 5 = 400

80 x 20 = 1,600

60 10 = 600

1,900

100 x 15 = 1,500

80 x 5 = 400

0

0

1,800

0

0

0

60 x 30 = 1800

These calculations show that workstation X is the bottleneck, because the aggregate work load at X exceeds the available capacity of 2,400 minutes per week.

Identifying the Bottleneck – 7.2

Draw a precedence diagram, complete I, F, J, and K

Application Problem 7.4

Drum-Buffer-Rope Systems

Application 7.2

Identifying the Bottleneck - 7.2

Application 7.2

(100)

a. What should be the line’s cycle time?

=

=

4.067 or 5 stations

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