PROBLEMS chapter 6

6.1. A manual production flow line is arranged with six stations and a conveyor system is used to move parts along the line. The belt speed is 4 ft/min and the spacing of raw work parts along the line is one every 3 ft. The total line length is 30 ft, hence each station length equals 5 ft. Determine the following :
(a) Feed rate f_p.
(b) Tolerance time T_t.
(c) Theoretical cycle time T_c.
6.2. Given the physical flow line configuration of Problem 6.1, is it likely that the line could be utilized to produce a job whose total work content time  = 5.0 min? What about a total work content time of 4.0 min ? 3.0 min ?
6.3. A manual assembly line is to be.designed with a production rate of 100 completed assemblies per hour. The line will have eight stations and the length of each station is 1.0 m. The minimum allowable tolerance time is to be 2.0 min. If the line is figured to have an up time efficiency of 97% (estimated from previous similar lines), determine the following parameters for the line:
(a) Ideal cycle time T_c.
(b) Conveyor speed V_c.
(c) Feed rate f_p.
(d) Part spacing s_p along the belt.
6.4. The total work content time of a certain assembly job is 7.8 min. The estimated downtime of the line is D = 5%, and the required production rate is R_P = 80 units/h.
(a) Determine the theoretical minimum number of workstations required to optimize the balance delay.
(b) For the number of stations determined in part (a), compute the balance delay d.
(c) What feed rate should be specified if a moving belt line is to be used?
6.5. A moving belt assembly line is to be designed for an assembly job that has a total work content of 21 min. From consideration of human factors the length of each station will be 6.0 ft. The belt speed is variable and can be set between 1.1 and 2.0 ft/min. The required production rate for the line must be 30,000 units/yr (assume 2000 h of operation per year). From past experience on similar lines, the up time proportion of this assembly line (line efficiency), E is expected to be 95%. Production management demands that the line be designed so that the balance delay d is between 0.06 and 0.10, and the line must be designed for a balance delay within this range.
(a) Determine the number of stations that should be designed on the assembly line.
(b) With good design practice in mind, determine the belt speed, spacing between parts on the line, and the tolerance time to be used.
6.6. The following list defines the precedence relationships and element times for a new model toy :
Element             T_e(min)              Immediate predecessors
1                     0.5                                  –
2                     0.3                                 1
3                     0.8                                 1
4                     0.2                                 2
5                     0.1                                 2
6                     0.6                                 3
7                     0.4                                 4,5
8                     0.5                                 3,5
9                     0.3                                 7,8
10                     0.6                                 6,9

(a) Construct the precedence diagram for this job.
(b) If the ideal cycle time is to be 1.0 min, what is the theoretical minimum number of stations required to minimize the balance delay?
(c) Compute the balance delay for the answer found in part (b).
6.7. Determine the assignment of work elements to stations using the largest-candidate rule for Problem 6.6.
(a) How many stations are required?
(b) Compute the balance delay.
6.8. Solve Problem 6.6 using the Kilbridge and Wester method.
6.9. Solve Problem 6.6 using the ranked positional weights method.
6.10. Solve for one iteration of Problem 6.6 using COMSOAL.
6.11. A proposal has been submitted to replace a group of assembly workers, each working individually, with an assembly line. The following table gives the individual work elements.

Element              T_c(min)              Immediate predecessors

1                       1.0                                     –
2                       0.5                                     –
3                       0.8                                  1,2
4                       0.3                                     2
5                       1.2                                     3
6                       0.2                                  3,4
7                       0.5                                     4
8                       1.5                                  5,6,7

The demand rate for this job is 1600 units/week (assume 40 h/week) and the current number of operators required to meet this demand is eight using the individual manual workers.
(a) Construct the precedence diagram from the data provided on work elements.
(b) Use the largest-candidate rule to assign work elements to stations. What is the balance delay for the solution?
(c) The initial cost to install the assembly line is $20,000. If the hourly rate for workers is $5.00/h, will the assembly line be justified using a 3-year service life? Assume 50 weeks/yr. Use a rate of return = 10%.
6.12. Solve Problem 6.1l(b) using the Kilbridge and Wester method.
6.13. Solve Problem 6.12(b) using the ranked positional weights method.
6.14. A manual assembly line operates with a mechanized conveyor. The conveyor moves at a speed of 5 ft/min, and the spacing between base parts launched onto the line is 4 ft. It has been determined that the line operates best when each station is separated from the adjacent stations by 6 ft. There are 14 work elements which must be accomplished to complete the assembly, and the element times and precedence æquirements are defined in the following table :

Element               Time (min)                     Preceded hv:

1                          0.2
2                          0.5                                    –
3                          0.2                                    1
4                          0.6                                    1
5                          0.1                                    2
6                          0.2                                    3, 4
7                          0.3                                    4
8                          0.2                                    5
9                          0.4                                    5
10                          0.3                                    6.7
11                          0.1                                    9
12                          0.2                                     8,10
13                          0.1                                   11
14                          0.3                                   12,13
3.7  = total work content time

(a) Determine the feed rate on the assembly line and the corresponding cycle time.
(b) Determine the tolerance time for each operator on the line.
(c) What is the ideal minimum number of workstations that will allow completion of the assembly on the line?
(d) Draw the precedence diagram for the table of work elements.
(e) Determine an efficient allocation of work elements to stations that can be used for the assembly line. Use one of the line balancing methods discussed in the chapter text. For your line balancing solution, determine the balance delay.
6.15. A manual assembly line is to be designed to make a small consumer product. The work elements, their times, and the precedence constraints are as follows :

Element       Time (min)        Preceded by:     Element        Time (min)        Preceded by :
1                   0.4                      –                       6                     0.2                     3
2                   0.7                      1                      7                     0.3                     4
3                   0.5                      1                      8                     0.9                     4, 9
4                   0.8                      2                      9                     0.3                     5, 6
5                   1.0                      2, 3                 10                     0.5                    7, 8

The workers will operate the line for 400 min per day and must produce 300 products per day. A mechanized belt, moving at a speed of 4.0 ft/min, will transport the products between workstations. Because of the variability in the time required to perform the assembly operations, it has been determined that the tolerance time should be equal to 1.5 times the cycle time of the line.
(a) Determine the ideal number of workstations on the line.
(b) Use the ranked positional weights method to balance the line.
(c) Compute the balance delay for your solution in part (b).
(d) Determine the required spacing between assemblies on the conveyor
(c) Determine the required length of each workstation in order to meet the specifications that have been placed on the design of the line.
6.16. A new small electrical appliance for the home do-it-your selfer is to be assembled manually on  a production flow line. The total job of assembling the product has been divided into minimum rational work elements and these are described in Table P6.16. Also given inthis table are tentative time standards as estimated by the industrial engineering department from similar jobs done previously. In the extreme right-hand column of the table are the immediate predecessors established by precedence requirements. The small appliance is to be assembled at the rate of one product per minute off the production line. You are to design the layout of stations along the line so as to meet this production requirement.
Use one of the methods of line balancing presented in Section 6.5 to balance the line as much as possible. How many stations are required? If the production rate is increased or decreased slightly (by not more than 20%), could the balance be improved? What is the percent balance delay? Make a sketch of the flow line layout, showing the positions of stations and operators along the line.

TABLE P6.16  List of Work Elements
T_c            Immediate
No.       Element description                                             (min)         predecessors
1         Place frame on workholder and clamp                 0.15            –
2         Assemble fan to motor                                           0.37            –
3         Assemble bracket i to frame                                  0.21            1
4         Assemble bracket 2 to frame                                 0.21            1
5         Assemble motor to frame                                      0.58            1, 2
6         Affix insulation to bracket 1                                   0.12            3
7         Assemble angle plate to bracket 1                        0.29            3
8         Affix insulation to bracket 2.                                  0.12            4
9         Attach link bar to motor and bracket 2                 0.30            4. 5
10         Assemble three wires to motor                              0.45            5
11         Assemble nameplate to housing                           0.18            –
12         Assemble light fixture to housing                          0.20           11
13         Assemble blade mechanism to frame                   0.65             6, 7, 8, 9
14         Wire switch, motor. and light                                 0.72           10, 12
15         Wire blade mechanism to switch                           0.25           13
16         Attach housing over motor                                     0.35           14
17         Test blade mechanism, light. etc.                          0.16            15,16
18         Affix instruction label to cover plate                      0.12             –
19         Assemble grommet to power cord                         0.10             –
20         Assemble cord and grommet to cover plate         0.23            18. 19
21         Assemble power cord leads to switch                   0.40            17, 20
22         Assemble cover plate to frame                               0.33            21
23         Final inspect and remove from work holder         0.25             22
24         Package                                                                    1.75            23

REFERENCES of chapter 6

[1] ARCUS, A. L., “COMSOAL–A Computer Method of Sequencing Operations for Assembly Lines,” International Journal of Production Research, Vol. 4, No. 4, 1966, pp. 259-277
[2] BUFFA, E. S., and W. H ., T AUBERT, Production-Inventory Systems : Planning and Control, Richard D. Irwin, Inc., Homewood, Ill., 1972, Chapters 8, 9.
[3] BUXLEY, G. M., H. D. SLACK, and R., WILD, “Production Flow Line System Design-A Review” AIIE Transactions, Vol. 5, No. 1, 1973, pp. 37-48.
[4] DAR-EL, E. M., “Solving Large Single-Model Assembly Line Balancing Problems-A Comparative Study,” AIIE Transactions, Vol. 7., No. 3, 1975, pp. 302-310.
[5] GROOVER, M. P., M. WEISS, R. N. NAGEL, and N. G. ODREY, Industrial Robotics: Technology, Programming, and Applications, McGraw-Hill Book Company, New York, 1986, Chapter 15.
[6] HELGESON, W. B., and D. P. BIRNIE, “Assembly Line Balancing Using Ranked Positional Weight Technique,” Journal of Industrial Engineering, Vol. 12, No. 6, 1961, pp. 394-398.
[7] KILBRIDGE, M. D., and L. WESTER, “A Heuristic Method of Assembly Line Balancing,” Journal of fndustrial Engineering, Vol. 12, No. 4, 1961, pp. 292-298.
[8] MAGAD, E. L., “Cooperative Manufacturing Research, “Industrial Engineering, Vol.4, No. 1, 1972, pp. 36-40.
[9] MASTOR, A. A., “An Experimental Investigation and Comparative Evaluation of Production Line Balancing Techniques,” Unpublished Ph.D. dissertation, UCLA, Los Angeles, 1966.
[10] MASTOR, A. A., “An Experimental Investigation and Comparative Evaluation of Production Line Balancing Techniques,” Management Science, Vol. 16, No. 11, 1970, pp., 728-746.
[11] PRENTING, T. O., and N. T. THOMOPOULOS, Humanism and Technology in Assembly Line Systems, Spartan Books, Hayden Book Co., Hasbrouk Heights, N. J., 1974.
[12] SHARP, W. I., JR., “Assembly Line Balancing Techniques,” Technical Paper MS77-313. Society of Manufacturing Engineers, Dearborn, Mich., 1977.
[13] WILD, RAY, Mass-Production Management, John Wiley & Sons Ltd., London, 1972.

6.8 FLEXIBLE MANUAL ASSEMBLY LINES

The well-defined pace of a manual assembly line has merit from the point of view of maximizing production rate. However, the workers on the assembly line often feel as if they are being driven too hard. Frequent complaints by the workers, poor-quality workmanship, sabotage of the line equipment, and other problems have occurred on high-production flow lines. To relieve some of these conditions, a new concept in assembly lines has developed in which the pace of the work is controlled largely by the workers at the individual stations rather than by a powered conveyor moving at a fixed speed.
The  new concept  was pioneered by Volvo in Sweden. It relies on the use of independently operated work carriers that hold major components and/or sub assemblies of the automobile and deliver them to the manual assembly workstations along the line. The work carriers in the system are called automated guided vehicles (AGVs), and they are designed to follow guide paths in the factory which are routed to the various stations. The guided vehicles are illustrated in Figure 6.7 operating in an American automobile assembly plant. We describe the technology of automated guided vehicle systems in more detail in Chapter 14, but for now, let us examine the characteristics of assembly systems that use AGVs as the work part transport system.
The independently operating work carriers allow the assembly system to be configured with parallel paths, queues of parts between stations, and other features not typically found on a conventional in-line assembly system. In addition, these manual assembly lines can be designed to be highly flexible, capable of dealing with variations in product and corresponding variations in assembly cycle times at the different work-stations. We have previously referred to this type of assembly system as a mixed-model line.

The type of flexible assembly system described here is generally used when there are many different models to be produced, and the variations in the models result in significant differences in the work content times involved. The work cycle time at any given station.might range between 4 and 10 min, depending on model type. Production throughput is determined by the number of similar stations in parallel. A provisioning station is often used before the bank of parallel assembly stations to load the work carrier with the components that will be needed. This permits flexibility in the routing of the carriers to the different stations. Hardware items common to all models are usually stocked at the workstations. The typical operation of the system allows for time variations at a given station resulting from worker skill and effort and from model differences. Instead of the sub assembly moving forward at a fixed rate as in a conventional flow line, the worker takes the time needed to accomplish the work elements required for the particular model currently being processed. When the work is completed, the work carrier is released by the worker to proceed toward the next assembly operation.
Benefits of this flexible assembly system compared to the conventional assembly line include greater worker satisfaction, better-quality product, increased capability to accommodate model variations, and greater ability to cope with problems that require more time rather than stopping the entire production line.

6.7 OTHER WAYS TO IMPROVE THE LINE BALANCE

The line balancing techniques described in Sections 6.5 and 6.6 represent strict and precise procedures for allocating work elements to stations according to a specified cycle time. For most flow line situations, these techniques result in allocations that possess a high degree of balance efficiency. However, the designer of a flow line, either manual or automatic, should not overlook other possible ways for improving the operation of the line. In this section, let us examine some of these possibilities.
Dividing work elements
In Section 6.4, a minimum rational work element was defined as the smallest practical indivisible task, which cannot be subdivided further. In some instances, it may be perfectly reasonable to define certain tasks as minimum rational work elements even though it would be technically possible to further subdivide these elements. For example, it is reasonable to identify the drilling of a hole as a work element, and therefore to perform this work element all at one station. However, if the drilling of a deep hole at one station were to cause a bottleneck situation, it could be argued that the drilling operation should be separated into two steps. The advantage of this would be not only to eliminate the bottleneck but also to increase the tool lives of the drill bits.
          This type of situation is more prevalent on mechanized processing lines, where operations such    as the drilling process described above are performed. In the initial definition of work elements to be done on the line, it may not seem to be as technologically feasible to subdivide such process operations as it is in the case of assembly operations.
Changing work head speeds at automatic stations
This again refers to automated (or semi automated) lines such as machining transfer lines. It may be possible to effect a reduction in the process time of a bottleneck station by increasing its speed or feed rate. There will normally be a penalty associated with such changes in the form of a shorter tool life. This will result in more frequent line stops for tool replacement.
         There is an opposite side to the coin. At a station where there is idle time, the work head feed and speed should probably be reduced to prolong the tool life. This would tend to reduce the frequency of downtime occurrences on the line.
         Through a process of increasing the speed/feed combinations at the stations with long process times, and reducing the speed/feed combinations at stations with idle time, it should be possible to improve the balance on the flow line.
Methods analysis
The customary use of the term methods analysis implies the study of human work activity for possible improvements. Such an analysis seems an obvious requirement for a manual flow line job, since the work elements need to be defined for the job before any line balancing can be performed. In addition, methods analysis can also be used to increase the rate of production at those stations that turn out to be the bottlenecks. The methods analysis may result in better workplace layout, redesigned tooling and fixturing, or improved hand and body motions. All of these improvements are likely to yield a superior balance of work on the manual flow line.
          Analysis of the operations on automated lines may also lead to improvements in work flow and balance. However, attempts to optimize the line balance on automated process lines are usually emphasized during the planning and design stages, since alterations of the finished line are difficult because of the fixed nature of the equipment.
Pre assembly of components
To reduce the total amount of work done on the regular assembly line, certain sub assemblies can be prepared off-line, either by another assembly cell in the plant, or by purchasing them from an outside vendor that specializes in the type of processes required. Although it may seem like simply a means of moving the work from one location to another, there are several good reasons for organizing the assembly operations in this  manner. They include: (1) the required process may be difficult to implement on the regular assembly line; (2) variations in process times (e.g., for adjustments or fitting) for the required assembly operations may result in a longer overall cycle time if done on the regular line; and (3) an assembly cell set up in the plant or a vendor with certain special capabilities to perform the work may be able to achieve higher quality.
Inventory buffers between stations
The justification for using storage buffers on automated now lines was discussed in Section 5.4. On manual flow lines, storage buffers can also be of benefit. Their principal use is to smooth the flow of work, which might otherwise be disrupted by worker process time variability. Although the line balancing techniques assume that process times are constant, any human activity (and most other physical processes, for that matter) is characterized by random variations. These variations are manifested in process time differences from cycle to cycle. The buffer stocks between workstations help to level these differences.
Parallel stations
One of the restrictions implicit in the previous heuristic methods is that the stations must be arranged sequentially. If this restriction can be disregarded, it allows the use of parallel stations where bottlenecks previously existed. To illustrate, suppose that a five-station line had station process times of I min at all but the fifth workstation. At this station the process time was 2 min. With the stations arranged in series, the output rate would be limited by the 2-min process time of the fifth station to R_c = 30 units/h. However, if two stations were arranged in parallel at the fifth station position, the output could be increased to R_c = 60 units/h. Each of the parallel stations would have a production rate of 0.5 unit/min, but since there are two of them, their effective output would be 1 unit/min. Most problems are not as easy at this.
EXAMPLE 6.6
Consider the sample problem (Example 6.1) we have been using to illustrate the various line balancing techniques. The total work content time is T_wc = 4.0 min. Therefore, with a cycle time of  T_c = 1.0 min, the theoretical minimum number of workstations needed should be four. However, none of the methods discussed in Sections 6.5 or 6.6 was able to achieve a solution with less than five stations.
           By utilizing a configuration with parallel stations, it is possible to achieve a perfectly balanced solution with four stations. The allocation of elements is listed in Table 6.13. Stations 1 and 2 both have the same work elements: 1, 2, 3, 4, and 8, whose total process time is 2.0 min. Since there are two stations, however, the effective output rate of the parallel arrangement is i unit/min. Stations 3 and 4 each have process times of I min, so the desired line cycle time of  T_c = 1.0 min is achieved. The solution is illustrated in Figure 6.6.
         There is no formalized procedure for developing a solution that utilizes parallel stations such as the above. Rather, a certain ingenuity and flexibility of mind are required in order for the analyst to perceive that the traditional approaches can be improved upon.
         The use of parallel stations in a manual flow line is easily accomplished because of the inherent flexibility of the human operator. In an automated line it is necessary to incorporate a switching device in the work part transfer mechanism which will alternate work units between the two parallel stations.

6.6 COMPUTERIZED LINE BALANCING METHODS

The three methods described in the preceding section are generally carried out manually. This does not preclude their implementation on the digital computer. In fact, computer programs have been developed based on several of the heuristic approaches. However, the use of the computer allows a more complete enumeration of the possible solutions to a line balancing problem than is practical with a manual solution method. Accordingly, the computer line balancing algorithms are normally structured to explore a wide range of alternative allocations of elements to workstations. In this section, we discuss some of the techniques for solving large-scale line balancing problems based on the use of the computer. The first of these, COMSOAL, is the only one for which we will detail the procedure.
Comsoal
This acronym stands for Computer Method of Sequencing Operations for Assembly Lines. It is a method developed at Chrysler Corporation and reported by Arcus in 1966 [1]. Although it was not the first computerized line balancing program to be developed, it seems to have attracted considerably more attention than those which preceded it. The procedure is to iterate through a sequence of alternative solutions and keep the best one. Let us outline the basic algorithm of COMSOAL and proceed to discuss it with regard to our sample problem.

PROCEDURE AND EXAMPLE 6.5
Step 1.   Construct list A, showing all work elements in one column and the total number of elements that immediately precede each element in an adjacent column. This is illustrated in Table 6.8. Note that these types of data would be quite easy to compile and manipulate by the computer.
Step 2.   Construct list B (Table 6.9), showing all elements from list A that have no immediate predecessors.
Step 3.    Select at random one of the elements from list B. The computer would be programmed to perform this random selection process. The only constraint is that the element selected must not cause the cycle time T_c to be exceeded.
Step 4.     Eliminate the element selected in step 3 from lists A and B and update both lists if necessary. Updating may be needed because the selected element was probably an immediate predecessor for some other elements(s). Hence, there may be changes in the number of immediate predecessors for certain elements in list A; and there may now be some new elements having nc immediate predecessors that should be added to list B. To illustrate, suppose in step 3 that element 1 is chosen at random for entry into the first workstation. This would mean that element 3 nc longer has any immediate predecessors. Tables 6.10 and 6.11 show the updated lists A and B, respectively.

Step 5.    Again select one of the elements from list B which is feasible for cycle time.
Step 6.    Repeat steps 4 and 5 until all elements have been allocated to stations within the T_c constraint. One possible solution to the problem is shown in Table 6.12. The balance delay is again d = 20%, the same efficiency as obtained with the largest candidate rule and the Kilbridge and Wester method.
Step 7.     Retain the current solution and repeat steps 1 through 6 to attempt to determine an improved solution. If an improved solution is obtained, it should be retained.

The steps involved in the COMSOAL algorithm represent an uncomplicated data manipulation procedure. It is therefore ideally suited to computer programming. Although there is much iteration in the algorithm, this is of minor consequence because of the speed with which the computer is capable of performing the iterations.
CALB
During the 1970s, the Advanced Manufacturing Methods Program (AMM) of the IIT Research Institute was the nucleus for research in line balancing methodology [8]. In 1968, this group introduced a computer package called CALB (for Computer Assembly Line Balancing or Computer-Aided Line Balancing), which has more or less become the industry standard. Its applications have included a variety of assembled products, including automobiles and trucks, electronic equipment, appliances, military hardware, and others.
CALB can be used for both single-model and mixed-model lines. For the single-model case, the data required to use the program include the identification of each work element T_e for each element, the predecessors, and other constraints that may apply to the line. Also needed to balance the line is information on minimum and maximum allowable time per workstation (in other words, cycle time data). The CALB program starts by sorting the elements according to their T_e and precedence requirements. Based on this sort, elements are assigned to stations so as to satisfy the minimum and maximum allowable station times. Line balancing solutions with less than 2% idle time have been described as common[11].

To use CALB on mixed-model lines, additional data are required such as the production requirements per shift for each model to be nin on the line, and a definition of relative elements usage per model. The solutions obtained by CALB are described as being nearly optimum.

ALPACA
This computer system was developed by one of the major users of assembly flow lines, General Motors [12]. The acronym represents “Assembly Line Planning and Control Activity.” It was first implemented in 1967, but improvements in computer hardware since that time have reduced the cost of using the package to 10% of the original usage cost. ALPACA is described as an interactive line balancing system in which the user can transfer work from one station to another along the flow line and immediately assess the relative efficiency of the change. One of the complex problems facing the automotive industry is the proliferation of car models and options. ALPACA was designed to cope with the complications on the assembly line that arise from this problem. The system user can quickly determine what changes in work element assignments should be made to maintain a reasonable line balance for the ever-changing product flow.

6.5 METHODS OF LINE BALANCING

In this section we consider several methods for solving the line balancing problem by hand, using Example 6.1 for purposes of illustration. These methods are heuristic approaches, meaning that they are based on logic and common sense rather than on mathematical proof. None of the methods guarantees an optimal solution, but they are likely to result in good solutions which approach the true optimum. The manual methods to be presented are :
1. Largest-candidate rule
2. Kilbridge and Wester’s method
3. Ranked positional weights method
In Section 6.6 we consider some computer procedures for solving the line balancing problem.
Largest-candidate rule
This is the easiest method to understand. The work elements are selected for assignment to stations simply on the basis of the size of their T_e values. The steps used in solving the line balancing problem are listed below, followed by Example 6.2, which is the application of these steps to Example 6.1.
PROCEDURE
Step 1. List all elements in descending order of T_e value, largest T_e at the top of the list.
Step 2. To assign elements to the first workstation, start at the top of the list and work down, selecting the first feasible element for placement at the station. A feasible element is one that satisfies the precedence requirements and does not cause the sum of the T_e values at the station to exceed the cycle time T_c.
Step 3. Continue the process of assigning work elements to the station as in step 2 until no further elements can be added without exceeding T_c.
Step 4. Repeat steps 2 and 3 for the other stations in the line until all the elements have been assigned.
One comment should be made which applies not only to the largest-candidate rule but to the other methods as well. Starting with a given T_c value, it is not usually clear how many stations will be required on the flow line. Of course, the most desirable number of stations is that which satisfies Eq. (6.10). However, the practical realities of the line balancing problem may not permit the realization of this number.
EXAMPLE 6.2
The work elements of Example 6.1 are listed in Table 6.2 in the manner prescribed by step 1. Also listed are the immediate predecessors for each element. This is of value in determining feasibility of elements that are candidates for assignment to a given station.
           Following step 2, we start at the top of the list and search for feasible work elements. Element 3 is not feasible because its immediate predecessor is element I, which has not yet been assigned, The first feasible element encountered is element 2. It is therefoæ assigned to station 1. We then start the search over again from the top of the list. Steps 2 and 3 result in the assignment of elements 2, 5, 1, and 4 to station 1. The total of their element times is 1.00 min. Hence, T_s1 = 1.0, which equals T_c, and station 1 is filled. Continuing the procedure for the remaining stations results in the allocation shown in Table 6.3. There are five stations, and the balance delay for this assignment is
The solution is illustrated in Figure 6.4. The largest-candidate rule provides an approach that is appropriate for only simpler line balancing problems. More sophisticated techniques are required for more complex problems.
Kilbridge and Wester’s method
This technique has received a good deal of attention in the literature since its introduction in 1961 {7]. The technique has been applied to several rather complicated line balancing problems with apparently good success [11]. It is a heuristic procedure which selects work elements for assignment to stations according to their position in the precedence diagram. The elements at the front of the diagram are selected first for entry into the solution. This overcomes one of the difficulties with the largest candidate rule, with which elements at the end of the precedence diagram might be the first candidates to be considered, simply because their T, values are large.
We demonstrate Kilbridge and Wester’s method on our sample problem. However, our problem is elementary enough that many of the difficulties which the procedure is designed to solve are missing. The interested reader is invited to consult the references, especially [2], 17], or (11], which apply the Kilbridge and Wester procedure to several more realistic problems.
PROCEDURE AND EXAMPLE 6.3
It will be convenient to discuss the method with reference to our sample problem.
Step 1. Constraint the precedence diagram so that nodes representing work elements of identical precedence are arranged vertically in columns. This is illustrated in Figure 6.5. Elements 1 and 2 appear in column I, elements 3, 4, and 5 are in column II, and so on. Note that element 5 could be located in either column II or III without disrupting precedence constraints.
Step 2. List the elements in order of their columns, column I at the top of the list. If an element can be located in more than one column, list all the columns by the element to show the transferability of the element. This step is presented for the problem in Table 6.4. The table also shows the T_c value for each element and the sum of the T_e values for each column.
Step 3. To assign elements to workstations, start with the column I elements. Continue the assignment procedure in order of column number until the cycle time is reached. T_c in our sample problem is 1.0 min. The sum of the T_e values for the columns is helpful because we can see how much of the cycle time is contained in each column. The total time of the elements in column I is 0.6 min, so all of the first-column elements can be entered at station 1. We immediately see that the column II elements cannot all fit at station 1. To select which elements from column II to assign, we must choose those which can still be entered without exceeding T_c. Immediately, element 3 is discarded from consideration since T_e3 = 0.7 min. When added to the column I elements, T_s would exceed 1.0 min. Accordingly, elements 4 and 5 are added to station 1 to make the total process time at that station equal to T_c. Unlike the largest-candidate rule, we need not   concern ourselves with precedence requirements, since this is automatically taken care of by ordering the elements according to columns.
            To begin on the second station, element 3 from column II would be entered first. The column II elements would be considered next. Element 6 is the only one that can be entered.
            The assignment process continues in this fashion until all elements have been allocated. Table 6.5 shows the line balancing solution yielded by the Kilbridge and Wester method. Since five stations are required, the balance delay is again equal to 20%, the same as that provided by the largest-candidate rule.  However, note that the work elements which make up the five stations are not the  same as those in Table 6.3. Also, for stations that do have the same elements, the sequence in which the elements are assigned is not necessarily identical. Station 1 illustrates this difference.
         In general, the Kilbridge and Wester method will provide a superior line balancing solution when compared with the largest-candidate rule. However, this is not always true, as demonstrated by our sample problem.
Ranked positional weights method
The ranked positional weights procedure was introduced by Helgeson and Birnie in 1961 [6]. In a sense, it combines the strategies of the largest-candidate rule and Kilbridge and Wester’s method. A ranked positional weight value (call it the RPW for short) is computed for each element. The RPW takes account of both the T_e value of the element and its position in the precedence diagram. Then, the elements are assigned to work stations in the general order of their RPW values.
PROCEDURE
Step 1. Calculate the RPW for each element by summing the element’s T_e together with the T_e values for all the elements that follow it in the arrow chain of the precedence diagram.
Step 2. List the elements in the order of their RPW, largest RPW at the top of the list. For convenience, include the T_e value and immediate predecessors for each element.
Step 3. Assign elements to stations according to RPW, avoiding precedence constraint and time-cycle violations.
EXAMPLE 6.4
Applying the RPW method to our example problem, we first compute a ranked positional weight value for each element. For element I, the elements that follow it in the arrow chain (see Figure 6.3) are 3, 4, 6, 7, 8, 9. 10, I1, and 12. The RPW for element I would be the sum of the T_e‘s for all these elements, plus T_e for element 1. This RPW value is 3.30. The reader can see that the trend will be toward lower values of RPW as we get closer to the end of the precedence diagram.
           Table 6.6 lists the work elements according to RPW. We begin the assignment process by considering elements at the top of the list and working downward. Each time an element is entered into solution,   we go back to the top of the list. The reader should follow through the solution in Table 6.7 to verify the order in which the work elements are assigned.
In the RPW line balance, the number of stations required is five, as before, but the maximum station process time is 0.92 min at number 3. Accordingly, the line could be operated at a cycle time of T_e   = 0.92 rather than 1.0 min. This would, of course, be beneficial, since the production rate would be increased to R_c =   1.075 units/min. The corresponding balance delay is
The RPW solution represents a more efficient assignment of work elements to stations than either of the two preceding solutions. However, it should be noted that we have accepted a cycle time different from that which was originally specified for the problem. If the problem were reworked with T_c  = 0.92 min using the largest-candidate rule or Kilbridge and Wester’s method, it might be possible to duplicate the efficiency provided by the RPW method.
           For large balancing problems, involving perhaps several hundred work elements, these manual methods of solution become awkward. A number of computer programs have been developed to deal witii these larger assembly line cases. In the following section we survey some of these computerized approaches.

6.4 THE LINE BALANCING PROBLEM

In flow line production there are many separate and distinct processing and assembly operations to be performed on the product. Invariably, the sequence of processing or assembly steps is restricted, at least to some extent, in terms of the order in which the operations can be carried out. For example, a threaded hole must be drilled before it can be tapped. In mechanical fastening, the washer must be placed over the bolt before the nut can be turned and tightened. These restrictions are called precedence constraints in the language of line balancing. It is generally the case that the product must be manufactured at some specified production rate in order to satisfy demand for the product. Whether we are concerned with performing these processes and assembly operations on automatic machines or manual How lines, it is desirable to design the line so as to satisfy all of the foregoing specifications as efficiently as possible.
The line balancing problem is to arrange the individual processing and assembly tasks at the workstations so that the total time required at each workstation is approximately the same. If the work elements can be grouped so that all the station times are exactly equal, we have perfect balance on the line and we can expect the production to flow smoothly. In most practical situations it is very difficult to achieve perfect balance. When the workstation times are unequal, the slowest station determines the overall production rate of the line.
In order to discuss the terminology and relationships in line balancing, we shall refer to the following example. Later, when discussing the various solution techniques, we shall apply the techniques to this problem.
EXAMPLE 6.1
A new small electrical appliance is to be assembled on a production flow line. The total job of assembling the product has been divided into minimum rational work elements. The industrial engineering department has developed time standards based on previous similar jobs. This information is given in Table 6.1. In the right-hand column are the immediate predecessors for each element as determined by precedence requirements. Production demand will be 120,000 units/yr. At 50 weeks/yr and 40 h/week, this reduces to an output from the line of 60 units/h or 1 unit/min.
Terminology
Let us define the following terms in line balancing. Some of the terms should be familiar to the reader from Chapters 4 and 5, but we want to give very specific meanings to these terms for our purposes in this chapter.

MINIMUM RATIONAL WORK ELEMENT. In order to spread the job to be done on the line among its stations, the job must be divided into its component tasks. The minimum rational work elements are the smallest practical indivisible tasks into which the job can be divided. These work elements cannot be subdivided further. For example, the drilling of a hole would normally be considered as a minimum rational work element. In manual assembly, when two components are fastened together with a screw and nut, it would be reasonable for these activities to be taken together. Hence, this assembly task would constitute a minimum rational work element. We can symbolize the time required to carry out this minimum rational work element as T_ej, where j is used to identify the element out of the n_e elements that make up the total work or job. For instance, the element time, T_ej, for element 1 in Example 6.1 is 0.2 min.
The time T_ej of a work element is considered a constant rather than a variable. An automatic work head most closely fits this assumption, although the processing time could probably be altered by making adjustments in the station. In a manual operation, the time required to perform a work element will, in fact, vary from cycle to cycle.
Another assumption implicit in the use of T_e values is that they are additive. The time to perform two work elements is the sum of the times of the individual elements. In practice, this might not be true. It might be that some economy of motion could be achieved by combining two work elements at one station, thus violating the additivity assumption.
TOTAL WORK CONTENT. This is the aggregate of all the work elements to be done on the line. Let T_wc be the time required for the total work content. Hence,
For the example, T_wc = 4.00 min.
WORKSTATION PROCESS TIME. A work station is a location along the flow line where work is performed, either manually or by some automatic device. The work performed at the station consists of one or more of the individual work elements and the time required is the sum of the times of the work elements done at the station. We use T_si to indicate the process time at station i of an n-station line. It should be clear that the sum of the station process times should equal the sum of the work element times.
         CYCLE TIME. This is the ideal or theoretical cycle time of the flow line, which is the time interval between parts coming off the line. The design value of T_c would be specified according to the required production rate to be achieved by the flow line Allowing for downtime on the line, the value of T_c must meet the following requirement :
where E is the line efficiency as defined in Chapter 5, and R_p the required production rate. As we observed in Chapter 5, the line efficiency of an automated line will be somewhat less than 100%. For a manual line, where mechanical malfunctions are less likely, the efficiency will be closer to 100%.
In Example 6.1, the required production rate is 60 units/h or I unit/min. At a line efficiency of 100%, the value of T_c would be 1.0 min. At efficiencies less than 100%, the ideal cycle time must be reduced (or what is the same thing, the ideal production rate R_c must be increased) to compensate for the downtime.
The minimum possible value of T_c is established by the bottleneck station, the one with the largest value of T_si. That is,
If T_c  =  max T_si, there will be idle time at all stations whose T_s values are less than T_c.
Finally, since the station times are comprised of element times,
This equation states the obvious: that the cycle time must be greater than or equal to any of the element times.
In Chapter 5 we defined the ideal cycle time to include the transfer time. In Eqs. (6.5) through (6.7), and in the remainder of this chapter, we assume that the transfer time is negligible. If this is not true, a correction must be made in the value of T_c used in Eqs. (6.6) and (6.7) to allow for parts transfer time.
PRECEDENCE CONSTRAINTS. These are also referred to as “technological sequencing requirements.” The order in which the work elements can be accomplished is limited, at least to some extent. In Example 6.1, the switch must be mounted onto the motor bracket before the cover of the appliance can be attached. The right-hand column in Table 6.1 gives a complete listing of the precedence constraints for assembling the hypothetical electrical appliance. In nearly every processing or assembly job, there are precedence requirements that restrict the sequence in which the job can be accomplished.
In addition to the precedence constraints described above, there may be other types of constraints on the line balancing solution. These concern the restrictions on the arrangement of the stations rather than the sequence of work elements. The first is called a zoning constraint. A zoning constraint may be either a positive constraint or a negative constraint. A positive zoning constraint means that certain work elements should be placed near each other, preferably at the same workstation. For example, all the spray-painting elements should be performed together since a special semi enclosed workstation has to be utilized. A negative zoning constraint indicates that work elements might interfere with one another and should therefore not be located in close proximity. As an illustration, a work element requiring fine adjustments or delicate coordination should not be located near a station characterized by loud noises and heavy vibrations.
Another constraint on the arrangement of workstations is called a position constraint. This would be encountered in the assembly of large products such as automobiles or major appliances. The product is too large for one worker to perform work on both sides. Therefore, for the sake of facilitating the work, operators are located on both sides of the flow line. This type of situation is referred to as a position constraint.
In the example there are no zoning constraints or position constraints Liven. The line balancing methods presented in Section 6.5 are not equipped to deal with these constraints conveniently. However, in real-life situations, they may constitute a significant consideration in the design of the flow line.
           PRECEDENCE DIAGRAM. This is a graphical representation of the sequence of work elements as defined by the precedence constraints. It is customary to use nodes to symbolize the work elements, with arrows connecting the nodes to indicate the order in which the elements must be performed. Elements that must be done first appear as nodes at the left of the diagram. Then the sequence of processing and/or assembly progresses to the right. The precedence diagram for Example 6.1 is illustrated in Figure 6.3. The element times are recorded above each node for convenience.
BALANCING DELAY.  Sometimes also called balancing loss, this is a measure of the line inefficiency which results from idle time due to imperfect allocation of work among stations. It is symbolized as d and can be computed for the flow line as follows :
The balance delay is often expressed as a percent rather than as a decimal fraction in Eq. (6.8).
The balance delay should not be confused with the proportion downtime, D, of an automated flow line, as defined by Eq. (5.6). D is a measure of the inefficiency that results from line stops. The balance delay measures the inefficiency from imperfect line balancing.
Considering the data given in Example 6.1, the total work content T_wc  = 4.00 min. We shall assume that T_c  = 1.0 min. If it were possible to achieve perfect balance with n  = 4 workstations, the balance delay would be, according to Eq. (6.8),
If the line could only be balanced with n = 5 stations for the 1.0-min cycle, the balance delay would be
Both of these solutions provide the same theoretical production rate. However, the second solution is less efficient because an additional workstation, and therefore an additional assembly operator, is required. One possible way to improve the efficiency of the five station line is to decrease the cycle time T_c. To illustrate, suppose that the line could be balanced at a cycle time of T_c = 0.80 min. The corresponding measure of inefficiency would be
This solution (if it were possible) would yield a perfect balance. Although five workstations are required, the theoretical production rate would be R_c = 1.25 units/min, an increase over the production rate capability of the four-station line. The reader can readily perceive that there are many combinations of n and T_c that will produce a theoretically perfect balance. Each combination will give a different production rate. In general, the balance delay d will be zero for any values n and T_c that satisfy the relationship
Unfortunately, because of precedence constraints and because the particular values of T_ej usually do not permit it, perfect balance might not be achievable for every nT_c combination that equals the total work content time. In other words, the satisfaction of Eq. (6.9) is a necessary condition for perfect balance, but not a sufficient condition.
As indicated by Eq. (6.5), the desired maximum value of T_c is specified by the production rate required of the flow line. Therefore, Eq. (6.9) can be cast in a different form to determine the theoretical minimum number of workstations required to optimize the balance delay for a specified T_c. Since n must be an integer, we can state :
Applying this rule to our example, with T_wc = 4.0 min and T_c = 1.0 min, the minimum n = 4 stations.
In the next section we examine methods that attempt (but do not guarantee) to provide line balancing solutions with minimum balance delay for a given T_c.

6.3 MANUAL ASSEMBLY LINES

Manual assembly lines, or, more generally, manual flow lines, are used in high-production situations where the work to be performed can be divided into small tasks (called work elements) and the tasks assigned to the workstations on the line. One of the key advantages of using manual assembly lines is specialization of labor. By giving each worker a limited set of tasks to do repeatedly, the worker becomes a specialist in those tasks and is able to perform them more quickly and more consistently. A typical assembly line is pictured in Figure 6.1. The general configuration of a manual assembly line is illustrated in figure 6.2.

Transfer of work between workstations
There are two basic ways in which the work (the sub assembly that is being built up) is moved on the line between operator workstations :
1. Non mechanical lines. In this arrangement, no belt or conveyor is used to move the parts between operator workstations. Instead, the parts are passed from station to station by hand. Several problems result from this mode of operation :

• Starving at stations, where the operator has completed his or her work but must wait for parts from the preceding station.
• Blocking of stations, where the operator has completed his or her work but must wait for the next operator to finish the task before passing along the part.

As a result of these problems, the flow of work on a non mechanical line is usually uneven. The cycle times vary, and this contributes to the overall irregularity. Buffer stocks of parts between work stations are often used to smooth out the production flow.
2.   Moving conveyor lines. These flow lines use a moving conveyor (e.g., a moving belt, conveyor, chain-in-the-floor, etc.) to move the sub assemblies between workstations. The transport system can be continuous, intermittent (synchronous), or asynchronous. Continuous transfer is most common in manual assembly lines, although asynchronous transfer is becoming more popular. With the continuously moving conveyor, the following problems can arise :

• Starving can occur as with non mechanical lines.
• Incomplete items are sometimes produced when the operator is unable to finish the current part and the next part travels right by on the conveyor. Blocking does not occur.

Again, buffer stocks are sometimes used to overcome these problems. Also, station overlaps can sometimes be allowed, where the worker is permitted to travel beyond the normal boundaries of the station in order to complete work.
In the moving belt line, it is possible to achieve a higher level of control over the production rate of the line. This is accomplished by means of the feed rate, which refers to the reciprocal of the time interval between work parts on the moving belt. Let f_p, denote this feed rate. It is measured in workpieces per time and depends on two factors : the speed with which the conveyor moves, and the spacing of work parts along the belt. Let V_c equal the conveyor speed (feet per minute or meters per second) and s_p, equal the spacing between parts on the moving conveyor (feet or meters per workpiece). Then the feed rate is determined by

To control the feed rate of the line, raw work parts are launched onto the line at regular intervals. As the parts flow along the line, the operator has a certain time period during which he or she must begin work on each piece. Otherwise, the part will flow past the station. This time period is called the tolerance time T_t. It is determined by the conveyor speed and the length of the workstation. This length we will symbolize by L_s, and it is determined largely by the operator’s reach at the workstation. The tolerance time is therefore defined by

For example, suppose that the desired production rate on a manual flow line with moving conveyor were 60 units/h. This would necessitate a feed rate of 1 part/min. This could be achieved by  a conveyor speed of 0.6 m/min and a part spacing of 0.5 m. (Other combinations of V_c and s_p would also provide the same feed rate.) If the length of each workstation were 1.5 m, the tolerance time available to the operators for each workpiece would be 3 min. It is generally desirable to make the tolerance time large to compensate for worker process time variability.
Model variations
In both non mechanical lines and moving conveyor lines it is highly desirable to assign work to the stations so as to equalize the process or assembly times at the workstations. The problem is sometimes complicated by the fact that the same production line may be called upon to process more than one type of product. This complication gives rise to the identification of three flow line cases (and therefore three different types of line balancing problems).
The three production situations on flow lines are defined according to the product or products to be made on the line. Will the flow line be used exclusively to produce one particular model? Or, will it be used to produce several different models, and if so, how will they be scheduled on the line? There are three cases that can be defined in response to these questions:
1.    Single-model line. This is a specialized line dedicated to the production of a single model or product. The demand rate for the product is great enough that the line is devoted 100% of the time to the production of that product.
2.    Batch-model line. This line is used for the production of two or more models. Each model is produced in batches on the line. The models or products are usually similar in the sense of requiring a similar sequence of processing or assembly operations. It is for this reason that the same line can be used to produce the various models.
3.    Mixed-model lines. This line is also used for the production of two or more models, but the various models are intermixed on the line so that several different models are being produced simultaneously rather than in batches. Automobile and truck assembly lines are examples of this case.
To gain   a better perspective of the three cases, the mader might consider the following. In the case of the batch-model line, if the batch sizes are very large, the batch model line approaches the.case of the single-model line. If the batch sizes become very small (approaching a batch size of 1), the batch-model line approximates to the case of the mixed-model line.
In principle, the three cases can be applied in both manual now lines and automated flow lines. However, in practice, the flexibility of human operators makes the latter two cases more feasible on the manual assembly line. It is anticipated that future automated lines will incorporate quick changeover and programming capabilities within their designs to permit the batch-model, and eventually the mixed-model, concepts to become practicable.
Achieving  a balanced allocation of workload among the stations of the line is a problem in all three cases. The problem is least formidable for the single-model case. For the batch-model line, the balancing problem becomes more difficult; and for the mixed-model case, the problem of line balancing becomes quite complicated.
In this chapter we consider only the single-model line balancing problem, although the same concepts and similar terminology and methodology apply for the batch- and mixed-model cases.

6.2 ASSEMBLY SYSTEMS

There are various methods used in industry to accomplish the assembly processes described above. The methods can be classified as follows :

1. Manual single-stations assembly
2. Manual assembly line
3. Automated assembly system

The manual single-station assembly method consists of a single workplace in which the assembly work is accomplished on the product or some major sub assembly of the product. This method is generally used on a product that is complex and produced in small quantities, sometimes one of a kind. The workplace may utilize one or more workers, depending on the size of the product and the required production rate. Custom-engineered products such as machine tools, industrial equipment, aircraft, ships, and prototype models of large, complex consumer products (e.g., appliances, cars) make use of a single manual station to perform the assembly work on the product.

Manual assembly lines consist of multiple workstations in which the assembly work is accomplished as the product (or sub assembly) is passed from station to station along the line. At each workstation one or more human workers perform a portion of the total assembly work on the product, by adding one or more components to the existing sub assembly. When the product comes off the final station, the work has been completed.

Automated assembly systems make use of automated methods at the workstations rather than human beings. As indicated in the chapter introduction, we defer discussion of automated assembly systems until Chapter 7.

6.1 THE ASSEMBLY PROCESS

As defined in Chapter 2, assembly involves the joining together of two or more separate parts to form a new entity. The new entity is called a sub assembly, or an assembly, or some similar name. The processes used to accomplish the assembly of the components can be divided into three major categories :

1. Mechanical fastening
2. Joining methods
3. Adhesive bonding

Mechanical fastening consists of a wide variety of techniques that employ a mechanical action to hold the components together. These techniques include :

• Threaded fasteners. These  are screws, nuts, bolts, and so on. The use of threaded fasteners is very common in industry and has the advantage of allowing the assembly to be taken apart (for repair, maintenance, adjustment, etc.) if necessary. Threaded fasteners are readily used by human assembly workers, but are more difficult for robots and automated systems.

• Rivets, crimping, and other methods. The fastener or one of the components to be assembled is mechanically deformed to retain the mating part(s).
• Press fits. In this assembly method, there is an interference fit between the two parts that are to be mated. For example, a shaft is fitted into a hole in which the shaft diameter is slightly larger than the hole diameter. To mate the two parts, the shaft must be pressed into the hole under high pressure. Once fitted, the parts are not easily separated.
• Snap fits. This method involves a temporary interference of the two parts to be mated which occurs only during assembly. One or both of the parts elastically deform when pressed together to overcome the interference and permit them to snap into place. Once together, the snap fit prevents separation of the two parts. Retainers, C-rings, and snap rings are examples of available commercial hardware in this category. Mating parts can sometimes be designed for assembly by snap fitting without the need for these hardware fasteners.
• Sewing and stitching. These are used to assemble soft, thin materials such as fabrics, cloth, leather, and thin flexible plastics.

The term joining method generally refers to the processes of welding, brazing, and soldering. In these processes, molten metal is used to fuse the two or more components together. The process of welding includes a variety of joining techniques whose common feature is that fusing and melting occur in the metal parts being joined. In some welding operations, filler metal is added to promote the joining action between the parent metals. Some of the welding processes used in industry for assembly include resistance welding, arc welding, friction welding, laser beam welding, and electron beam welding.

Brazing and soldering are joining processes that make use of a filler metal which becomes molten for the joining process, but the metal components themselves do not melt. The distinction between brazing and soldering is usually defined by the melting point of the filler metal used in the processes. In brazing, the melting point of the filler is above 450°C, and in soldering the filler melting point is below 450°C. Because there is no fusing of the parent metals in brazing and soldering, these processes do not create as strong an assembly connection as in welding.

Adhesive bonding involves the use of an adhesive material to join components together. The   use of adhesives is growing rapidly today as an assembly technology in industry, and new adhesives are being developed to satisfy new applications. Adhesives can be classified into two types: thermoplastic and thermosetting. Thermoplastic adhesives are easy to apply but cannot withstand high-temperature applications. The use of thermosetting adhesives (e.g., epoxies) involves a chemical reaction that is brought on by a chemical hardener and/or heat. This assembly process is therefore more complicated than with thermoplastic adhesives, but the resulting bonds are generally stronger and capable of withstanding higher temperatures in service.