Multiple Stations and Parallel Lines

Given a capacity or production rate requirement, we can meet requirement with a single line with a cycle time, c, or with two parallel lines with a cycle time, 2c, or with three parallel lines with a cycle 3c, and so forth. Line balancing programs have been developed that enable us to use multiple parallel lines. As the number of parallel lines increases, so does the scope of jobs; and finally, we have complete horizontal job enlargement. The point is that alternatives do exist, even with the line organization of work.

In addition to increasing job scope, there are a number of advantages that result from the parallel line multiple station concept. First, from the line balancing point of view, balance may be easier to achieve because the larger cycle time offers a greater likelihood of attaining a good fit with residual idle time. This is particularly true when some of the task times are nearly equal to the single line cycle time. Furthermore, a multiple line design increases the flexibility of operations enormously. Output gradations are available; that is, one can have one, two, three, or more lines operating or not operating and one can work overtime or under time with all of the line combination. There are fewer dependent operations; for example, if there is a difficulty with an operation in line 1, it may not affect line 2. A machine breakdown in line 1 need not stop the operation of line 2.

From human organization viewpoint, the parallel multiple station concept has all the advantages of horizontal job enlargement. Work groups can be smaller and more cohesive. A team spirit may be engendered by competition among line teams on the bases of output, quality, safety, and other dimensions. On the other hand, capital investment is likely to increase with parallel line designs because of the duplication of equipment.

Computerized Line Balancing Techniques:

Practical line balancing problems are relatively large scale, involving up to 1000 tasks and 200 stations. Therefore, the algorithms need to be computerized so that optimal solutions can be generated in a relatively short time. As an example, we will present in the basis Ranked Positional Weight Technique, followed by an improvement by called MALB, a heuristic technique that has computerized. The improvement by Mansoor (1964) went relatively unnoticed until it was computerized for large scale problems by Dar-El (1973). (Dar-El and Mansoor are the same person). MALB is most easily explained by first presenting the basic Ranked Positional Weight Technique.

Ranked Positional Weight Technique for line balancing:

The basis for the assignment of tasks to stations for this rule is to determine weights for each task based on the sum of the time to perform that task plus the performance times of all the tasks that follow it in the precedence chart. The tasks are then listed in descending order of the weights together with corresponding immediate predecessor tasks. Tasks with the largest weights are then assigned to station1, taking account of precedence constraints. When station 1 has assignments that fill the cycle time, then assignments are made to station 2 in the same way, and so on. Successive iterations may be made to determine the minimum cycle time for a given number of stations. This solution will give the most even distribution of work across stations.

An example

Let us assume the balancing problem posed by the precedence diagram. The numbers inside the circles are the task numbers, and those outside are the task performance times in seconds. Below the diagram we have calculated the positional weights, taking advantage of the fact that the weight for a task is its own task time plus the positional weight of the tasks that follow it and are dependent on it. (Any duplication are eliminated). Therefore, hand computing time is reduced by computing positional weights from right to left in the precedence diagram.

Next, consider the range of possible solutions. Note that the largest task time is t = 45 seconds for task 3, and the sum of all task times is 185 seconds. Therefore, the maximum number of stations that we wish to consider is 185 / 45 = 4.1 or 4. We could have, then, 4, 3, 2 or 1 station.

The balance delay graphs for 4, 3 and 2 stations. Balance delay d, is defined as

D = 100(nc – Σti) / nc

n= Number of stations on the line
c= cycle time
ti = Task times
and n, c, and ti are integer numbers.

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