Precedence diagram, positional weight and line efficiency

Why it matters

A precedence diagram is not a list that puts tasks in order of duration. Each node represents a concrete task, and each arrow represents the requirement that this task be completed before another. If several arrows reach a task, all of their conditions must be met. Branching in the diagram does not by itself prove that tasks can be done at the same time; it shows only that there are options with respect to the required order. To decide at which station tasks will be performed, these relationships are used together with an assignment rule. In this lesson, the relationships are built first, then a candidate is generated using positional weight. Equipment and competency checks are left to the acceptance process learned in the previous lesson; generating a candidate does not mean final approval.

Positional weight is the sum of a task's own time and the times of all unique tasks that must follow it. This value takes into account not only the long task but also how much work lies behind it. Reaching a successor by two different paths does not make it two separate tasks. The same time is counted once in the weight calculation. At the start, only tasks without predecessors can be selected. After each assignment, the eligible tasks are determined again. The highest weight does not override the eligibility condition. A task whose predecessor is not yet finished cannot be selected merely because its weight is large. Likewise, a task that does not fit the remaining time cannot be forced into the station.

A rule of this kind provides a systematic starting point among a large number of possible allocations. Because the same criterion is used at each selection, the decision is traceable; it can be explained why one task was selected before another. On the other hand, a heuristic ordering is not proof that it finds the best solution to every problem. Fewest stations, shortest highest workload and easiest implementation are different goals. An allocation may be good on one of these goals and weaker on another. The result is therefore written together with the objective used and the acceptance conditions. If it matches a lower bound, only what that criterion proves is stated; no general claim of optimality is made for all goals.

Line efficiency and balance loss summarize how the resulting allocation uses the total time capacity. Which cycle time is put in the denominator must be clear. Evaluation with the target cycle time and evaluation with a shorter ideal cycle time can give different results. Waiting is not added to work content to inflate the percentage; loss is not eliminated by reclassification. Assigning the same tasks to different stations can preserve total human work but change the highest workload. In this lesson the progression is from diagram to candidate, and from candidate to numerical comparison. At every stage it is kept in view that the final decision requires verifying resources and safe implementation as well as precedence.

Formula