Line Balancing

Page 109 of the Handbook gives a brief set of definitions and formulas that we will amplify here. Let an operation be a collection of n tasks, numbered i = 1, 2,..., n, each having a processing time t _i. Given the tasks, a line is a collection of N stations, each station performing a subset of the tasks. The line is perfectly balanced if the total processing times are the same at every station, but perfect balancing is not always possible if N > 1.

If the required production rate (operations per shift) is OR and the total of all the processing times is ? t minutes, then at least OR ? t total operating minutes are required per shift. If the shift length is OT minutes, then at least N _min = ( OR ? t)/ OT stations are required if the number of lines is one; if there are to be L lines operating in parallel, then N _min = ( OR ? t)/( OT L). We can hope to find a balance so that the actual number of stations N is not much greater than N _min.

Consider the following set of 9 tasks...