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A factory has a four workstations assembly line which produces a bluetooth speaker. This production requires twelve assembly operations, respecting some precedence constraints. Table 4 indicates the duration of every task (in minutes) and the list of its immediate predecessors (the abbreviation PCB used in this table stands for ’printed circuit board’). The order of processing of the tasks should respect the precedences that are given in this table and illustrated on the graph of Figure 2. The production manager would like to distribute the tasks among the four workstations, subject to the precedence constraints, in order to balance the line to obtain the shortest possible cycle time, that is, the total time required for assembling a bluetooth speaker. Every task needs to be assigned to a single workstation that has to process it without interruption. Every workstation deals with a single operation at a time. We talk about cycle time because the operations on every workstation will be repeated for every speaker. When a product is finished, the bluetooth speaker at stations 1 to 3 advance by one station, and the assembly of a new speaker is started at the first workstation.

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    $\begingroup$ Please have a look at our policy on homework questions: or.meta.stackexchange.com/questions/229/…. $\endgroup$
    – prubin ♦
    Jan 7 at 22:57
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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Jan 8 at 1:05
  • $\begingroup$ Question: Formulate an integer programming model for the problem. $\endgroup$
    – user11048
    Jan 9 at 19:18
  • $\begingroup$ @user11048 I suggest to be inspired by Manne’s Model "On the Job-Shop Scheduling Problem" elischolar.library.yale.edu/cgi/… in order to formulate precedence constraints and no-simultaneous task on the same station. Stations can be viewed to identical machines which operate in parallel. Identical machines hypothesis permits to simplify the problem. The problem can be formulated such as a job-shop where jobs represent the tasks and machines represent the workstations. $\endgroup$
    – marco tognoli
    Jan 13 at 20:55

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