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By W. Grzechca

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When is negative or zero for all the tasks in existing , open a new station and = is restored for . 9. Repeat steps 1 to 8 until the assignment of all tasks. 10. Generate all feasible solutions. 11. Check the solutions with predefined station numbers. If the solutions are not feasible, repeat the above steps with = + 1 and so on until the desired number of stations are met. 12. When a number of feasible solutions are achieved, store finally updated as the cycle time. Store and return the workstation based solutions with the station assignment information for next stage.

Task Immediate predecessors 1 2 3 4 5 6 7 8 9 10 11 - - - 1, 2 3 2, 5 4 6 7 8 9 Table 3. Resulting precedence relations by considering rule NT for selecting subgraphs. Then, by applying rule RPW for selecting the next task to be assigned, the solution presented in Table 4 is obtained. Table 4 includes the number of required workstations m, the tasks assigned to each workstation, and the corresponding workstation time wt. m=6 Tasks wt I 2, 1 11 II 3 17 workstation III IV 4, 5 6, 7 16 16 V 8, 10 15 VI 9, 11 15 Table 4.

2009)) and random choice assignment. Basically, these rules are determined by considering the cycle time and task precedence relations and by measuring tasks processing times. The following notation is considered: n Number of tasks ct Cycle time Upper bound on the number of workstations mmax Duration of task i when processed through route r (i = 1,…,n ; r Ri) tir Pir Set of immediate predecessors of task i, if processed through route r (i=1,…,n ; rRi) Set of all successors of task i, if it is processed through route r (i=1,…,n; r Ri) Sir Once the set of selected routes SR is known, the following values can be defined: sub(i) Subgraph chosen for task i (  i  AVT ); in this way it is possible to know the duration of task i (ti,sub(i)).

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