Slack Based Lower Bound And Heuristic for Permutation Flowshop Models
Slack Based Lower Bound And Heuristic for Permutation Flowshop Models
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If the tour contains arcs (n+lj) and (j'. N+l) then jobs j and j' are the first and last jobs in the sequence. and if it contains arc (p, q), for p, q < n, then job q follows job p. Since the makespan of an\ job sequence (for NIS/NW systems) is the interval time on machine 1 plus the processing time for the last job on machines 2 through n, the length of the corresponding traveling salesman tour plus the total processing time TPj for all jobs on machine I equals the makespan. Minimizing the length of the traveling salesman tour, therefore, solves the NIS/NW/M model optimally. Instead of solving the equivalent TSP optimally, we apply the following assignment- patching (AF) heuristic. We can formulate the TSP as an integer program using the binar\ sequencing variables Y^: for all i, j = 1, ... , n+1, i *]. Y- is 1 if job i precedes job j. And otherwise. The formulation has assignment constraints (to assign each node to one position in the sequence, and one node to each of the n positions) and subtour breaking constraints (Dantzig, Fulkerson, and Johnson [1954]).
What to read after Slack Based Lower Bound And Heuristic for Permutation Flowshop Models?
You can find similar books in the "Read Also" column, or choose other free books by Anantaram Balakrishnan to read online
To quickly assess the difficulty of the text, read a short excerpt:
If the tour contains arcs (n+lj) and (j'. N+l) then jobs j and j' are the first and last jobs in the sequence. and if it contains arc (p, q), for p, q < n, then job q follows job p. Since the makespan of an\ job sequence (for NIS/NW systems) is the interval time on machine 1 plus the processing time for the last job on machines 2 through n, the length of the corresponding traveling salesman tour plus the total processing time TPj for all jobs on machine I equals the makespan. Minimizing the length of the traveling salesman tour, therefore, solves the NIS/NW/M model optimally. Instead of solving the equivalent TSP optimally, we apply the following assignment- patching (AF) heuristic. We can formulate the TSP as an integer program using the binar\ sequencing variables Y^: for all i, j = 1, ... , n+1, i *]. Y- is 1 if job i precedes job j. And otherwise. The formulation has assignment constraints (to assign each node to one position in the sequence, and one node to each of the n positions) and subtour breaking constraints (Dantzig, Fulkerson, and Johnson [1954]).
What to read after Slack Based Lower Bound And Heuristic for Permutation Flowshop Models?
You can find similar books in the "Read Also" column, or choose other free books by Anantaram Balakrishnan to read online
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