Lagrangean relaxation for integer programming

1974 ◽  
pp. 82-114 ◽  
Author(s):  
A. M. Geoffrion
Keyword(s):  
Integer Programming ◽  
Lagrangean Relaxation

AUTOMATIC SCHEDULING OF HYPERMEDIA DOCUMENTS WITH ELASTIC TIMES

2004 ◽  
Vol 14 (01) ◽  
pp. 45-59 ◽  
Author(s):  
MAIRA T. MEDINA ◽  
CELSO C. RIBEIRO ◽  
LUIZ F. G. SOARES
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Lagrangean Relaxation ◽  
Approximate Solutions ◽  
Mixed Integer ◽  
Integer Programming Problem ◽  
Temporal Consistency ◽  
Time Scheduling ◽  
Automatic Scheduling ◽  
Primal Heuristic

The problem of automatic scheduling hypermedia documents consists in finding the optimal starting times and durations of objects to be presented, to ensure spatial and temporal consistency of a presentation while respecting limits on shrinking and stretching the ideal duration of each object. The combinatorial nature of the minimization of the number of objects whose duration is modified makes it the most difficult objective to be tackled by optimization algorithms. We formulate this scheduling problem as a mixed integer programming problem and report some preliminary investigations. We propose an original approach to the minimization of the number of objects which are shrinked or stretched. A simple primal heuristic based on variable fixations along the solution of a sequence of linear relaxations of the mixed integer programming formulation is described. Computational experiments on realistic size problems are reported. The effectiveness of the heuristic in finding good approximate solutions within very small processing times makes of it a quite promising approach to be integrated within existing document formatters to perform compile time scheduling or even run time adjustments. We also discuss results obtained by Lagrangean relaxation and propose a dual heuristic using the modified costs, which consistently improves the solutions found by the primal heuristic.

Penjadwalan Mesin dengan Metode Integer Linear Programming pada PT. XYZ

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Fransiskus Lauson Matondang ◽  
Rosnani Ginting
Keyword(s):  
Integer Programming ◽  
Time Delays ◽  
Parallel Machines ◽  
Research Concept ◽  
Total Settlement ◽  
Approach Method ◽  
Additional Costs ◽  
Maximum Completion Time ◽  
Completion Times ◽  
Better Than

PT XYZ sering mengalami keterlambatan waktu karena dalam setiap keterlambatan yang dilakukan selalu ada penalty yang diberikan kepada perusahaan dan hal ini mengakibatkan tambahan biaya , oleh karena itu hal ini harus dihindari dengan membuat penjadwalan yang efisien, dalam hal ini dilakukanlah perbaikan dengan meminimisasi waktu penyelesaian maksimum Cmax pada mesin paralel yang berpola aliran flowshop (dan tidak boleh dilakukan interupsi yang dilakukan pada pekerjaan yang sedang diproses, untuk melakukan pekerjaan lainnya, satu lintasan hanya memproduksi satu produk dan hanya satu produk juga yang dikerjakan secara langsung. Waktu penyelesaian yang berbeda dari setiap mesin dengan pengerjaannya juga adalah masalah yang dihadapi untuk menjadikan mesin mesin ini sesuai menjadi satu penjadwalan yang terintegrasi dengan metode integer programming yang membuat penjadwalan dengan konsep riset operasi dengan metode pendekatan 0-1 utuk menjadi lebih efisien lagi , dihasilkan minimisasi keterlambatan total penyelesaian order dengan 42,28 menit lebih baik dari sebelumnya.   PT XYZ often experiences time delays because in every delay made there is always a penalty given to the company and this results in additional costs, therefore this must be avoided by making efficient scheduling, in this case repairs are carried out by minimizing the maximum completion time of Cmax on parallel machines that are patterned with flowshop flow (and no interruptions should be carried out on the work being processed, to do other work, one track only produces one product and only one product is directly worked. Different completion times of each machine with the workmanship is also the problem faced to make this machine suitable to be one scheduling integrated with integer programming methods that makes scheduling with the operational research concept with the 0-1 approach method to be more efficient, resulting in minimization of the delay in the total settlement of orders with 42.28 minutes was better than before.

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