1) The document presents a study applying Tabu Search to schedule jobs in a textile manufacturing system in order to minimize maximum lateness on a single machine. 2) An example problem is described with 20 jobs, including processing times and due dates. An initial schedule is generated using the Earliest Due Date dispatching rule. 3) Tabu Search is then applied for 20 iterations to improve the schedule. The results show that Tabu Search is an effective heuristic for job scheduling problems like this one.

1. Scheduling by Applying Tabu Search : A Textile Case Prepared by: Ali Orhan AYDIN

2. Scope of the Presentation To present a study which explains job scheduling example in a textile system by applying Tabu Search

3. Introduction Systems are set of components which are related by some form of interaction, and which act together to achieve some objectives. One of the most important man-made systems is production system . Major aim of the most of the manufacturing and service systems is to make profit. Therefore, they produce goods and services by using scarce resources. To achieve this purpose efficiently use of resources becomes key succession factor. Scheduling promises in helping production systems to pursue this goal.

4. Introduction Scheduling is a series of activities aim of which is to assign jobs and/or resources to men and/or machines in production systems . By performing these activities, it is targeted to minimize production time and costs, by providing information to a production system on what to make, when to make, with which staff, and on which machine .

5. Introduction M any tools and approaches are proposed to achieve a good schedule . Pioneer tool for scheduling and planning is Gantt Chart .

6. Introduction Most basic method for scheduling purposes is to use dispatching rules. SIRO: Service in Random Order ERD: Earliest Release Date First EDD: Earliest Due Date First MS: Minimum Slack First WSPT: Weighted Shortest Processing Time First LPT: Longest Processing Time First SST: Shortest Setup Time First CP: Critical Path LNS: Largest Number of Successors SQNO: Shortest Queue at the Next Operation

7. Introduction T here are also some composite dispatching rule s. ATC: Apparent Tardiness Cost is a rule that combines WSPT and MS . ATCS: Apparent Tardiness Cost with Setups is a rule that combines WSPT, MS and SST . All of these dispatching rules prioritize all the jobs that are waiting for processing on a machine.

8. Introduction To find optimum schedule there are exact optimization methods. If the scheduling problem is inherently easy linear programs can be used to solve them. I nteger program ming B ranch-and-bound methods C utting plane methods S ome hybrid methods

9. Introduction On the other hand, scheduling problems are usually Non-Deterministic Polynomial-Time Hard (NP-Hard) . In some cases, solving NP-Hard problems may take enormous time. Usually, in real life that amount of computer time is not available. Therefore, finding optimal solution is nearly impossible . M any methods proposed to find a good solution to scheduling problems of production systems in a relatively short time . Those solutions are acceptable and feasible solutions that presumably is not far from optimal .

10. Introduction M any methods proposed to find a good solution to scheduling problems of production systems in a relatively short time . In such cases, beam search, local search and global search heuristics can be applied .

11. Introduction Local Search Heuristics Hill-Climbing Min-Conflicts Min-Conflicts-Random-Walk Steepest-Descent-Random-Walk GSAT WalkSat Simulated Annealing Tabu-Search.

12. Introduction Global Search Heuristics Evolutionary algorithms Genetic algorithms Memetic algorithms Population based algorithms. Particle swarm algorithms Ant colony algorithms Bees algorithms

13. Introduction All of these approaches have some advantages and disadvantages. It is a fact that global search heuristics requires more time to achieve acceptable solution. On the other hand, global and local search heuristics give nearly the same results. Therefore, in this paper one of the local search heuristic tabu search is applied in scheduling problem of a textile system.

14. Literature Review: Greedies Among many heuristic algorithms local search algorithms are reviewed in this section. In local search, an initial configuration (valuation of variables) is generated and the algorithm moves from the current configuration to a neighborhood configurations until a solution (decision problems) or a good solution (optimization problems) has been found or the resources available are exhausted. Usually, local search algorithms are called as greedy algorithms; since, they try to reach global maximum or minimum by searching the space locally. Local search algorithms move from solution to solution in the space of candidate solutions (the search space) until a solution deemed optimal is found or a time bound is elapsed.

15. Literature Review: Greedies General Psuedo Code of local-search algorithms

16. Literature Review: Greedies Hill-climbing is probably the most known algorithm of local search. Algorithm of hill-climbing

17. Literature Review: Greedies Psuedo Code of Min-Conflicts

18. Literature Review: Greedies Min-Conflicts-Random-Walk algorithm

19. Literature Review: Greedies Steepest-Descent-Random-Walk algorithm

20. Literature Review: Greedies Tabu Search algorithm

21. Literature Review: Greedies Tabu search is applied in many resource allocation problems like: cell formation problem designing manufacturing cells optimization of Process Plans Parallel Flowshop Scheduling project scheduling flow-shop scheduling job shop scheduling

22. Literature Review: Greedies There are also hybrid algorithms which are developed by combining tabu search and other heuristics to find better solutions to the problems. Tabu Search and Simulated Annealing is combined by Zolfaghari and Liang Tabu Search and Genetic Algorithm is hybridized by Ombuki and Ventresca Tabu and Scatter Search is combined by Blazewicz, Glover, and Kasprzak

23. Literature Review: Greedies Moreover, like it is aimed in this paper, tabu search is used in scheduling jobs in textile manufacturing systems and proved to be efficient. In their paper, Tucci and Rinaldi [31] describes a typical fabric production system and applies tabu search.

24. Applying Tabu Search: A Textile Case Aim of this paper is to apply tabu search in a textile manufacturing industry. Specifically, fabric production is taken under consideration. In such systems, to produce fabric first raw strings are dyed. Afterwards, they are tied to conics and sent to fabric department to be weaved. Final stage is quality control and while controlling fabric, they are rolled on cylinders.

25. Applying Tabu Search: A Textile Case This paper focuses on scheduling jobs in weaving process while trying to minimize maximum lateness on single machine.

26. Applying Tabu Search: A Textile Case Bill-of-Material of such fabric product

27. Applying Tabu Search: A Textile Case As an example, here 20 jobs are described .

28. Applying Tabu Search: A Textile Case Length of ordered fabrics and total processing time of each job.

29. Applying Tabu Search: A Textile Case Due dates of jobs.

30. Applying Tabu Search: A Textile Case In the frame of the given information, initial solution for the problem is obtained by applying dispatching rule Earliest Due Date.

31. Applying Tabu Search: A Textile Case Afterwards, Tabu Search is applied. 20 iterations are performed by using OpenTS open source code in JAVA environment.

32. Conclusion Tabu Search is an effective algorithm to achieve job scheduling objectives like maximum lateness/tardiness minimization. It requires less processing time than global search heuristics. As the job size increase, time requirement also increases to generate a schedule. Therefore, Tabu Search can be suggested to mass production systems; since, they deal with many jobs.

33. Conclusion The study just tried to simply explain the Tabu Search concept. The problem provided is oversimplified. Actual textiles systems deal with much more higher amount of jobs. Because, it is aimed to show how Tabu Search can be used in minimize maximum tardiness problem. In this manner, a good feasible solution but not optimal is found.

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