Job shop scheduling

A standard continuous-time job-shop scheduling formulation [3] can be used to model the basic aspects of the production decisions, such as sequencing and assignment of jobs. Here, the key of the mathematical solution is to capture the durations of each processing step and to relate it to the amounts of material. Therefore, only a top-down approach will be presented to illustrate some main principles of the model. 

A recent and very promising application of the reachability analysis of TA is scheduling. This development, however, required the introduction of the notion of cost. In contrast to the verification of whether a behavior fulfills a specification or not, costs introduce a quantitative measure to evaluate the individual behaviors. Successful applications of priced TA [15, 16] by using the standard and a special version of Uppaal are documented in [17-19]. The first application to deterministic job-shop scheduling was published by Abdeddaim [20] and Abdeddaim and Maler [21], In order to further motivate the use of TA, the next section shows how the schedule in Figure 10.2 and the plant on which the operations are scheduled naturally translate into a set of timed automata. 

Abdeddaim, Y. and Maler, O. (2001) Job-shop scheduling using timed automata. Computer-Aided Verification (CAV) (eds G. Berry and H. Comon), vol. 2102 of LNCS, Springer, Berlin, pp. 478-492. 

S. (2004a) Job-Shop Scheduling by Combining Reachability Analysis with Linear Programming. Proceedings of the IFAC... 

These combinatorial problems, and many others as well, have a finite number of feasible solutions, a number that increases rapidly with problem size. In a job-shop scheduling problem, the size is measured by the number of jobs. In a traveling salesman problem, it is measured by the number of arcs or nodes in the graph. For a particular problem type and size, each distinct set of problem data defines an instance of the problem. In a traveling salesman problem, the data are the travel times between cities. In a job sequencing problem the data are the processing and set-up times, the due dates, and the penalty costs. 

Y. Abdeddaim and O. Maler, 2001, Job-shop scheduling using timed automata. 

As mentioned above, Cho and Wysk (1993) utilized the multilayer perceptron to take the place of the knowledge-based system in selecting candidate scheduling rules. In their proposed framework, the neural network will output a goodness index for each rule based on the system attributes and a performance measure. Sim et al. (1994) used an expert neural network for the job shop scheduling problem. In their approach, an expert system will activate one of 16 subnetworks based on whether the attribute corresponding to the node (scheduling rules, arrival rate factor, and criterion) is applicable to the job under consideration. Then the job with the smallest output value wiU be selected to process. 

A number of approaches have been utihzed in the application of genetic eilgorithms (GA) to job shop scheduling problems (Davis 1985 Goldberg and Lingle 1985 Starkweather et til. 1992) ... 

Heuristic genetic algorithms have been applied to job shop scheduling. In these genetic schemes, problem specific heuristics are incorporated in the recombination operators (such as optimization operators based). 

Davis, L. (1985), Job Shop Scheduling with Genetic Algorithms, in Proceedings of an International Conference on Genetic Algorithms and Their Applications (Carnegie Mellon University), pp. 136— 140. 

Farhoodi, F. (1990), A Knowledge-Based Approach to Dynamic Job-Shop scheduling, International Journal of Computer Integrated Manufacturing, Vol. 3, No. 2, pp. 84—95. 

Foo, Y. S., and Takefuji, Y. (1988a), Stochastic Neural Networks for Solving Job-Shop Scheduling. Part 1 problem representation, in IEEE International Joint Conference on Neural Networks, Vol. 2, pp. 275-282. 

Fox, M. (1983), Constraint-Directed Search A Case Study of Job Shop Scheduling, Ph.D. dissertation, Carnegie Mellon University. 

Zhang, C., Yan, R, and Chang, T. (1991), Solving Job-Shop Scheduling Problem with Priority Using Neural Network, in IEEE International Joint Cor erence on Neural Networks, pp. 1361-1366. 

Zhang, W., and Dietterich, T. (1996), High-Performance Job-Shop Scheduling with a Time-delay TD(() network, Advances in Neural Information Processing Systems, MIT Press, Cambridge, MA, pp. 1025-1030. 

Job Shop Scheduling Sequence a collection of jobs j with steps s = 1,. 5) on processors p to minimize the time to complete all jobs processor sequence for any job is fixed Tj, = duration of step s Pj = processor of step s. 

The job shop has a more general structure than the flow shop in which each job go through multiple processing stages (or machines) in an order that might be different than other jobs. The basic job shop scheduling problem holds the same assumptions that were made for the basic flow shop problem. In addition it is assumed that each job may be processed by a machine at most once, i.e., without recirculation. 

Fayad, C. and Petrovic, S., 2005. A ftizzy genetic algorithm for real-world job shop scheduling. Innovations in Applied Artificial Intelligence, 3533, 524-533. 

Guo, Z.X., Wong, W.K., Leung, S.Y.S., Fan, J.T. and Chan, S.F., 2006. Mathematical model and genetic optimization for the job shop scheduling problem in a mixed- and multi-product assembly environment A case study based on the apparel industry. Computers and Industrial Engineering, 50(3), 202-219. 

Kondakci, S. and Gupta, R., 1991. An interactive approach for a dual conshaint job shop scheduling problem. Computers and Industrial Engineering, 20(3), 293-302. 

Morton, T, and A. Vepsalainen. 1987. Priority Rules and Leadtime Estimation for Job Shop Scheduling with Weighted Tardiness Costs, Management Science 33, 1036-1047. 

In order to provide a real-time response to an order request in an ATO/MTO/CTO environment, a fast procedure is required to allocate material and production resources to a single order in real time. The type of approach required depends on the complexity in production processes and material requirements. For example, at the simplest level, the required procedure can be viewed as one of incrementally grabbing the best available materials and production resources as each order arrives. The problem becomes more complex in the case of a job shop production environment. Here the literature of on-line algorithms for job shop scheduling becomes relevant. 

J. Adams, E. Balas, and D. Zawack. The shifting bottleneck procedure for job shop scheduling. Management Science, 34 391-401, 1988. 

K.R. Baker and J. J. Kanet. Job shop scheduling with modified due dates. Journal of Operations Management, 4(1) 11-23, 1983. 

S. Eilon and LG. Chowdhury. Due dates in job shop scheduling. International Journal of Production Research, 14(2) 223-237,1976. 

S. Eilon and R.M. Hodgson. Job shop scheduling with due dates. International Journal of Production Research, 6(1) 1-13,1967. 

An Ant Colony Optimization aigorithm for Flexible Job shop scheduling probiem... 

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