The study indicates that SA consistently gives better results for a number of realistic instances compared with simple heuristics within acceptable computational time. Tan et al develop a SA approach for minimizing tardiness on a single machine in a sequence-dependent setup environment and with a common measure of due-date performance.
SA is used to solve the sequence problem and its performance is compared with random search. The results indicate that the proposed algorithm can find a good solution fairly quickly and can rework schedules frequently to react to variations in the schedule. The fundamental idea of this approach is based on the rescheduling activity of the human scheduler.
By viewing a Gantt chart of a non-optimal schedule, the human scheduler often finds a better schedule by changing its operation sequence. On the basis of this fact a rescheduling procedure of the human scheduler as a deterministic algorithm is used to adopt the SA to avoid local minimum states. The results show the effectiveness of the proposed approach. A simultaneous lot sizing and scheduling algorithm by combining local search with dual re-optimization has been presented by Meyr In this study, the problem of integrating continuous lot sizing and scheduling of several products on a single, capacitated production line is modeled and solved, taking into consideration sequence-dependent setup times.
A dual re-optimization algorithm has been applied to solve a mixed integer- programming problem. A systematic procedure for setting parameters in SA algorithms has been developed by Park et al This method has been presented in order to get good parameter values quickly without much human intervention by using the simplex method for nonlinear programming.
The suggested procedure has been applied for flow shop scheduling and short-term production scheduling problem. The results are compared with the traditional approaches and seem to be promising. It has been successfully applied to obtain optimal or sub-optimal solutions to scheduling, timetabling, traveling sales man problem, and layout optimization. The basic idea of the method, described by Glover et al , is to explore the search space of all feasible solutions by a sequence of moves. A move from one solution to another is the best available.
However, to escape from locally optimal but not globally optimal solutions and to prevent cycling, some moves, at one particular iteration, are classified as forbidden or tabu or taboo.
Tabu moves are based on the short-term and long-term history of the sequence of moves. Figure 2 presents a flow chart of TS algorithm. A simulation-search heuristic procedure based on TS combined with simulation, is presented by Lutz et al Simulation is used to model the manufacturing process and TS is used to guide the search to overcome the problem of being trapped at local optimal solutions. The procedure employs a swap and global search routines. For swap search the procedure identifies good performing buffer profiles and determines maximum output level for any given storage level.
With the global search, the procedure allocates promising neighbors of buffer profiles quickly. The results indicate the capability of the procedure to model a variety of manufacturing processes with variety of scheduling policies and dispatching rules.
An algorithm of finding a minimum makespan in a non-preemptive open shop is presented by Liaw The algorithm is based on TS technique with a neighborhood structure defined using blocks of operations on a critical path. An efficient procedure is also developed for evaluating a neighborhood. The algorithm is tested on randomly generated problems and a set of 60 benchmarks. The study reports that the algorithm finds extremely high-quality solutions for all the test problems in reasonable amount of time and demonstrates the potential of the algorithm to efficiently schedule open shops.
A TS approach to minimize total tardiness for the job shop scheduling problem has been presented by Armentano et al The method uses dispatching rules to obtain an initial solution and searches for new solutions in a neighborhood based on the critical paths of the jobs. Diversification and intensification strategies are suggested. The results show promising effectiveness.
In this model, the problem is formulated as a mathematical program and a heuristic method, based on TS to determine good approximate solutions, is used. The resulted data compared with actual production schedules indicate that the proposed model produce significantly better schedules.
A TS method guided by shifting bottleneck for minimizing the makespan of the job shop scheduling problem is introduced by Pezzella et al The shifting bottleneck procedure is used for generating the initial solution and refinement of the next current solutions. Computational experiments on standard set of problem instances show that, in several cases, the presented approach, in reasonable amount of computer time, yields better results than the considered heuristics.
GAs are applied whose a population set of individuals as solutions is considered. Each individual is characterized by its fitness. The fitness of an individual is measured by associated value of the objective function. The procedure works iteratively, and each iteration is generation. The population of one generation consists of individuals surviving from the previous generation plus the new solutions or children from the previous generation.
The population size usually remains constant from one generation to the next. The children are generated through reproduction and mutation of individuals that were part of the previous generation. At each iterative step a number of different solutions are generated and carried over to the next step. In SA and TS, only a single solution is carried over from one iteration to the next. In genetic algorithms the neighborhood concept is not based on a single solution, but rather on a set of solutions.
The design of the neighborhood of the current population of solutions is based on more general technique than those used in SA and TS.
A new solution can be constructed by combining parents of solution. This process is often referred to as crossover. A genetic algorithm for multi-level, multi-machine lot sizing and scheduling has been presented by Kimms This problem is also solved by mixed-integer programming. The efficiency of GA is due to an encoding of solutions, which uses a two-dimensional matrix representation with non binary entries rather than a simple bit string. Computational results reveal that the proposed GA works amazingly fast and competes with TS.
A GA for scheduling grouped jobs on single machine to minimize the total flow time is presented by Wang et al In GA search, some jobs are combined based on the combinatorial rules of optimality conditions. The numerical results show that the combinatorial performance of the proposed GA depends on combinatorial rules of combination process and not on the number of jobs.
The procedure has potential for practical application in large-scale production systems. Khouja et al develop a GA for solving economic lot size scheduling problem. The problem is formulated using the basic period approach which result in a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced. The results of the GA under different binary representations, crossover methods, and initialization methods are compared to identify the best settings.
The results indicate that for this particular problem, binary representation works better than gray coding, 2-point crossover is best, and an infeasible solution is better than feasible. A GA for planning and scheduling multi-product problem is developed by Ip et al Many parameters are considered in the proposed approach such as earliness, tardiness, lot sizing, and capacity.
The GA is applied in order to achieve the optimal solution. Also the output schedules attained by the proposed procedure indicate good solutions compared with the traditional considered approaches. A GA approach to earliness and tardiness production scheduling and planning problem is introduced by Li et al The proposed method includes lot-size and conflicting issue of capacity balancing.
A large-scale discrete problem, where the restriction of linearity, convexity and differentiability in the cost function, is new one completely relaxed by the presented approach. The simulation process indicates that this new scheduling scheme is an effective and efficient technique to tackle the problem. Kim and Kim introduced an approach using SA and GA for scheduling products with multi-level product structure with the objective of minimizing the weighted sum of tardiness and earliness of the items.
Computational experiments were carried out using randomly generated test problems. The resulted report indicates that some operations should be aggregated into two basic operations, machining and assembly, and the processing units should be aggregated in the manufacturing system into machining shop and assembly shop.
The field goes by many names, such as connectionism; parallel distributed processing, neuro- computing, natural intelligent systems, machine learning algorithm, and artificial neural networks. It is an attempt to simulate within specialized hardware or sophisticated software. This simulation is achieved through multiple layers of simple processing elements called neurons.
Each neuron is linked to a certain of its neighbors with varying coefficients of connectivity that represent the strengths of these connections. Learning is accomplished by adjusting these strengths to cause the overall network to output appropriate results.
A neural network model for solving the lot-size scheduling problem is presented by Gafaar et al The model is applied to material requirement planning problem of lot sizing. Results show that ANN model is capable of solving the lot size problem with notable consistency and reasonable accuracy. A decision support system for the design of flexible manufacturing systems has been developed by Chan et al.
In the proposed system, artificial neural network system, expert system, and fuzzy system have been used. In this model an integrated approach for the automatic design of FMS is reported, which uses simulation and multi-criteria decision-making. The results obtained from the study are promising. A parallel neural network and genetic algorithm are presented for job-shop scheduling problem by Lee et al In this study, a brief review of the classical method of schedule generation, the basics of evolutionary programming and artificial neural networks are introduced and their possible use in the schedule generation process is examined.
Good schedules are achieved compared with some considered heuristics. A new neural network approach to solve the single machine tardiness scheduling problem is presented by Sabuncuoglu et al The approach considers the minimum makespan job shop- scheduling problem. The proposed network combines the characteristics of neural networks and algorithmic approaches. The performance of the network is compared with the existing scheduling algorithms under various experimental conditions.
The study exhibits acceptable results. The proposed approach is prototyped and tested on four different job shop scheduling problems based on problem size, namely; small, medium, large, and a sample problem provided by a company. The comparative results indicate that the proposed approach is consistently better than those of heuristic algorithms used extensively in industry.
A record of each past attempt is stored as a case. The collection of historical cases, the case base, then becomes the model. When a CBR system solves a problem, rather than starting from scratch, it searches its case base for cases whose attributes are similar to the problem it is asked to solve. The CBR system then creates a solution by synthesizing the similar cases and adjusting the final answer for differences between the current situation and the ones described in the cases.
As the case bases grow, the accuracy of the system should improve. A CBR model is presented by Schmidt for production scheduling problem. The model merges CBR with the theory of scheduling to solve production planning and control using an iterative problem-solving framework.
The study reported that the schedules attained by this approach are of acceptable level. A production scheduling system for parallel injection modeling machines in an electrical appliance company has been developed by Lin et al The architecture and data interface of the system is presented.
A Tabu-search with case-based reasoning model has been developed by Grolimund et al for incapacitated and capacitated facility location problems.
The model investigates the use of AI technique for configuring a basic meta-heuristic without any user interface.
A case-based reasoning model has been developed by Dong et al for production scheduling system. The objective of the model is to find a promising sequence for job processing. In this system, a schedule case is represented in the form of ordered tree and each job is represented in the format of attribute- value pairs.
Li et al. Four sources of production disturbances have been identified; incorrect work, machine breakdowns, rework due to quality problem, and rush orders. Martiez et al developed an automatic resource scheduling system ARSS , which is a computer based tool to keep, benchmark, and use customers and resources information to improve the quality of services while improving the productivity of the resources used in a service granting organization. Hamada et al used interdigitation approach, expert systems, and GAs to develop an optimization technique solver for Steel-making scheduling problems.
The approach is based on dividing a problem into several subproblems without losing its original structure and applying the most suitable solving method to each subproblem. A petri net is a graphical and mathematical modeling tool. It consists of places, transitions, and arcs that connect them.
A model for scheduling piecewise constant product flows using a petri-net approach has been presented by Porth et al The model presents manufacturing systems as controllable output petri-nets. The model can generate near optimal schedule of acceptable level. A new extended stochastic high-level evaluation petri-net model is suggested by Yan et al for scheduling and simulation of FMS.
The structural and methodological features of a new optimal planning and dynamic scheduling system for a total plant continues petri-net manufacturing process is presented by Rong et al Hybrid petri-net, a combination of timed continuous petri-net and extended petri-net, is developed to model the process together with static equipment models and expert knowledge.
A heuristic search approach for scheduling FMS with due date based on petri-net state equation has been presented by Jeng et al In the model, the jobwise petri-net is introduced.
N jobs are split into N jobwise nets and then are combined to formulate the state equations where the search algorithm can be implemented. The objective of the model is to minimize weighted tardiness. The Study shows that the resulted solutions are very near to the optimal solution. With beam search only the most promising nodes at level K are selected as nodes to branch from.
The remaining nodes at that level are discarded permanently. The number of nodes retained is the beam width of the search. Lotfi Zadeh pioneered it in approximately Fuzzy sets are actually functions that map a value which might be a member of the set to a number between zero and one indicating its actual degree of membership.
A beam search heuristic approach has beem presented by Sabuncuoglu et al In this model, at any level only the promising nodes are kept for further branching and remaining nodes are prund off. The presented model is used to schedule job shop problem. Both the makespan and mean tardiness are used as the performance measures. The proposed model is compared with other search methods and heuristic search. The study shows that the developed beam search is very competitive and promising tool. A beam search model has been introduced by Sabuncuoglu et al for reactive scheduling in job shop environment.
The study tests scheduling policies under machine breakdowns in a classical job shop system. Also, the effect of system size and type of work allocation on system performance is measured. The performance of the suggested model is measured as a function of tardiness and makespan criteria. Beam search-based algorithm for scheduling flexible manufacturing system has been introduced by Ihsan et al The performance of the algorithm is compared with several machine and vehicle dispatching rules using mean flow time, mean tardiness, and makespan.
The study indicates better performance of the proposed algorithm over the most dispatching rules. A model of local search algorithms for flow shop scheduling with fuzzy due-dates is developed by Ishibuchi et al In this model the due date for each job is given as a fuzzy set.
Therefore, we have a number of jobs j to be manufactured over a number of machines i. The production scheduling problem deals with obtaining the date for each job to enter on each machine Not necessarily physical machines, they may be stages consisting on several machines or labour in a manufacturing process 6. Jobs have to be manufactured in each machine in a certain order known as route during a certain time period known as processing time.
Tomcat Ltd. Three main steps can be distinguished in this process:. The number and type of devices that have been order by each customer This process depends on the number and type of components. The route through the steps is given by the technological process and does not depend on the specific order of the customer 8.
The plant in which Tomcat Ltd. Obviously, a new order cannot start until the worker completes the current order Let us assume that an order cannot overtake another order, i. According to the nature of each order components, type, etc. The objective of the company is to keep the average time to assembly a computer as lowest as possible Or the order of the jobs is not relevant for the final result?
Motherboard Devices 15 10 12 Test 7 5 5 A representation of an specific solution of a scheduling problem in terms of the machines and jobs. Using the data of the Example1, try to represent the sequences [1,2,3] and [3,2,1] by a Gantt chart job1 , job2 , job3 Motherboard Devices 15 10 12 Test 7 5 5.
The environment or framework of a scheduling problem refers to the way the jobs must visit the machines:. The simplest of all machine environments One may reduce the different steps sections in the plant to a single machine Interesting case: bottleneck process, the important issue is scheduling jobs in the bottleneck.
All machines are identical A job can be processed on any machine Generalization of the single machine Special case of the flexible flow shop and flexible job shop. Each job has, in general, a different route to be processed by the machines It is one of the most complex cases. Each job has, in general, a different route to be processed at all stages Each stage has ms machines in parallel It is even more complex than the job shop. Ci,j: Time in which job j is finished in machine I Cj: Time in which the job j is finished in the last machine.
Therefore, one can assign a weight wj to each job representing the relative importance of each job. Scheduling objectives III Due date related objectives I For this kind of problems, we assume that each job j has, in general, a due date dj and a release date rj. The due date represents the commitment of the company with a customer The release date implies the non availability of raw materials from the beginning.
Indicator of the service level However, finishing the order as soon as possible much before the due date is not a good idea. Time after finishing one job and before starting the next one It can be shown that minimising makespan is equivalent to minimising idle time. Open navigation menu. Close suggestions Search Search. User Settings. Skip carousel. Carousel Previous. Carousel Next.
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