Job Shop Scheduling

Abstract – The job-Shop Scheduling problem (JSSP) attracted a lot of researchers from various research disciplines, mainly Operations Research, Management Science, Computer Science, and Manufacture Science for the last 50 years. JSSP is a typical NP-hard problem in the strong sense. Although the literature is full of researches concerning the JSSP, practitioners are not able to get benefit of the majority of these researches because of the assumptions which take the problem very far away from the real life JSSP. The aim of our research is to build a simulation model for the JSSP to be able to relax some of these assumptions to simulate the real life JSSP. We used discrete event simulation as it's suitable for the JSSP. We used Arena simulation software version 14 to build the model on a Dell® Vostro PC (Intel® Core(TM) i5–2400 CPU @ 3.10GHZ with 4 GB RAM).In this paper we will just show the basic model which is able to solve the famous benchmarks for the JSSP to prove that our model is ready for the real life JSSP. In the following papers we will show how to relax some of these assumptions one by one. The computational results for 9 benchmarks of different sizes showed that the proposed model is both effective and efficient. It gave good solutions in reasonable amounts of time.

Abstract: In this paper, a new data-based mechanism has been proposed to solve job shop scheduling problems (JSPs). The proposed method is an intelligent-algorithm-based approach implanted with data- and rule-based scheduling algorithm. The proposed data-based framework is based on decision tree algorithm and rule mining technique to solve the scheduling in job shop with abundant information and massive unforeseen events. A data- and rule- based scheduling system framework for JSP was developed, and then, the knowledge discovery and rule-based adaptive scheduling algorithm were developed. The simulation result of a simplified scheduling problem is presented as a preliminary validation to show the feasibility of the proposed integrated scheduling mechanism. The state-of-the art research on the key technologies of data-based scheduling is introduced together with some related research results of information based or rule based ones. The results show that data- and rule-based scheduling offers better solutions.

Job-Shop Scheduling Problem is the hardest optimization problem. JSSP is referred amongst the class of NP- hard problems” [A Jain S. Meeram, 1998], there is a lot of research on the existing techniques. Large solution space is considered to solve JSSP. For n jobs and m machines the number of possible solutions may be given by to (n!) m .

Applying Shortest processing time (SPT) rule , Unlike flow shop each job has unique route or order to visit machine. In figure 5.2 , there are 3 jobs and 3 machines. Every job has unique path or order to visit machine. In Job Shop Scheduling each job has prespecified path of machine.The JSSP consists of n jobs and m machines. Each job must go through m machines to complete its work. We consider one job consists of m operations. Each operation uses one of m machines to complete one job‘s work for a fixed time interval. Here two jobs (J1,J2) are given to machines (M1,M2). Each job having processing time for particular machine. For eg. Job1 having 7 processing time for machine1,for machine3 it takes 8 units of time and for machine2 it require 10 units of time. Each machine has processing time which is shown in snapshots. This GUI contains the eight main processing steps as load the datasets in jobs, machines along with processing time, number of generation, population, mutation rate, SPT and Genetic algorithm. Gantt chart is a tool to represent result of job shop scheduling. Once one operation is processed on a given machine, it cannot be interrupted before it finishes the job‘s work. The sequence of operations of one job should be predefined and may be different for any job. In general, one job being processed on one machine is considered as one operation noted as Oji (means jth job being processed on ith machine,1 ≤ j ≤ n,1 ≤ i′ ≤ m). The JSSP has n jobs to b processed on m machines.

The initial population is usually chosen at random. But in a combinatorial problem such as job shop scheduling, some constraints such as precedence and resources constraints must be satisfied. In this case, the binary representation is not convenient and chromosome syntax must be found to fit the problem. For these reasons, we have designed a matrix representation of the chromosome, and in order to create and to permit our set of solutions to evolve in a very large domain, we shall use a combination of some methods. We use a combination of the following priority rules. SPT: a high priority for the operation that has the Shortest Processing Time. LPT: a high priority for the operation that has the Longest Processing Time. LM: a high priority for the operation that permits to balance the load of the machine. Accordingly two solutions of the example (table 1) are taken as parent fig. 2 with C max = 11 and fig.3 with C max = 13.

Abstract — This paper present new combinations of dis- patch scheduling for Job Shop Scheduling Problem. The Job Shop Scheduling Problem is one of the NP hard op- timization problems, and it is difficult to obtain the exact optimal solution. Scheduling methods based on the dispatch rule are a set of efficient approximate methods. In this pa- per, by combining several dispatch rules, we have proposed three new rules. The first rule is the rule that combines two simple dispatch rules which are often adopted in actual production systems. The proposed rule gives better result than that of any single dispatch rule. The second rule is the rule that keeps balance of remaining load of all machines. In this rule, the weight is decided in early stage of the sched- ule. It gives good solutions with high probability. The third rule is the rule that predetermines the mixing ratio, which accompanies a sequence of operations. This rule often gives better results than any other dispatch rules.

The Job Shop Scheduling Problem (JSSP) arises in the context of high-performance computing and belongs to the NP-hard combinatorial optimization problems. The purpose of JSSP is to find the order of execution of a set of jobs on a group of machines, subject to certain precedence and resource availability constraints. The objective in this problem is minimizing the makespan that is the time elapsed from the starting time of the first job until the completion time of the last job. In this paper, a novel hybrid algorithm named AntGenSA for solving JSSP is proposed. AntGenSA uses Ant Colony System (ACS), Simulated Annealing (SA), and Genetic Algorithm (GA). To assess the performance of this algorithm, it is executed in a parallel computer, using a set of instances proposed by Fisher-Thompson, Yamada-Nakano, Taillard, Lawrence, and Applegate-Cook. The evaluation of this algorithm was performed mainly by the quality of the solution but the execution time was measuring as well. The experimental results show that the performance of the parallel execution of AntGenSA is highly competitive with the state-of-the-art algorithms.

dibuat. Hal ini berdasar pada kenyataan bahwa begitu banyak parameter yang harus diperhatikan. Karena scheduling, khususnya job shop scheduling, merupakan suatu permasalahan combinatorial optimization yang kompleks maka permasalahan scheduling dapat dikategorikan sebagai permasalahan np-hard, yaitu suatu permasalahan yang pencarian solusinya (waktu komputasinya) akan naik secara eksponensial seiring dengan naiknya ukuran permasalahan secara linier [2]. Untuk itu diperlukan suatu metode yang lebih baik dalam memecahkan permasalahan ini.

Job shop scheduling, in general, contains a set of concurrent and conflicting goals to be satisfied using a finite set of resources. The resources are called machines and the basic tasks are called jobs. Each job is a request for scheduling a set of opera- tions according to a process plan (or referred to as process routing) which specifies the precedence restrictions. The main constraint on jobs and machines is that one machine can process only one operation at a time and operations cannot be interrupted. Usually we denote the general JSSP as nxm, where n is the number of jobs and m is the number of machines. The operation of job i on machine j is denoted by operation (i, j). The prob- lem is to minimize some performance criterion. This paper discusses the most widely used criterion, i.e., the time to completion of the last job to leave the system -- the makespan.

Classical Job Shop Scheduling Problems (JSSP) considers the allocation of n jobs to m different machines or equipment. Each job has to undergo multiple operations in various equipment, with its own set of processing times and routing characteristics. The processing time of each job on an equipment Phj is known as well as the due date for each job Dj.

The job-shop scheduling problem (JSSP) is one of the most difficult non-deterministic polynomial hard combinatorial complexity optimization problems [1, 2]. Since the mid-50s, research on JSSP has continued given its widespread applications in industry, manage- ment, transportation, business, and service sectors. Its history is characterized by the proposal of exact methods, such as branch and bound algorithms [3] and integer programming [4]. Although exact algorithms for very small-size instances of combinatorial optimi- zation problems are guaranteed to find an optimal solution in bounded time, an exact algorithm to solve JSSP in polynomial time is unavailable. Current algorithms are applicable only for small-size instances. Thus, researchers focused on heuristic and meta- heuristic algorithms as approximation methods. These algorithms, namely, memetic algorithm [5], genetic algorithm [6, 7], bee colony optimization [8], ant colony optimization [9], particle swarm optimization [10], artificial immune system [11], electromagnetic- like mechanism [12], chemical reaction optimization [13], DNA computing [14], and others [15–17], are mostly population-based algorithms. These algorithms

Job Shop Scheduling problem (JSSP) is a famous problem in which jobs are assigned to machines at particular times, while trying to minimize the total length of the schedule (Makespan). This characteristic of the problem make it be NP-Hard problem that cannot be solved by using the exact algorithms in polynomial time. So this study used the Differential Evolution (DE) algorithm, one of the approximate algorithms, to solve Job Shop Scheduling problem. Based on our experiment, we could indicate that the results of small and medium size problems using DE approach obtained the optimal solution reliably and effectively.

developed an efficient method based on genetic algorithm to address JSP. The scheduling method based on single genetic algorithm and parallel genetic algorithm was designed. In the scheduling method, the initial population was generated through integrating representation and G&T algorithm, the new genetic operators and selection method were designed to better transmit the temporal relationships in the chromosome, and island model PGA were proposed[14]. Dirk and Christian considered a job shop scheduling problems with release and due-dates, as well as various tardiness objectives. The genetic algorithm can be applied to solve this kind of problem. The heuristic reduction of search space can help the algorithm to find better solution in a shorter computation time [15]. Jose presented a hybrid genetic

Intuitively we expect that a very simple DR may be easy to interpret but is likely to perform poorly in complex decision situations. However, it is desirable that a well performing (effective) DR be interpretable at least in commonly used components, and when these are selected (conditions). In this chapter the job shop investigated is again the ten-machine dy- namic job shop, with the objective of minimising the total weighted tar- diness. The ATC and WCOVERT rules introduced in Section 2.2.3 (see page 42) are very good, small, compact and interpretable dispatching ru- les. These are major reasons that they are used in practice and are excel- lent examples of the rules we are trying to find automatically. Grammar- based GP has been used as a hyper-heuristic for the automatic genera- tion of timetabling heuristics for the exam timetabling problem [4]. The advantages of grammar-based approaches are that it restricts the search space and encodes knowledge of the problem domain. STGP is one form of grammar-based GP. In STGP the grammar is used to prescribe the type system. STGP does not have all the benefits of other forms of grammar- guided GP; online grammar adaption is not possible in STGP. However, grammar-based GP approaches (including STGP) have not been used to improve the interpretability of DRs in dynamic job shop scheduling.

by using branch and bound and simulated annealing approach. We notice that the optimal solution obtained by these two approaches is the same i.e. we get a makespan of 11 hours. In the branch and bound approach, we have to find every possible branching procedure and calculate the lower bound. It takes a long time, as the problem grows larger. For instance, in Example 1, it needs 8 stages to get the optimal schedule by using branch and bound technique. On the other hand, the same example is solved within 4 stages by simulated annealing approach. Hence, we can conclude that simulated annealing is a better solution approach for solving job shop scheduling problem. However, the only disadvantage of simulated annealing is sometimes it may not get an optimal solution but just a near optimal solution. It is because this approach does not consider all the possible sequence of each job on each machine when the problem getting larger.

Abstract— The majority of researches on scheduling assume setup times negligible or as a part of the processing time. In this paper, job shop scheduling with sequence dependent setup times is considered. After defining the problem, a mathematical model is developed. Implementing the mathematical model in large problems presents a weak performance to find the optimum results in reasonable computational times. Although the proposed mathematical model presents a good performance to obtain feasible solutions, it is unable to reach the optimum results in larger problems. Thus, a heuristic model based on priority rules is developed. Because of the inability to find optimum solutions in reasonable computational times, 3 different innovative lower bounds are developed, which could be implemented to evaluate different heuristics and metaheuristics in large problems. The performance of the heuristic model evaluated with a well- known example in the literature insures that the model seems to have a strong ability to solve jobshop scheduling with sequence dependent setup times problems and to obtain good solutions in reasonable computational times.

Thus, there is a need for an effective, general approach to solve the growing class of scheduling prob- lems that explicitly considers the completion time of intermediate operations. In this paper we address this need by developing an efficient, effective heuristic algorithmic framework useful for addressing job shop scheduling problems for a large class of objectives where operation completion times have a direct impact on the total cost. To clarify the exposition, we present our results in the context of explicitly min- imizing intermediate holding costs, although our approach applies directly and without modification to other classes of problems where operation completion times are critical. This framework builds on the notion of the optimal timing problem for a job shop scheduling problem. For any scheduling problem where intermediate holding costs are considered, the solution to the problem is not fully defined by the sequence of operations on machines – it is necessary to specify the starting time of each operation on each machine, since the time that each job is idle between processing steps dictates intermediate holding costs. The problem of determining optimal start times of operations on machines given the sequence of operations on machines is known as the optimal timing problem, and for many job shop scheduling problems, this optimal timing problem can be expressed as an LP.

The abovementioned studies on this subject examined only static cases in which all jobs are ready to start at time zero. However, in numerous real systems, this scheduling problem is even more difficult because jobs arrive on a continuous basis, which is why the process is called, dynamic scheduling. This paper considers the dynamic job shop scheduling problem with multiple delivery dates, where the time between two consecutive delivery dates is a given constant. This study focuses on scheduling jobs to minimize the sum of the total due-date cost and the total earliness penalty. This study is perhaps the first of its kind for developing dispatching rules to address the scheduling problem with fixed interval delivery dates. A thorough investigation was performed to observe the performance and their interactions of these decision factors regarding the total cost of jobs.

El Job Shop Scheduling Problem (JSP) es un problema de optimización combinatoria catalogado de tipo NP- Hard. Para dar solución a este problema han sido utilizados diversos métodos heurísticos y metaheurísticos. Con el objetivo de minimizar el makespan se propone un algoritmo memético (MA) que combina la exploración del espacio de búsqueda mediante un algoritmo genético (GA) y la explotación de las soluciones, usando una búsqueda local basada en la estructura de vecindario de Nowicki y Smutnicki. La estrategia genética usa una representación basada en operaciones que le permite generar programas factibles y una probabilidad de selección de los mejores individuos que son cruzados usando el operador JOX. Los resultados obtenidos en la ejecución demuestran que el algoritmo es competitivo frente a otros enfoques propuestos en la literatura.

In this dissertation, we studied complex job shop scheduling problems, which can take place in many industrial sectors. Four scheduling problems in manufacturing, logistics, transportation, and healthcare service have been introduced as examples of such complex job shop problems. Chapter 2 systematically studied ten practical aspects of job shop scheduling that are not cov- ered in the classical job shop (JS) model and groups them in three categories involving jobs, processors, and job processing. This collection of features, though still incomplete, enabled us to identify dierent complexifying features of a given practical job shop problem and model it accordingly. Similar to any other optimization problem, a job shop extension problem can be addressed by formulating it as a mixed integer linear programming (MILP) problem and then solving it by a commercial MILP solver. We applied this approach, rst by selecting experi- mentally the Manne formulation for the JS as a foundation upon which various formulations for single-feature job shop extensions have been developed. These formulations can be combined to formulate more complex JS problems. Our computational experiments showed that despite today's impressive performance of commercial MILP solvers when solving some optimization problems, a lot remains to be improved before one can use the mathematical programming approach with MILP formulations and commercial solvers to practically solve job shop related problems.