Parallel machine scheduling problems considering regular measures of performance and machine cost

<p style='text-indent:20px;'>Under support of industry 4.0, researchers have shown an increased interest in MapReduce scheduling problems to process big data. However, very few studies investigate MapReduce scheduling problems under parallel batch machine environment, which is also common in practice. Motivated by this, we study a parallel batch machine scheduling problem in which all the jobs are belonging to MapReduce type. The objective of the considered problem is of minimizing the total weighted tardiness. For solving this problem, we first establish a mixed integer linear programming model, and then a rule-based genetic algorithm is developed to solve it. Numerical experiments are also conducted to demonstrate the effectiveness of the proposed method.</p>

In this study, the objective of minimizing makespan has been considered for a scheduling problem of identical parallel machines with a single server and unavailability constraints. The unavailability constraints correspond to preventive maintenance periods. In this study, the jobs and the maintenance periods are scheduled simultaneously. This scheduling problem has a wide range of potential application areas in the manufacturing environment. In addition, the studied problem is a challenging one from theoretical point of view, due to its NP-Hardness. To conduct the study, a lower bound ( LB ) for the problem, and three metaheuristics namely Simulated Annealing ( SA ), Tabu Search ( TS ), and Genetic Algorithm ( GA ) have been proposed. The best parameters settings of the proposed algorithms were conducted using pilot runs with a Taguchi design. The algorithms performance has been assessed by using a set of test problems generated randomly. These test problems are based on a literature benchmark. The size of the instances, or number of jobs, were up to 500. Along with the performance analysis of the proposed algorithms, the effect of varying processing times and unavailability periods on the performance of the proposed algorithms is studied. The present work provides strong evidence of the efficiency and the performance of the proposed algorithms.

A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines

This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.

In this paper, we discuss scheduling problems in semiconductor manufacturing. Starting from describing the manufacturing process, we identify typical scheduling problems found in semiconductor manufacturing systems. We describe batch scheduling problems, parallel machine scheduling problems, job shop scheduling problems, scheduling problems with auxiliary resources, multiple orders per job scheduling problems, and scheduling problems related to cluster tools. We also present important solution techniques that are used to solve these scheduling problems by means of specific examples, and report on known implementations. Finally, we summarize some of the challenges in scheduling semiconductor manufacturing operations.

Machine scheduling is one of the most studied problems due to its technical challenges and prevalence in real life. In the literature, continuous- and discrete-time formulations are the two most known formulations for scheduling problems. However, continuous-time formulations often suffer from weak linear relaxations, while discrete-time formulations struggle with large numbers of variables. In contrast, the bucket-indexed formulation is an alternative that mitigates both issues by working with partial time discretization. We propose a mixed-integer linear programming model based on a bucket-indexed formulation to solve a nonpreemptive scheduling problem of identical parallel machines considering release dates, deadlines, precedence, eligibility, and machine availability constraints. We evaluate the proposed formulation against real-world instances comprising more than 400 jobs and 100 machines, comparing its performance against equivalent continuous- and discrete-time formulations. Remarkably, our formulation can be solved to optimality for all instances, outperforming both continuous- and discrete-time formulations.

We consider the parallel-machine flexible-resource scheduling (PMFRS) problem in which a set of jobs must be scheduled over a set of parallel machines, where the processing time of each job is a function of the amount of allocated resource. Resource flexibility provides the capability to dynamically reassign a renewable resource across machines to break processing bottlenecks and improve system performance as measured by schedule makespan. The PMFRS problem has many important applications, including production scheduling of manufacturing cells where a cross-trained work force can be dynamically reallocated among cells. The problem is also NP-hard, motivating the development of effective heuristics that approximately determine the allocation of resource to jobs, the sequence of jobs on each machine, and the associated job start times that minimize system makespan. This paper explores heuristics for the PMFRS problem, and in particular the application of tabu-search methodology to this problem setting. We review an existing heuristic (SBH), define two tabu-search heuristics, and discuss extensive computational experience with the procedures. The computational results indicate that the heuristics are effective in obtaining approximate solutions to the PMFRS problem. In particular, the approach that uses tabu-search methodology in tandem with SBH consistently yields high-quality solutions with modest computational effort.

Identical parallel machine scheduling problem for minimizing the makespan is a very important production scheduling problem which has been proven to be NP-hard. The problem further compounds with additional constraints. Genetic algorithms (GA) have shown great advantages in solving the combinatorial optimization problem in view of its characteristic that has high efficiency and that is fit for practical application. In this chapter we present a spreadsheet based GA approach for minimizing the makespan for scheduling of a set of tasks for identical parallel machines and worker assignment to machines. The results obtained from the proposed approach are compared with two sets of benchmark problems consisting of 100 problems each. It has been demonstrated that the performance of proposed approach is superior to the results that have been obtained earlier. The proposed approach produces optimal solution for almost 95% of the problems demonstrating the effectiveness of the proposed approach. An empirical analysis of GA parameters has also been carried out to see the effect on the performance of the proposed algorithm.

The Wafer Probing Scheduling Problem (WPSP) is a practical generalization of the parallel-machine scheduling problem, which has many real-world applications, particularly, in the Integrated Circuit (IC) manufacturing industry. In the wafer probing factories, the jobs are clustered by their product types, which must be processed on groups of identical parallel machines and be completed before the due dates. The job processing time depends on the product type, and the machine setup time is sequentially dependent on the orders of jobs processed. Since the wafer probing scheduling problem involves constraints on job clusters, job-cluster dependent processing time, due dates, machine capacity, and sequentially dependent setup time, it is more difficult to solve than the classical parallel-machine scheduling problem. In this paper, we consider the WPSP and formulate the WPSP as an integer programming problem to minimize the total machine workload. We demonstrate the applicability of the integer programming model by solving a real-world example taken from a wafer probing shop floor in an IC manufacturing factory.

SUMMARY The deterministic job-shop scheduling problem exhibits the fundamental computational difficulty implicit in determining an optimal timetable for sharing production resources among competing production activities. While adaptation of the formal model to industrial practice is fraught with difficulties, we show that the underlying binary-disjunctive formulation itself is more robust than might be immediately apparent. Straightforward extensions of the underlying model are sufficient to capture such practical problem features as assembly and disassembly sequences, due-dates and out-processing operations, scheduled maintenance, nonzero release times and dispatch operations, certain sequence-dependent set-ups and materials handling delays, and a great range of operational side-constraints. Technological sequences need not be total orders, job priorities can be assigned explicitly or implicitly, and any regular measure of performance can be represented. The principal structural limitation is that machin...

In this study, we address a rescheduling problem in parallel machine environments under machines failures. To make a balance between efficiency and stability of the reschedules, we consider the total number of tardy jobs as efficiency measure and the number of jobs processed on different machines in the initial and revised schedules as a stability measure. Then a heuristic algorithm which synthesizes beam search (BS) and repair-based constraint satisfaction algorithm is developed. Numerical experiments are processed to evaluate the performance and efficiency of the proposed algorithm. The experimental results show that the proposed algorithm improves the results significantly.

Approximate dynamic programming for an energy-efficient parallel machine scheduling problem

Self-growth learning-based machine scheduler to minimize setup time and tardiness in OLED display semiconductor manufacturing

Hybrid proactive approach for solving maintenance and planning problems in the scenario of Industry 4.0

In simple flow shop problems, each machine operation center includes just one machine. If at least one machine center includes more than one machine, the scheduling problem becomes a flexible flow shop problem (FFSP). Flexible flow shops are thus generalization of simple flow shops. Flexible flow shop scheduling problems have a special structure combining some elements of both the flow shop and the parallel machine scheduling problems. FFSP can be stated as finding a schedule for a general task graph to execute on a multiprocessor system so that the schedule length can be minimized. FFSP is known to be NP-hard. In this study, we present a particle swarm optimization (PSO) algorithm to solve FFSP. PSO is an effective algorithm which gives quality solutions in a reasonable computational time and consists of less numbers parameters as compared to the other evolutionary metaheuristics. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast towards near-optimal solution and hence reduce computational efforts further. The performance of schedules is evaluated in terms of total completion time or makespan (Cmax). The results are presented in terms of percentage deviation (PD) of the solution from the lower bound. The results are compared with different versions of genetic algorithm (GA) used for the purpose from open literature. The results indicate that the proposed PSO algorithm is quite effective in reducing makespan because average PD is observed as 2.961, whereas GA results in average percentage deviation of 3.559. Finally, influence of various PSO parameters on solution quality has been investigated.