Efficient Approach for Parallel Machine Scheduling Problem

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.

A vibration damping optimization algorithm for a parallel machines scheduling problem with sequence-independent family setup times

Scheduling identical parallel machines with tooling constraints

Minimizing the total completion time on a parallel machine system with tool changes

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

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.

Thin‐film transistor liquid‐crystal displays (TFT‐LCDs) have gradually replaced cathode‐ray tubes because of their compact size and efficient use of power. Since product lifecycles are shortening, consumers require instant order delivery, which affects fluctuations in supply and demand. As various product types in the LCD industry exist, manufacturing time has to be reduced to satisfy consumer demand. This study investigates the dispatching of parallel machines for TFT‐LCD manufacturing. Since customers’ orders and suppliers’ deliveries vary significantly and the manual adjustment of production planning is time consuming, an appropriate production planning and scheduling system is necessary. Consequently, this study develops a genetic algorithm to solve the scheduling problem of unrelated parallel machines, taking account of multiple performance measurement indicators. We also adopt LINGO to solve the problem and compare the obtained solution quality and computation time of the two approaches to justify the effectiveness of the proposed genetic algorithm.

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.

SYNOPTIC ABSTRACTIn this article, we consider a parallel machine scheduling problem that integrates partial maintenance activities due to job-dependent machine deteriorations. In this problem, we are given identical parallel machines, each with an initial maintenance level which is a non-negative integer value to represent its maintenance state, and a set of jobs each with a non-preemptive processing time and a machine deterioration. For each job, its machine deterioration qualifies the decrement of the machine maintenance level after processing it. When each machine processes jobs, one should guarantee a non-negative maintenance level at any time point. Thus, whenever necessary, a maintenance activity must be performed to restore the machine maintenance level. The goal of this problem is to schedule the jobs and the maintenance activities, such that the makespan achieves the minimum. We take the partial maintenance activity pattern, in which each activity can be performed to increase the machine maintenance level to any level not exceeding the maximum. To tackle this problem, we first model it by an integer programming formulation, and then propose an LP-based approximation algorithm with an instance-dependent approximation factor and show the approximability lower bound. Finally, we present a fast heuristic algorithm followed by a numerical example to show how this algorithm works.

• Examines scheduling on m identical parallel machines with a common server. • Considers sequence-dependent setup times in parallel machine scheduling. • Introduces an arc-based MILP formulation for makespan minimization. • Presents a GRASP-enhanced Iterated Greedy algorithm with strong performance. • Reports 21 new best-known solutions across benchmark test instances. The identical parallel machine scheduling problem with a single server and sequence-dependent setup times is a challenging optimization problem with important applications in manufacturing and service industries. In such environments, several machines depend on a common server to perform setup operations before production can begin, which creates strong interdependencies and demands more effective scheduling strategies. This characteristic highlights the practical relevance of the problem. The interaction between machine availability and server operations often becomes a critical bottleneck. This study introduces two complementary approaches. The first is an exact method based on a novel arc-based mixed-integer linear programming (ABF) model, which extends the modeling capability of existing formulations by capturing server-related constraints more effectively. The second is an approximation method built on an Iterated Greedy (IG) algorithm. The IG procedure is improved by two evaluation mechanisms: one model-based evaluation derived from the proposed ABF model, and another employing a greedy randomized adaptive search procedure (GRASP)-based strategy that integrates greedy selection, randomization, and reconstruction to enhance solution quality. Computational experiments are conducted on existing benchmark instances. The results show that the proposed ABF model performs well on small and medium-sized instances compared to existing exact methods, while the IG variants, particularly the proposed GRASP-based version, deliver strong performance against state-of-the-art metaheuristics developed for this problem. In addition, 21 new best-known solutions are reported, further demonstrating the effectiveness of the proposed approaches.

This paper develops an efficient variant of a Genetic Algorithm (GA) for a ship routing and scheduling problem (SRSP) with time-window in industrial shipping operation mode. This method addresses the problem of loading shipments for many customers using heterogeneous ships. Constraints relate to delivery time windows imposed by customers, the time horizon by which all deliveries must be made and ship capacities. The results of a computational investigation are presented and the solution quality and execution time are explored with respect to problem size. The proposed algorithm is compared, in terms of solution quality and computational time, with an exact method that uses Set Partitioning Problem (SPP). It is found that while the exact method solves small scale problem efficiently, treating large scale problems with the exact method becomes involved due to computational problem, a deficiency that the GA can encounter. Meantime, GA consistently returns better solution than other published work using Tabu Search method in term of solution quality.

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.

This paper studies a multi-stage and parallel-machine scheduling problem with job splitting which is similar to the traditional hybrid flow shop scheduling (HFS) in the solar cell industry. The HFS has one common hypothesis, one job on one machine, among the research. Under the hypothesis, one order cannot be executed by numerous machines simultaneously. Therefore, multiprocessor task scheduling has been advocated by scholars. The machine allocation of each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage is determined. However, machine allocation and production sequence decisions are highly interactive. As a result, this study, motivated from the solar cell industry, is going to explore these issues. The multi-stage and parallel-machine scheduling problem with job splitting simultaneously determines the optimal production sequence, multiprocessor task scheduling and machine configurations through dynamically splitting a job into several sublots to be processed on multiple machines. We formulate this problem as a mixed integer linear programming model considering practical characteristics and constraints. A hybrid-coded genetic algorithm is developed to find a near-optimal solution. A preliminary computational study indicates that the developed algorithm not only provides good quality solutions but outperforms the classic branch and bound method and the current heuristic in practice.

We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP‐hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two‐phase heuristics and dynamic two‐phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

The Quadratic Assignment Problem (QAP) is a difficult and important problem studied in the domain of combinatorial optimisation. It is possible to solve QAP instances with 10--20 facilities using exhaustive parallel algorithms within a few days on a cluster machine. However, large QAP instances with more than 100 facilities are not solvable using exhaustive techniques. We have explored a variety of Genetic Algorithm crossover operators for this problem and verified its performance experimentally using well-known instances from the QAPLIB library. By increasing the number of processors, generations and population sizes we have been able to find solutions that are the same as (or very close to) the best reported solutions for large QAP instances in QAPLIB. In order to parallelise the Genetic Algorithm we generate and evolve separate solution pools on each cluster processor, using an island model. This model exchanges 10% of each processor’s solutions at the initial stages of optimisation. We show experimentally that both execution times and solution qualities are improved for large QAP instances by using our Island Parallel Genetic Algorithm.