Exact algorithm over an arc-time-indexed formulation for parallel machine scheduling problems

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.

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

Evolutionary programming method for minimizing the number of tardy jobs

A resource-constrained identical parallel machine scheduling problem with machine eligibility restrictions is investigated in this study. For the considered problem, three optimization models; an integer programming (IP) model, a constraint programming (CP) model and a combined IP/CP model are developed. A problem-based search procedure to be used in CP and IP/CP combined models is also proposed to give quick and efficient results. All three optimization models are constructed and solved in OPL Studio 3.7™ setting 1000 second run-time limit. Computational results show that the combined IP/CP OPL™ model with the proposed problem-based search procedure not only achieves magnitude reduction in computational time but also gives optimal results in 174 out of 200 test problems, while IP and CP models prove optimality in only 47 and 6 problems, respectively. Finally, computational results are also analysed and discussed in terms of various problem parameters.

The aim of this paper is to compare the performance of two meta-heuristic methods proposed to solve the identical parallel machine scheduling problem with sequence dependent setup times. The goal is to minimize the makespan. The first algorithm is a tabu search based heuristic and the second a memetic approach, which combines a population-based method with local search procedures. As benchmarks for small-sized instances, optimal and lower bound values are used provided by a dichotomous search. For larger instances, the comparisons rely on the best known solutions provided by an exhaustive search variant of the tabu procedure.

• 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.

Using a variable neighborhood search to solve a bi-objective identical parallel machine scheduling problem

In this paper, we develop a fast local search for the identical parallel machine scheduling problem with maintenance activities and the position‐based deteriorating under the maximum lateness minimization. Our approach allows us to calculate criterion values in a constant time per solution in a neighbourhood. The application is given on the basis of the Nawaz–Ensore–Ham method, iterative local search, tabu search, and a family of memetic search algorithms, where their efficiency equipped with our method is compared with their classical versions. The computational experiments confirm the theoretical analysis that our approach essentially overwhelms the typical implementation and speeds up the related algorithms over 200 times for reasonable problem sizes. Thereby it allows us to search for significantly larger solution space at the same time and, therefore, radically improve the criterion values of the obtained solutions.

This paper addresses a bi-objective cutting parallel machine scheduling problem aiming to minimize the total makespan and total tardiness. This problem is inspired from a structural metal-cutting plant that combines identical and unrelated parallel machine scheduling problems. To formulate this complicated problem, a new mixed-integer programming (MIP) model is presented in consideration of total makespan and total tardiness. The machine-job-dependent processing times are considered along with the setup times, pickup times, different delivery times, and machine eligibility constraints. Owing to the complex characteristics of the problem, an appropriate non-dominated sorting Genetic Algorithm III (NSGAIII) with an embedded variable neighborhood structure strategy (VNSGAIII) is developed. A number of randomly generated datasets are used to test the performance of VNSGAIII in comparison with NSGAII, and NSGAIII on solving the engineering problem addressed herein. The experimental results demonstrate that the suggested VNSGAIII statistically outperforms the compared algorithms, especially in the distribution of Pareto solutions. The e-constrained method is implemented in the direct MIP model by CPLEX for comparison with the proposed evolutionary algorithms. The proposed algorithm performs efficiently when obtaining the Pareto solutions.

Scheduling of jobs has been a challenging task in manufacturing and the most real life scheduling problems, which involves multi-objectives and multi-machine environments. This paper presents tabu search and simulated annealing approaches for scheduling jobs on identical parallel machines. The identical parallel machine scheduling problem has been considered to minimize the mean tardiness for the jobs. Initially, an initial solution has been obtained using EDD dispatching rule then, simulated annealing and tabu search have been applied to reach a near optimal solution. Computational experiments are performed on problems with up to 10 machines and 150 jobs. The computational results indicate that the two proposed approaches are capable of obtaining better solutions for the given scheduling problem. Moreover, the tabu search approach provides better solution then simulated annealing approach.

This paper addresses a real-life production scheduling problem with identical parallel machines, originating from a plant producing Acrylonitrile-Butadiene-Styrene (ABS) plate products. In the considered practical scheduling problem, ABS plate has some specific specifications and each specification has several different levels. Because there is at least one different level of specification between two ABS plate products, it is necessary to make a set-up adjustment on each machine whenever a switch occurs from processing one ABS plate product to another product. As tardiness leads to extra penalty costs and opportunity losses, the objective of minimising total tardiness has become one of the most important tasks for the schedule manager in the plant. The problem can be classified as an identical parallel machine scheduling problem to minimise the total tardiness. A dispatching rule is proposed for this problem and evaluated by comparing it with the current scheduling method and several existing approaches. Moreover, an iterated greedy-based metaheuristic is developed to further improve the initial solution. The experimental results show that the proposed metaheuristic can perform better than an existing tabu search algorithm, and obtain the optimal solution for small-sized problems and significantly improve the initial solutions for large-sized problems.

Event driven strategy based complete rescheduling approaches for dynamic m identical parallel machines scheduling problem with a common server

Identical parallel machine scheduling problem with controllable processing times is investigated in this research. In such an area, our focus is mostly motivated by the adoption of just-in-time (JIT) philosophy with the objective of minimizing total weighted tardiness and earliness as well as job compressions/expansion cost simultaneously. Also the optimal set amounts of job compressions/expansion plus the job sequence are determined on each machine. It is assumed that the jobs processing times can vary within a given interval, i.e., it is permitted to compress or expand in return for compression/expansion cost. A mixed integer linear programming (MILP) model for the considered problem is firstly proposed and thereafter the optimal jobs set amounts of compression and expansion processing times in a known sequence are determined via parallel net benefit compression–net benefit expansion called PNBC–NBE heuristic. An intelligent water drop (IWD) algorithm, as a new swarm-based nature-inspired optimization one, is also adopted to solve this multi-criteria problem. A heuristic method besides three meta-heuristic algorithms is then employed to solve small- and medium- to large-size sample-generated instances. Computational results reveal that the proposed IWDNN outperforms the other techniques and is a trustable one which can solve such complicated problems with satisfactory consequences.

This article investigates an energy-efficient, identical parallel machine scheduling problem. The objective is to minimize the total completion time while total energy costs do not exceed a given limitation. First, a reasonable range of total energy cost limits and the NP-hardness of this problem are analysed. Then, a mixed-integer programming model is presented. Afterwards, an improved simulated annealing (ISA) algorithm is devised. The ISA algorithm incorporates four effective neighbourhood operators, a method for adaptive selection of operators, and an initial feasible solution generation method. Comparison with genetic algorithms (GAs) and simplified swarm optimization (SSO) algorithms verifies the effectiveness and efficiency of the ISA algorithm. Results demonstrate that the ISA algorithm can provide near-optimal or better solutions than CPLEX ® in small- and medium-scale instances. Experimental results on large-scale instances show that ISA significantly outperforms GAs and SSOs. ISA, in particular, can find the best values for all instances of 500 jobs except one.

This research deals with the parallel machine scheduling problem for identical machines that need additional operational resources during the changeover. The production strategy is mainly based on make-to-stock. When the current inventory is less than the quantity of the new order, the corresponding products will be scheduled for production in predetermined production batches that are larger than the quantity of the order. Because the additional resources are limited, batch splitting, which increases the number of changeovers, is not permitted. The objective is to minimize both the makespan and total tardiness. A two-phase methodology is proposed. In the first phase, a mixed-integer program is developed to minimize the makespan. The resulting minimal makespan becomes the constraint in the second phase. An extended mixed-integer program is then developed to minimize the total tardiness. A case study of a plastic pallet manufacturing company is introduced. The experimental results show that the proposed methodology can minimize the makespan and total tardiness efficiently. Moreover, it also shows the promise of the proposed methodology for solving practical applications.