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

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.

• 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.

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.

An exact method for [formula omitted] 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.

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.

Evolutionary programming method for minimizing the number of tardy jobs

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 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

In this paper, we discuss a scheduling problem for jobs on identical parallel machines. Ready times of the jobs, precedence constraints, and sequence-dependent setup times are considered. We are interested in minimizing the performance measure total weighted tardiness. Scheduling problems of this type are quite important in semiconductor manufacturing. We suggest a variable neighborhood search (VNS) scheme for this problem. Based on computational experiments with stochastically generated test instances we are able to show that the VNS approach clearly outperforms heuristics based on the apparent tardiness cost with setups and ready times (ATCSR) dispatching rule in many situations.

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

Artificial chromosomes with genetic algorithm 2 (ACGA2) for single machine scheduling problems with sequence-dependent setup times

With the rapid development of make-to-order pattern including E-commerce and takeout and catering service in restaurants, the study of integrated scheduling and distribution receives more and more attentions. Based on a practical order picking and distribution system, a three-stage hybrid flow shop scheduling problem with distribution is studied. Each order is processed on the hybrid flow shop which consists of identical parallel machines with sequence-dependent setup times at stage 1, identical parallel machines at stage 2 and dedicated machines at stage 3, followed by a multi-trip traveling salesman problem with capacitated vehicles for customers of different destination areas. A mixed-integer linear programming model is formulated to minimize the maximum delivery completion time. A variable neighborhood search (VNS)-based method, a four-layered constructive heuristic method (denoted by $$CH_{VNS}$$) and a hybrid heuristic method (denoted by $$CONS_{VNS}$$) which combines the VNS method and the $$CH_{VNS}$$ method are developed to solve the problems with practical size. Computational experiments show the effectiveness and efficiency of the proposed methods.

Distributed scheduling is seldom investigated in hybrid flow shops. In this study, distributed two-stage hybrid flow shop scheduling problem (DTHFSP) with sequence-dependent setup times is considered. A collaborative variable neighborhood search (CVNS) is proposed to simultaneously minimize total tardiness and makespan. DTHFSP is simplified by incorporating factory assignment into machine assignment of a prefixed stage, and its solution is newly represented with a machine assignment string and a scheduling string. CVNS consists of two cooperated variable neighborhood search (VNS) algorithms, and neighborhood structures and global search have collaborated in each VNS. Eight neighborhood structures and two global search operators are defined to produce new solutions. The current solution is periodically replaced with a member of the archive farthest from it. Experiments are conducted , and the computational results validate that CVNS has good advantages over the considered DTHFSP.