Job Sequence-dependent Setup Times Research Articles

A multi-objective production scheduling model and dynamic dispatching rules for unrelated parallel machines with sequence-dependent set-up times

This study presents a production scheduling for unrelated parallel machines with machine and job sequence-dependent setup times. The system performance measures to minimize include makespan, total tardiness, and number of tardy jobs. The aim of the study is to develop a solution methodology that can solve the problem for the large scale. First, the problem is formulated as a mixed-integer linear programming model. The augmented ɛ-constraint method is applied to find Pareto solutions for small problem instances. The purpose is to demonstrate that Pareto solutions, which balance the trade-offs among three measures of performance, can be found for these instances. Dispatching rule-based heuristics is developed to solve large problem instances. The heuristics feature three dispatching rules that are designed to handle the dependent setup time. In addition, these rules are combined into six variants using a time-based rule-switching mechanism. The heuristics are tested with 18 problem instances, containing 244 to 298 jobs, in two demand scenarios derived from the monthly demand data from an industrial user. Under each demand scenario, a set of heuristics that provides the best performance with respect to the three measures is identified. The heuristics include combinations of the shortest completion time and due date-based rules. Finally, a multi-criteria decision-making analysis is performed to determine the conditions specified by the weight given to each measure, with which one heuristic is preferred over the others.

Hybrid meta-heuristics for the unrelated parallel machine scheduling problem with setup times

This study focuses on an unrelated parallel machine scheduling problem with machine and job sequence-dependent setup times (UPMST) aiming to minimise the makespan. Recently, adaptive large neighbourhood search with learning automata (LA-ALNS) has been employed to tackle the UPMST with excellent performance. However, its search efficiency is heavily affected by re-visiting the recent solutions, which is known as the short-term cycle. Moreover, it remains challenging to balance the computational cost and quality of the solutions. To address these challenges, we propose a hybrid meta-heuristic method based on LA-ALNS and tabu search (LA-ALNS-TS). In the proposed algorithm, LA-ALNS is used to guide the exploration and TS is used to alleviate the short-term cycle experienced during the search process. In addition, we design two local search operators to achieve a balanced trade-off between the search efficiency and quality of the solutions. A dynamic perturbation scheme is proposed to improve the solution and help the algorithm escape from local optima. Comprehensive experiments were conducted to assess the performance of the algorithm on two exhaustive benchmarks. Experimental results demonstrate the effectiveness and efficiency of the proposed hybrid meta-heuristic method.

Bi-objective parallel machine scheduling with additional resources during setups

We present a bi-objective parallel machine scheduling problem with machine and job sequence dependent setup times, with the additional consideration of resources needed during setups. The availability of such resources is limited. This models many practical situations where setup times imply, for example, cleaning and/or the reconfiguration of productive equipment. These setups are performed by personnel, who are of course limited in number. The objectives considered are the minimization of the makespan and the minimization of the number of resources. Fewer available resources reduce production costs but inevitably increase the makespan. On the contrary, a greater number of resources increase costs but allow for more setups to be done in parallel and a reduced makespan. An algorithm based on iterated greedy approaches is proposed to search for the Pareto front of the problem. This algorithm is compared with state-of-the art methods adapted to the problem. Computational experiments, supported by statistical analyses, indicate that the proposed approach outperforms all other tested procedures.

Ant colony optimization, genetic algorithm and hybrid metaheuristics: A new solution for parallel machines scheduling with sequence-dependent set-up times

The parallel machine scheduling problem (PMSP) is one of the most difficult classes of problem. Due to the complexity of the problem, obtaining optimal solution for the problems with large size is very time consuming and sometimes, computationally infeasible. So, heuristic algorithms that provide near-optimal solutions are more practical and useful. The present study aims to propose a hybrid metaheuristic approach for solving the problem of unrelated parallel machine scheduling, in which, the machine and the job sequence dependent setup times are considered. A Mixed-Integer Programming (MIP) model is formulated for the unrelated PMSP with sequence dependent setup times. The solution approach is robust, fast, and simply structured. The hybridization of Genetic Algorithm (GA) with Ant Colony Optimization (ACO) algorithm is the key innovative aspect of the approach. This hybridization is made in order to accelerate the search process to near-optimal solution. After computational and statistical analysis, the two proposed algorithms are used to compare with the proposed hybrid algorithm to highlight its advantages in terms of generality and quality for short and large instances. The results show that the proposed hybrid algorithm has a very good performance as regards the instance size and provides the acceptable results.

Learning-Based Metaheuristic for Scheduling Unrelated Parallel Machines With Uncertain Setup Times

Setup time consists of all the activities that need to be completed before the production process takes place. The extant scheduling predominantly relies on simplistic methods, like the average value obtained from historical data, to estimate setup times. However, such methods are incapable of representing the real industry situation, especially when the setup time is subject to significant uncertainties. In this situation, the estimation error increases proportionally to the problem size. This study proposes a Random-Forest-based metaheuristic to minimize the makespan in an Unrelated Parallel Machines Scheduling Problem (UPMSP) with uncertain machine-dependent and job sequence-dependent setup times (MDJSDSTs). Taking the forging industry as an example, the numerical experiments show that the error percentage for the setup time estimation substantially decreases when the proposed approach is applied. This improvement is particularly significant when large-scale problems are sought. Overall, this study highlights the role of advanced analytics in bridging the gap between scheduling theory and practice.

Enhanced symbiotic organisms search algorithm for unrelated parallel machines manufacturing scheduling with setup times

. This paper deliberates on the non-pre-emptive unrelated parallel machine scheduling problem with the objective of minimizing makespan. Machine and job sequence dependent set-up times are considered for the proposed scheduling methods, which are NP-hard, even without set-up times. The addition of sequence dependent setup times introduces additional complexity to the problem, which makes it very difficult to find optimal solutions, especially for large scale problems. Due to the NP-hard nature of the problem at hand, three different approaches are proposed to solve the problem including: An Enhanced Symbiotic Organisms Search (ESOS) algorithm, a Hybrid Symbiotic Organisms Search with Simulated Annealing (HSOSSA) algorithm, and an Enhanced Simulated Annealing (ESA) algorithm. A local search procedure is incorporated into each of the three algorithms as an improvement strategy to enhance their solution qualities. The computational experiments carried out showed that ESOS and HSOSSA performed better than the other methods on large problem instances with 12 machines and 120 jobs. The performance of each method is measured by comparing the quality of its solutions to the optimal solutions for the varying problem combinations. The results of the proposed methods are also compared with other techniques from the literature. Moreover, a comprehensive statistical analysis was performed and the results obtained show that the proposed algorithms significantly outperform the compared methods in terms of generality, quality of solutions, and robustness for all problem instances.

Unrelated Parallel Machine Scheduling with Sequence-Dependent Setup Times in Frozen Food Industry

In this paper, a scheduling problem in the freezing station of a frozen food industry is addressed. It is a case of the unrelated parallel machines with machine-dependent and job sequence-dependent setup times problem. In a production shift, each freezing machine is allowed to process only products in the same product family. A mathematical model is developed to solve the problem in order to minimize the production related cost including production cost, fixed production cost, setup cost, inventory holding cost, and backlog cost. The proposed model is tested with a set of various problems. The results demonstrate that the proposed mathematical model could optimally solve the small sized problems.

An artificial bee colony algorithm approach for unrelated parallel machine scheduling with processing set restrictions, job sequence-dependent setup times, and due date

The problem dealt with in this study has job sequence-dependent setup times under suitable machine constraints and due date constraints. The performance criterion for this problem is to minimize the sum of makespan and total tardiness. In the literature, an application of ABC algorithm for the problems which includes all the properties that we have dealt has not been discussed. Because there is no appropriate test data, a real-life data was collected from a factory. In this study, a new approach has been proposed for the solution with meta-heuristics of unrelated parallel machine scheduling problems which is a combinatorial problem. This new neighborhood approach provides different machine assignments for every candidate job sequences. This approach is used by integrating into ABC and GA. To evaluate the performances of the algorithms, the real-life problem was solved by using ABC and GA algorithms under similar conditions. It was found that all jobs can be completed in two shifts without the need for a third shift. Computational results show that ABC algorithm has better performance than GA.

ABC-based manufacturing scheduling for unrelated parallel machines with machine-dependent and job sequence-dependent setup times

To date, the topic of unrelated parallel machine scheduling problems with machine-dependent and job sequence-dependent setup times has received relatively little research attention. In this study, a hybrid artificial bee colony (HABC) algorithm is presented to solve this problem with the objective of minimizing the makespan. The performance of the proposed HABC algorithm was evaluated by comparing its solutions to state-of-the-art metaheuristic algorithms and a high performing artificial bee colony (ABC)-based algorithm. Extensive computational results indicate that the proposed HABC algorithm significantly outperforms these best-so-far algorithms. Since the problem addressed in this study is a core topic for numerous industrial applications, this article may help to reduce the gap between theoretical progress and industrial practice.

Hybrid GRASP Heuristics to Solve an Unrelated Parallel Machine Scheduling Problem with Earliness and Tardiness Penalties

This paper considers an unrelated parallel machine scheduling problem with the objective of minimizing the total earliness and tardiness penalties. Machine and job-sequence dependent setup times and idle times are considered. Since the studied problem is NP-Hard, we test the applicability of algorithms based on Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic to determine near-optimal solutions. We propose three different heuristics. The first is a simple GRASP heuristic, the second heuristic includes an intensification procedure based on Path Relinking technique, and the third uses an Iterated Local Search (ILS) heuristic in the local search phase of the GRASP algorithm. The results obtained by the heuristics are compared using a set of small, medium and large instances. Comprehensive computational and statistical analyses are carried out in order to compare the performance of the algorithms.

A Reformulation for the Problem of Scheduling Unrelated Parallel Machines with Sequence and Machine Dependent Setup Times

In this paper we propose an improved formulation for an unrelated parallel machine problem with machine and job sequence-dependent setup times that outperforms the previously published formulations regarding size of instances and CPU time to reach optimal solutions. The main difference between the proposed formulation and previous ones is the way the makespan has been linearized. It provides improved dual bounds which speeds up the solution process when using a branch-and-bound commercial solver. Computational experiments show that, using this model, it is possible to solve instances four times larger than what was previously possible using other mixed integer programming formulations in the literature and obtain optimal solutions on instances of the same size up to three orders of magnitude faster.

ACO Algorithm for Scheduling Complex Unrelated Parallel Machine

This Paper Addresses an Unrelated Parallel Machine Scheduling Problem with Job Sequence-Dependent Setup Times. Jobs Have Precedence Constraints. the Objective Is to Minimize the Makespan. the Problem Has Applications in Industries such as TFT-LCD, Textile Manufactures. the Problem Is NP-Hard in Strong Sense. Therefore, an Ant Colony Optimization (ACO) Algorithm Is Introduced to Solve this NP-Hard Problem. the Proposed ACO Tackles the Special Structure of the Problem. its Performance Is Evaluated by Comparing its Solutions with Cplex Method. the Results Show that ACO Outperformed the Cplex Method.

Scheduling unrelated parallel machines with resource-assignable sequence-dependent setup times

A novel scheduling problem that results from the addition of resource-assignable setups is presented in this paper. We consider an unrelated parallel machine problem with machine and job sequence-dependent setup times. The new characteristic is that the amount of setup time does not only depend on the machine and job sequence but also on the amount of resources assigned, which can vary between a minimum and a maximum. The aim is to give solution to real problems arising in several industries where frequent setup operations in production lines have to be carried out. These operations are indeed setups whose length can be reduced or extended according to the amount of resources assigned to them. The objective function considered is a linear combination of total completion time and the total amount of resources assigned. We present a mixed integer program (MIP) model and some fast dispatching heuristics. We carry out careful and comprehensive statistical analyses to study what characteristics of the problem affect the MIP model performance. We also study the effectiveness of the different heuristics proposed.

A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times

In this work a genetic algorithm is presented for the unrelated parallel machine scheduling problem in which machine and job sequence dependent setup times are considered. The proposed genetic algorithm includes a fast local search and a local search enhanced crossover operator. Two versions of the algorithm are obtained after extensive calibrations using the Design of Experiments (DOE) approach. We review, evaluate and compare the proposed algorithm against the best methods known from the literature. We also develop a benchmark of small and large instances to carry out the computational experiments. After an exhaustive computational and statistical analysis we can conclude that the proposed method shows an excellent performance overcoming the rest of the evaluated methods in a comprehensive benchmark set of instances.

Makespan minimization for scheduling unrelated parallel machines with setup times

This study considers the problem of scheduling jobs on unrelated parallel machines with machine-dependent and job sequence-dependent setup times. In this study, a restricted simulated annealing (RSA) algorithm which incorporates a restricted search strategy is presented to minimize the makespan. The proposed RSA algorithm can effective reduce the search effort required to find the best neighborhood solution by eliminating ineffective job moves. The effectiveness and efficiency of the proposed RSA algorithm is compared with the basic simulated annealing and existing meta-heuristics on a benchmark problem dataset used in earlier studies. Computational results indicate that the proposed RSA algorithm compares well with the state-of-the-art meta-heuristic for small-sized problems, and significantly outperforms basic simulated annealing algorithm and existing algorithms for large-sized problems.

Integrating dominance properties with genetic algorithms for parallel machine scheduling problems with setup times

This paper deals with an unrelated parallel machine scheduling problem with the objective of minimizing the makespan. There are machine-dependent and job sequence-dependent setup times and all jobs are available at time zero. This is a NP-hard problem and a set of dominance properties are developed including inter-machine (i.e., adjacent and non-adjacent interchange) and intra-machine switching properties as necessary conditions of job sequencing orders in an optimal schedule. As a result, by applying these dominance properties for a given sequence, a near-optimal solution can be derived. In addition, a new meta-heuristic is introduced by integrating the dominance properties with genetic algorithm to further improve the solution quality for larger problems. The performance of this meta-heuristic is evaluated by using benchmark problems from the literature. The intensive experimental results show that GADP can find all optimal solutions for the small problems and outperformed the solutions obtained by the existing heuristics for larger problems.

Algorithms for a realistic variant of flowshop scheduling

This paper deals with a realistic variant of flowshop scheduling, namely the hybrid flexible flowshop. A hybrid flowshop mixes the characteristics of regular flowshops and parallel machine problems by considering stages with parallel machines instead of having one single machine per stage. We also investigate the flexible version where stage skipping might occur, i.e., not all stages must be visited by all jobs. Lastly, we also consider job sequence dependent setup times per stage. The optimization criterion considered is makespan minimization. While many approaches for hybrid flowshops have been proposed, hybrid flexible flowshops have been rarely studied. The situation is even worse with the addition of sequence dependent setups. In this study, we propose two advanced algorithms that specifically deal with the flexible and setup characteristics of this problem. The first algorithm is a dynamic dispatching rule heuristic, and the second is an iterated local search metaheuristic. The proposed algorithms are evaluated by comparison against seven other high performing existing algorithms. The statistically sound results support the idea that the proposed algorithms are very competitive for the studied problem.

Heuristics for the Unrelated Parallel Machine Scheduling Problem with Setup Times

The problem addressed in this paper is the non-preemptive unrelated parallel machine scheduling problem with the objective of minimizing the makespan. Machine-dependent and job sequence-dependent setup times are considered, all jobs are available at time zero, and all times are deterministic. This is a NP-hard problem and in this paper, optimal solutions are found for small problems only. For larger problems, a new meta-heuristic, Meta-RaPS, is introduced and its performance is evaluated by comparing its solutions to the solutions of an existing heuristic for the same problem. The results show that Meta-RaPS found all optimal solutions for the small problems and outperformed the solutions obtained by the existing heuristic for larger problems.

Unrelated parallel machine scheduling with setup consideration and a total weighted completion time objective

This paper addresses the problem of scheduling a set of independent jobs on unrelated parallel machines with job sequence dependent setup times so as to minimize a weighted mean completion time. The study of the problem stemmed from a real service industry problem. This problem is at least NP-hard in the ordinary sense, even when there are only two identical machines with no setups. Seven heuristic algorithms are proposed and tested by simulation. The results and analysis of quite extensive computational experiments are reported and discussed. The findings through the computational results are presented. Whether this problem is strongly NP-hard is left as an open question.