MIP models and hybrid algorithm for minimizing the makespan of parallel machines scheduling problem with a single server

This paper considers the identical parallel machines scheduling problem (PMSP) with a single server in charge of job setups. A job can be processed with a precedent setup by a server on one of the machines. The setup can be processed at only one machine at any time. In this paper, the problem P, S1|s_j|C_max with a general job set is formulated using mixed integer programming in two ways. The first one is developed by taking into account the characteristics of the single server problem, and the second one is developed by adding the concept of the server waiting time suggested by Abdekhodaee and Wirth (2002) [3]. Abdekhodaee and Wirth (2002) [3] define the equation of the server waiting time applied to only the special case with two machines and a regular job set. The general model for several machines is studied in this paper by developing the properties on the server waiting time. The hybrid heuristic algorithm is developed for the practical use, which can yield a near-optimal schedule in a reasonable computational time. The performance of algorithm is evaluated by comparing with the results of MIP models and heuristics appearing in the literature.     

Makespan minimization on single batch-processing machine via ant colony optimization

This paper investigates the problem of minimizing makespan on a single batch-processing machine, and the machine can process multiple jobs simultaneously. Each job is characterized by release time, processing time, and job size. We established a mixed integer programming model and proposed a valid lower bound for this problem. By introducing a definition of waste and idle space (WIS), this problem is proven to be equivalent to minimizing the WIS for the schedule. Since the problem is NP-hard, we proposed a heuristic and an ant colony optimization (ACO) algorithm based on the theorems presented. A candidate list strategy and a new method to construct heuristic information were introduced for the ACO approach to achieve a satisfactory solution in a reasonable computational time. Through extensive computational experiments, appropriate ACO parameter values were chosen and the effectiveness of the proposed algorithms was evaluated by solution quality and run time. The results showed that the ACO algorithm combined with the candidate list was more robust and consistently outperformed genetic algorithm (GA), CPLEX, and the other two heuristics, especially for large job instances.     

Ant colony optimization for multi-objective flow shop scheduling problem

Flow shop scheduling problem consists of scheduling given jobs with same order at all machines. The job can be processed on at most one machine; meanwhile one machine can process at most one job. The most common objective for this problem is makespan. However, multi-objective approach for scheduling to reduce the total scheduling cost is important. Hence, in this study, we consider the flow shop scheduling problem with multi-objectives of makespan, total flow time and total machine idle time. Ant colony optimization (ACO) algorithm is proposed to solve this problem which is known as NP-hard type. The proposed algorithm is compared with solution performance obtained by the existing multi-objective heuristics. As a result, computational results show that proposed algorithm is more effective and better than other methods compared.     

A simulated annealing algorithm for the job shop cell scheduling problem with intercellular moves and reentrant parts

This paper addresses the problem of scheduling parts in job shop cellular manufacturing systems by considering exceptional parts that need to visit machines in different cells and reentrant parts which need to visit some machines more than once in non-consecutive manner. Initially, an integer linear programming (ILP) model is presented for the problem to minimize the makespan, which considers intercellular moves and non-consecutive multiple processing of parts on a machine. Due to the complexity of the model, a simulated annealing (SA) based solution approach is developed to solve the problem. To increase the efficiency of the search algorithm, a neighborhood structure based on the concept of blocks is applied. Subsequently, the efficiency of the ILP model and the performance of the proposed SA are assessed over a set of problem instances taken from the literature. The proposed ILP model was coded in Lingo 8.0 and the solution obtained by the proposed SA was compared to the optimal values. The computational results demonstrate that the proposed ILP model and SA algorithm are effective and efficient for this problem.     

A genetic algorithm approach to the multiple machine tool selection problem

A number of earlier researches have emphasized the on-the-job scheduling problems that occur with a single flexible machine. Two solutions to the problem have generally been considered; namely minimization of tool switches and minimization of tool switching instances. Methods used to solve the problems have included KTNS heuristic, dual-based relaxation heuristic, and non-LP-based branch-and-bound methods. However, scant literature has considered the case of job scheduling on multiple parallel machines which invokes another problem involving machine assignment. This paper addresses the problem of job scheduling and machine assignment on a flexible machining workstation (FMW) equipped with multiple parallel machines in a tool-sharing environment. Under these circumstances, the authors have attempted to model the problem with the objective of simultaneously minimizing both the number of tool switches and the number of tool switching instances. Furthermore, a set of realistic constraints has been included in the investigation. A novel genetic algorithm (GA) heuristic has been developed to solve the problem, and performance results show that GA is an appropriate solution.     

A heuristic method for two-stage hybrid flow shop with dedicated machines

This paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines, in which the first stage contains a single common critical machine, and the second stage contains several dedicated machines. Each job must be first processed on the critical machine in stage one and depending on the job type, the job will be further processed on the dedicated machine of its type in stage two. The objective is to minimize the makespan. To solve the problem, a heuristic method based on branch and bound (B&B) algorithm is proposed. Several lower bounds are derived and four constructive heuristics are used to obtain initial upper bounds. Then, three dominance properties are employed to enhance the performance of the proposed heuristic method. Extensive computational experiments on two different problem categories each with various problem configurations are conducted. The results show that the proposed heuristic method can produce very close-to-optimal schedules for problems up to 100 jobs and five dedicated machines within 60 s. The comparisons with solutions of two other meta-heuristic methods also prove the better performance of the proposed heuristic method.     

Bi-objective parallel machines scheduling with sequence-dependent setup times using hybrid metaheuristics and weighted min–max technique

In the literature of multi-objective problem, there are different algorithms to solve different optimization problems. This paper presents a min–max multi-objective procedure for a dual-objective, namely make span, and sum of the earliness and tardiness of jobs in due window machine scheduling problems, simultaneously. In formulation of min–max method when this method is combined with the weighting method, the decision maker can have the flexibility of mixed use of weights and distance parameter to yield a set of Pareto-efficient solutions. This research extends the new hybrid metaheuristic (HMH) to solve parallel machines scheduling problems with sequence-dependent setup time that comprises three components: an initial population generation method based on an ant colony optimization (ACO), a simulated annealing (SA) as an evolutionary algorithm employs certain probability to avoid becoming trapped in a local optimum, and a variable neighborhood search (VNS) which involves three local search procedures to improve the population. In addition, two VNS-based HMHs, which are a combination of two methods, SA/VNS and ACO/VNS, are also proposed to solve the addressed scheduling problems. A design of experiments approach is employed to calibrate the parameters. The non-dominated sets obtained from HMH and two best existing bi-criteria scheduling algorithms are compared in terms of various indices and the computational results show that the proposed algorithm is capable of producing a number of high-quality Pareto optimal scheduling plans. Aside, an extensive computational experience is carried out to analyze the different parameters of the algorithm.     

双资源生产车间调度问题的研究

将遗传算法(GA)和模拟退火算法(SA)相结合研究了双资源生产车间的调度优化问题,该混合算法将机床设备和工人合理地分配给加工任务,使评价性能指标获得最优。通过与国内外学者的算法进行比较,本算法获得的生产周期最短,机床利用率和工人利用率都较高,并且在某些情况下,平均流动时间也较短。因此可以证明本算法具有一定的优越性。     

A robust hybrid approach based on particle swarm optimization and genetic algorithm to minimize the total machine load on unrelated parallel machines

This paper dealt with an unrelated parallel machines scheduling problem with past-sequence-dependent setup times, release dates, deteriorating jobs and learning effects, in which the actual processing time of a job on each machine is given as a function of its starting time, release time and position on the corresponding machine. In addition, the setup time of a job on each machine is proportional to the actual processing times of the already processed jobs on the corresponding machine, i.e., the setup times are past-sequence-dependent (p-s-d). The objective is to determine jointly the jobs assigned to each machine and the order of jobs such that the total machine load is minimized. Since the problem is NP-hard, optimal solution for the instances of realistic size cannot be obtained within a reasonable amount of computational time using exact solution approaches. Hence, an efficient method based on the hybrid particle swarm optimization (PSO) and genetic algorithm (GA), denoted by HPSOGA, is proposed to solve the given problem. In view of the fact that efficiency of the meta-heuristic algorithms is significantly depends on the appropriate design of parameters, the Taguchi method is employed to calibrate and select the optimal levels of parameters. The performance of the proposed method is appraised by comparing its results with GA and PSO with and without local search through computational experiments. The computational results for small sized problems show that the mentioned algorithms are fully effective and viable to generate optimal/near optimal solutions, but when the size of the problem is increased, the HPSOGA obtains better results in comparison with other algorithms.     

Two-stage hybrid batching flowshop scheduling with blocking and machine availability constraints using genetic algorithm

This research investigates a two-stage hybrid flowshop scheduling problem in a metal-working company. The first stage consists of multiple parallel machines and the second stage has only one machine. Four characteristics of the company have substantiated the complexity of the problem. First, all machines in stage one are able to process multiple jobs simultaneously but the jobs must be sequentially set up one after another. Second, the setup time of each job is separated from its processing time and depends upon its preceding job. Third, a blocking environment exists between two stages with no intermediate buffer storage. Finally, machines are not continuously available due to the preventive maintenance and machine breakdown. Two types of machine unavailability, namely, deterministic case and stochastic case, are identified in this problem. The former occurs on stage-two machine with the start time and the end time known in advance. The latter occurs on one of the parallel machine in stage one and a real-time rescheduling will be triggered. Minimizing the makespan is considered as the objective to develop the optimal scheduling algorithm. A genetic algorithm is used to obtain a near-optimal solution. The computational results with actual data are favorable and superior over the results from existing manual schedules.     

Flexible job shop scheduling with parallel machines using Genetic Algorithm and Grouping Genetic Algorithm

Based on Genetic Algorithm (GA) and Grouping Genetic Algorithm (GGA), this research develops a scheduling algorithm for job shop scheduling problem with parallel machines and reentrant process. This algorithm consists of two major modules: machine selection module (MSM) and operation scheduling module (OSM). MSM helps an operation to select one of the parallel machines to process it. OSM is then used to arrange the sequences of all operations assigned to each machine. A real weapon production factory is used as a case study to evaluate the performance of the proposed algorithm. Due to the high penalty of late delivery in military orders and high cost of equipment investment, total tardiness, total machine idle time and makespan are important performance measures used in this study. Based on the design of experiments, the parameters setting for GA and GGA are identified. Simulation results demonstrate that MSM and OSM respectively using GGA and GA outperform current methods used in practice.     

A two-stage Ant Colony optimization algorithm to minimize the makespan on unrelated parallel machines—part II: enhancements and experimentations

In a previous paper (Arnaout et al in J Intell Manuf 21:693–701, 2010), an Ant Colony optimization (ACO I) algorithm was introduced for minimizing the schedule’s makespan on unrelated parallel machines with sequence-dependent setup times. Optimal solutions for small instances of this problem were obtained by solving a mixed integer program. However, for larger instances (up to 10 machines and 120 jobs), heuristic and approximate algorithms were necessary to reach solutions in reasonable computational times. ACO I’s performance was evaluated by comparing its solutions to solutions obtained using Tabu Search and MetaRaPS (metaheuristic for Randomized Priority Search). While the results indicated that ACO I outperformed the other heuristics, it also showed that MetaRaPS had a better performance when all ratios of N/M (jobs to machines ratio) were considered. In this paper, we introduce an enhanced ACO which will be referred to as ACO II and compare its performance to other existing and new algorithms including ACO I, MetaRaPS, and SA. The extensive and expanded experiments conducted prove the superiority of the enhanced ACO II.     

Solving Part-Type Selection and Operation Allocation Problems in an FMS: An Approach Using Constraints-Based Fast Simulated Annealing Algorithm

Production planning of a flexible manufacturing system (FMS) is plagued by two interrelated problems, namely 1) part-type selection and 2) operation allocation on machines. The combination of these problems is termed a machine loading problem, which is treated as a strongly NP-hard problem. In this paper, the machine loading problem has been modeled by taking into account objective functions and several constraints related to the flexibility of machines, availability of machining time, tool slots, etc. Minimization of system unbalance (SU), maximization of system throughput (TH), and the combination of SU and TH are the three objectives of this paper, whereas two main constraints to be satisfied are related to time and tool slots available on machines. Solutions for such problems even for a moderate number of part types and machines are marked by excessive computational complexities and thus entail the application of some random search optimization techniques to resolve the same. In this paper, a new algorithm termed as constraints-based fast simulated annealing (SA) is proposed to address a well-known machine loading problem available in the literature. The proposed algorithm enjoys the merits of simple SA and simple genetic algorithm and is designed to be free from some of their drawbacks. The enticing feature of the algorithm is that it provides more opportunity to escape from the local minimum. The application of the algorithm is tested on standard data sets, and superiority of the same is witnessed. Intensive experimentations were carried out to evaluate the effectiveness of the proposed algorithm, and the efficacy of the same is authenticated by efficiently testing the performance of algorithm over well-known functions     

A scheduling problem in blocking hybrid flow shop robotic cells with multiple robots

This paper addresses the robotic scheduling problem in blocking hybrid flow shop cells that consider multiple part types, unrelated parallel machines, multiple robots and machine eligibility constraints. Initially, a mixed integer linear programming (MILP) model is proposed to minimize the makespan for this problem. Due to the complexity of the model, a simulated annealing (SA) based solution approach is developed for its solution. To increase the efficiency of the SA algorithm, a new neighborhood structure based on block properties is applied. The performance of the proposed SA is assessed over a set of randomly generated instances. The computational results demonstrate that the SA algorithm is effective with the employed neighborhood structure. Additionally, this study shows that the appropriate number of robots depends on the sequence of processing operations to be performed at each stage.     

Preemptive scheduling on two parallel machines with a single server

This paper addresses a preemptive scheduling problem on two parallel machines with a single server. Each job has to be loaded (setup) by the server before being processed on the machines. The preemption is allowed in this paper. The goal is to minimize the makespan. We first show that it is no of use to preempt the job during its setup time. Namely, every optimal preemptive schedule can be converted to another optimal schedule where all the setup times are non-preemptively performed on one machine. We then present an algorithm with a tight bound of 4/3 for the general case. Furthermore, we show that the algorithm can produce optimal schedules for two special cases: equal processing times and equal setup times, which are NP-hard in the non-preemptive version.     

Scheduling with multiple servers

In this paper, we consider the problem of scheduling a set of jobs on a set of identical parallel machines. Before the processing of a job can start, a setup is required which has to be performed by a given set of servers. We consider the complexity of such problems for the minimization of the makespan. For the problem with equal processing times and equal setup times we give a polynomial algorithm. For the problem with unit setup times, m machines and m − 1 servers, we give a pseudopolynomial algorithm. However, the problem with fixed number of machines and servers in the case of minimizing maximum lateness is proven to be unary NP-hard. In addition, recent algorithms for some parallel machine scheduling problems with constant precessing times are generalized to the corresponding server problems for the case of constant setup times. Moreover, we perform a worst case analysis of two list scheduling algorithms for makespan minimization.     

Glass container production scheduling through hybrid multi-population based evolutionary algorithm

Driven by a real-world application in the capital-intensive glass container industry, this paper provides the design of a new hybrid evolutionary algorithm to tackle the short-term production planning and scheduling problem. The challenge consists of sizing and scheduling the lots in the most cost-effective manner on a set of parallel molding machines that are fed by a furnace that melts the glass. The solution procedure combines a multi-population hierarchically structured genetic algorithm (GA) with a simulated annealing (SA), and a tailor-made heuristic named cavity heuristic (CH). The SA is applied to intensify the search for solutions in the neighborhood of the best individuals found by the GA, while the CH determines quickly values for a relevant decision variable of the problem: the processing speed of each machine. The results indicate the superior performance of the proposed approach against a state-of-the-art commercial solver, and compared to a non-hybridized multi-population GA.     

A two-stage Ant Colony Optimization algorithm to minimize the makespan on unrelated parallel machines with sequence-dependent setup times

This paper addresses the non-preemptive unrelated parallel machine scheduling problem with machine-dependent and sequence-dependent setup times. All jobs are available at time zero, all times are deterministic, and the objective is to minimize the makespan. An Ant Colony Optimization (ACO) algorithm is introduced in this paper and is applied to this NP-hard problem; in particular, the proposed ACO tackles a special structure of the problem, where the ratio of the number of jobs to the number of machines is large (i.e., for a highly utilized set of machines). Its performance is evaluated by comparing its solutions to solutions obtained using Tabu Search and other existing heuristics for the same problem, namely the Partitioning Heuristic and Meta-RaPS. The results show that ACO outperformed the other algorithms.     

An approach for modeling a new single machine scheduling problem with deteriorating and learning effects

This paper presents a new approach to model a mixed-integer mathematical programming for a single machine scheduling problem with deteriorating and learning effects. Neglecting the effect of performing a job on its own processing time is mentioned as a deficiency in the literature of industrial scheduling. At first, self-influential factors are defined and then equations are presented to utilize these new factors. GAMS IDE/CPLEX software is used to validate the represented model by solving small to medium-sized sample problems, in which the associate results are compared with a hybrid meta-heuristic algorithm based on Ant Colony Optimization (ACO), Genetic Algorithm (GA) and Imperialist Competitive Algorithm (ICA). The vitality of considering and modeling the effect of learning and deteriorating made by a job, on its own processing time is tested for several sample problems. Then a significant improvement is observed by comparing the results acquired by neglecting the self-influential factors with the results based on considering them. Finally, the computational results are analyzed and the conclusion is given.     

Scheduling problem in a two-machine flow line with the N-step prior-job-dependent set-up times

The purpose of this study is to develop effective scheduling methodologies for the shop scheduling problem of a flow line. The flow line consists of two machines where only the second machine has separable, external, and sequence-dependent set-up times. The length of set-up times required for a job depends not on the immediately preceding job but on the job which is n steps prior to it. The problem is solved by a dynamic programming with the objective of minimizing the make span. An optimal schedule is found utilizing the sequence dominance condition. Since the computational requirements of the dynamic programming are impracticably demanding for large-sized problems, a genetic algorithm is developed and its performance is examined through a comparative study.