Ant colony optimization for unrelated parallel machine scheduling

Meeting due dates is a major issue in most manufacturing systems, and one effective measure for due dates is total weighted tardiness. In this research, we consider an ant colony optimization (ACO) algorithm incorporating a number of new ideas (heuristic initial solution, machine reselection step, and local search procedure) to solve the problem of scheduling unrelated parallel machines to minimize total weighted tardiness. The problem is NP-hard in the strong sense, because the single machine case is already NP-hard in the strong sense. Computational results show that the proposed ACO algorithm outperforms other existing algorithms in terms of total weighted tardiness.     

A scheduling model for serial jobs on parallel machines with different preventive maintenance (PM)

In factories during production, preventive maintenance (PM) scheduling is an important problem in preventing and predicting the failure of machines, and most other critical tasks. In this paper, we present a new method of PM scheduling in two modes for more precise and better machine maintenance, as pieces must be replaced or be repaired. Because of the importance of this problem, we define multi-objective functions including makespan, PM cost, variance tardiness, and variance cost; we also consider multi-parallel series machines that perform multiple jobs on each machine and an aid, the analytic network process, to weight these objectives and their alternatives. PM scheduling is an NP-hard problem, so we use a dynamic genetic algorithm (GA) (the probability of mutation and crossover is changed through the main GA) to solve our algorithm and present another heuristic model (particle swarm optimization) algorithm against which to compare the GA’s answer. At the end, a numerical example shows that the presented method is very useful in implementing and maintaining machines and devices.     

The tricriteria flowshop scheduling problem

Multicriteria flowshop scheduling problems have been one of the most attractive subjects in recent years. In the multicriteria flowshop scheduling literature, a very limited number of studies have been performed on problems which include a tardiness criterion. In this paper a multicriteria (tricriteria) two-machine flowshop scheduling problem with a tardiness criterion is tackled. The objective is to minimise a weighted sum of total completion time, total tardiness and makespan. An integer programming model is proposed for the problem which belongs to NP-hard class. The modified NEH (Nawaz, Enscore and Ham) algorithm, a tabu search-based heuristic method, random search and the EDD rule (the earliest due date rule) are used to solve problems with up to 2,500 jobs. A computational analysis is conducted to evaluate the performance of the heuristics. The analysis shows that the heuristics are quite efficient, and the performance of the tabu search based heuristic is the best of all in terms of solution quality.     

A multi-objective electromagnetism algorithm for a bi-objective hybrid no-wait flowshop scheduling problem

This article studies multi-objective hybrid no-wait flowshop scheduling problems to minimize both makespan and total tardiness. This article mathematically formulates the problem using an effective multi-objective mixed integer linear programming models. Since the problem is NP-hard and it is difficult to find an optimal solution in a reasonable computational time, an efficient multi-objective electromagnetism algorithm (MOEA) is presented as the solution procedure. Electromagnetism algorithm is known as a flexible and effective population-based algorithm utilizing an attraction/repulsion mechanism to move the particles towards optimality. MOEA is carefully evaluated for its performance against multi-objective immune algorithms and the adaptation of a well-known multi-objective simulated annealing in the relevant literature by means of multi-objective performance measures and statistical tools. The results show that the proposed solution method outperforms the others.     

A drastic hybrid heuristic algorithm to approach to JIT policy considering controllable processing times

Job scheduling has always been a challenging task in modern manufacturing and the most real life scheduling problems which involves multi-criteria, multi-machine environments. In this research, the single-machine scheduling problem is studied in which job processing times are controllable, namely, they may vary within a specified interval. The goal of this research is to minimize total tardiness and earliness on a single machine, simultaneously. In this context, we first propose a mathematical model for the considered problem and then a net benefit compression–net benefit expansion heuristic is presented for obtaining the set of amounts of compression and expansion of jobs processing times in a given sequence. Two meta-heuristic approaches are then employed to solve medium-to-large-sized problems as local search methods. Thereafter, we apply a hybrid method based on our heuristic as well as these two meta-heuristics in order to obtain solutions with higher quality within lesser computational time. The addressed problem is NP-hard since the single machine total tardiness problem is already NP-hard. The computational results show that our proposed heuristics can effectively solve such Just-In-Time problem with a high-quality solution.     

Designing integrated cellular manufacturing systems with scheduling considering stochastic processing time

This paper addresses a new mathematical model for cellular manufacturing problem integrated with group scheduling in an uncertain space. This model optimizes cell formation and scheduling decisions, concurrently. It is assumed that processing time of parts on machines is stochastic and described by discrete scenarios enhances application of real assumptions in analytical process. This model aims to minimize total expected cost consisting maximum tardiness cost among all parts, cost of subcontracting for exceptional elements and the cost of resource underutilization. Scheduling problem in a cellular manufacturing environment is treated as group scheduling problem, which assumes that all parts in a part family are processed in the same cell and no inter-cellular transfer is needed. Finally, the nonlinear model will be transformed to a linear form in order to solve it for optimality. To solve such a stochastic model, an efficient hybrid method based on new combination of genetic algorithm (GA), simulated annealing (SA) algorithm, and an optimization rule will be proposed where SA and optimization rule are subordinate parts of GA under a self-learning rule criterion. Also, performance and robustness of the algorithm will be verified through some test problems against branch and bound and a heuristic procedure.     

Hybrid evolutionary algorithm with marriage of genetic algorithm and extremal optimization for production scheduling

This paper presents a hybrid evolutionary algorithm with marriage of genetic algorithm (GA) and extremal optimization (EO) for solving a class of production scheduling problems in manufacturing. The scheduling problem, which is derived from hot rolling production in steel industry, is characterized by two major requirements: (i) selecting a subset of orders from manufacturing orders to be processed; (ii) determining the optimal production sequence under multiple constraints, such as sequence-dependant transition costs, non-execution penalties, earliness/tardiness (E/T) penalties, etc. A combinatorial optimization model is proposed to formulate it mathematically. For its NP-hard complexity, an effective hybrid evolutionary algorithm is developed to solve the scheduling problem through combining the population-based search capacity of GA and the fine-grained local search efficacy of EO. The experimental results with production scale data demonstrate that the proposed hybrid evolutionary algorithm can provide superior performances in scheduling quality and computation efficiency.     

Bi-objective hybrid flow shop scheduling with sequence-dependent setup times and limited buffers

The bi-objective hybrid flow shop problem with sequence-dependent setup times and limited buffers is mentioned in this paper. In this environment, there are limited buffer spaces between any two successive stages; thus, maybe there is not enough room for queues of jobs that are waiting in the system for their next operations. This problem is shown to be NP-hard in the strong sense. Up to now, some heuristic and metaheuristic approaches are proposed to minimize makespan or total tardiness of jobs. This paper presents several methods for optimization which consider two objectives simultaneously. The resolution of several specific instances from the open literature with the adaptations of non-dominated sorting genetic algorithm and sub-population genetic algorithm suggest that the proposed algorithms are effective and useful methods for solving this problem.     

A hybrid GA–PSO approach for reliability optimization in redundancy allocation problem

This paper presents a novel hybrid genetic algorithm (GA)-particle swarm optimization (PSO) approach for reliability redundancy allocation problem (RRAP) in series, series–parallel, and complex (bridge) systems. The proposed approach maximizes overall system reliability while minimizing system cost, system weight and volume, simultaneously, under nonlinear constraints. To meet these objectives, an adaptive hybrid GA–PSO approach is developed to identify the optimal solutions and improve computation efficiency for these NP-hard problems. An illustrative example is applied to show the capability and effectiveness of the proposed approach. According to the results, in all three cases, reliability values are improved. Moreover, computational time and variance are decreased compared to the similar studies. The proposed approach could be helpful for engineers and managers to better understand their system reliability and performance, and also to reach a better configuration.     

A greedy heuristic and simulated annealing approach for a bicriteria flowshop scheduling problem with precedence constraints—a practical manufacturing case

This paper considers a flowshop scheduling problem with two criteria, where the primary (dominant) criterion is the minimization of material waste and the secondary criterion is the minimization of the total tardiness time. The decision maker does not authorize trade-offs between the criteria. In view of the nature of this problem, a hierarchical (lexicographical) optimization approach is followed. An effective greedy heuristic is proposed to minimize the material waste and a simulated annealing (SA) algorithm is developed to minimize the total tardiness time, subjective to the constraint computed for the primary criterion. The solution accuracy is compared with the optimal solution obtained by complete enumeration for randomly generated problem sets. From the results, it is observed that the greedy heuristic produces the optimal solution and the SA solution does not differ significantly from the optimal solution.     

A genetic algorithm for the single machine preemptive scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we consider the single machine preemptive scheduling problem with linear earliness and quadratic tardiness penalties, with no machine idle time. The problem is strongly NP-hard. We proposed a new mathematical model, with non-linear terms and integer variables. We develop a genetic algorithm for solving the problem in medium and large size. The proposed procedure is compared with optimal solutions for the smaller instance sizes. The genetic procedure is also quite close to the optimum and provided an optimal solution for most of the test problems. Numerical examples show that the proposed algorithm is efficient and effective. Scheduling with early and tardy penalties has received extensive attention from the scheduling community because of its practical significance. Single machine scheduling environments actually occur in several practical applications. Also, the performance of many production systems is often determined by the schedules for a single bottleneck machine. Furthermore, the study of single machine problems frequently provides outcomes that prove functional for more complex scheduling areas.     

Production allocation optimization by combining distribution free approach with open queueing network theory

We consider production allocation in a discrete manufacturing system formulated as an open queueing network (OQN) composed of some GI/G/1 queueing systems. The lead time performance, such as expectation and variance, in the manufacturing system has been analyzed and discussed using the OQN theory in the previous works. Through the improvement of lead time performance, we can discuss the decrease of the tardiness cost for delivery in the manufacturing system. Then, although the distribution of lead time is frequently required in order to evaluate the tardiness cost for delivery, it is difficult to understand the distribution of lead time exactly. In this article, we have a challenge of assessing the tardiness cost by using only the limited information, such as the expectation and variance of lead time. Concretely, we evaluate the upper bound of tardiness cost by combining the distribution free approach (DFA) with the OQN analysis. Then, a new optimal allocation policy for the production and tardiness costs is proposed.     

Scheduling in a two-machine flow-shop for earliness/tardiness under learning effect

In the literature, earliness/tardiness (E/T) problem was known as weighted absolute deviation problem, and both tardiness and earliness is very important performance criteria for scheduling problem. While total tardiness criteria provides adaptation for due date (ignoring results of earliness done jobs), it deals with only cost of tardiness. However this phenomenon has been started to change with just-in-time (JIT) production concept. On JIT production, earliness is as important as tardiness. The phenomenon of the learning effect has been extensively studied in many different areas of operational research. However, there have been a few studies in the general context of production scheduling such as flow-shop scheduling. This paper addresses the minimization of the total earliness/tardiness penalties under learning effects in a two-machine flow-shop scheduling problem. Jobs have a common due date. We present mathematical model to obtain an optimal schedule for a given job sequence. We also present heuristics that use genetic algorithm and tabu search, based on proposed properties. Furthermore, random search was used for showing the significance of the study by comparison purpose. A new set of benchmark problems is presented with the purpose of evaluating the heuristics. The experimental results show that the performance of proposed approach is quite well, especially for the instances of large size.     

A hybrid particle swarm optimization for parallel machine total tardiness scheduling

The parallel machine scheduling problem has received increasing attention in recent years. This research considers the problem of scheduling jobs on parallel machines with a total tardiness objective. In the view of its non-deterministic polynomial-time hard nature, the particle swarm optimization (PSO), which is inspired by the swarming or collaborative behavior of biological populations, is employed to solve the parallel machine total tardiness problem (PMTP). Since it is very hard to directly apply standard PSO to this problem, a new solution representation is designed based on real number encoding, which can conveniently convert the job sequences of PMTP to continuous position values. Moreover, in order to enhance the performance of PSO, we introduce clonal selection algorithm (CSA) into PSO and therefore propose a new CSPSO method. The incorporation of CSA can greatly improve the swarm diversity and avoid premature convergence. We further investigate three parameters of PSO and CSPSO, finding that the parameters have marginal impact on CSPSO, which indicates that CSPSO is a very stable and robust method. The performance of CSPSO is evaluated in comparison with traditional genetic algorithm (GA) and standard PSO on 250 benchmark instances. Experimental results show that CSPSO significantly outperforms GA and PSO, with obtaining the optimal solutions of 237 instances. Additionally, PSO appears more effective than GA.     

Genetic algorithms for minimizing makespan in a flow shop with two capacitated batch processing machines

This paper considers a flow shop with two batch processing machines. The processing times of the job and their sizes are given. The batch processing machines can process multiple jobs simultaneously in a batch as long as the total size of all the jobs in a batch does not exceed its capacity. When the jobs are grouped into batches, the processing time of the batch is defined by the longest processing job in the batch. Batch processing machines are expensive and a bottleneck. Consequently, the objective is to minimize the makespan (or maximize the machine utilization). The scheduling problem under study is NP-hard, hence, a genetic algorithm (GA) is proposed. The effectiveness (in terms of solution quality and run time) of the GA approach is compared with a simulated annealing approach, a heuristic, and a commercial solver which was used to solve a mixed-integer formulation of the problem. Experimental study indicates that the GA approach outperforms the other approaches by reporting better solution.     

Multi-machine earliness and tardiness scheduling problem: an interconnected neural network approach

This paper addresses the problem of scheduling a set of independent jobs with sequence-dependent setups and distinct due dates on non-uniform multi-machines to minimize the total weighted earliness and tardiness, and explores the use of artificial neural networks as a valid alternative to the traditional scheduling approaches. The objective is to propose a dynamical gradient neural network, which employs a penalty function approach with time varying coefficients for the solution of the problem which is known to be NP-hard. After the appropriate energy function was constructed, the dynamics are defined by steepest gradient descent on the energy function. The proposed neural network system is composed of two maximum neural networks, three piecewise linear and one log-sigmoid network all of which interact with each other. The motivation for using maximum networks is to reduce the network complexity and to obtain a simplified energy function. To overcome the tradeoff problem encountered in using the penalty function approach, a time varying penalty coefficient methodology is proposed to be used during simulation experiments. Simulation results of the proposed approach on a scheduling problem indicate that the proposed coupled network yields an optimal solution which makes it attractive for applications of larger sized problems.     

ACO-based multi-objective scheduling of parallel batch processing machines with advanced process control constraints

This research was motivated by a scheduling problem in the dry strip operations of a semiconductor wafer fabrication facility. The machines were modeled as parallel batch processing machines with incompatible job families and dynamic job arrivals, and constraints on the sequence-dependent setup time and the qual-run requirements of advanced process control. The optimization had multiple objectives, the total weighted tardiness (TWT) and makespan, to consider simultaneously. Since the problem is NP-hard, we used an Ant Colony Optimization (ACO) algorithm to achieve a satisfactory solution in a reasonable computation time. A variety of simulation experiments were run to choose ACO parameter values and to demonstrate the performance of the proposed method. The simulation results showed that the proposed ACO algorithm is superior to the common Apparent Tardiness Cost-Batched Apparent Tardiness Cost rule for minimizing the TWT and makespan. The arrival time distribution and the number of jobs strongly affected the ACO algorithm’s performance.     

Ant colony system for job shop scheduling with time windows

Scheduling for a job shop production system is an integral aspect of production management. Scheduling operations must minimize stock, waste, and idle time and ensure on-time delivery of goods in a time window problem. In this study, due date is considered as an interval instead of a time point. This study addresses scheduling with a time window of job shop scheduling problem (JSP) and yields a solution that is close to the time window. The total penalty due to earliness and tardiness is minimized. As the problem is NP-hard, a mathematical model of the JSP with a time window is initially constructed, and data are then simulated. Solutions are obtained by ant colony optimization (ACO) programs written in C-language and are compared with the best solution obtained using LINGO 7.0 to determine the efficiency and robustness. Test results indicate that ACO is extremely efficient. Solution time using ACO is less than that using LINGO. Hence, ACO is both effective and efficient, which are two qualities stressed in business management.     

Solving single-machine total weighted tardiness problems with sequence-dependent setup times by meta-heuristics

Simulated annealing (SA), genetic algorithms (GA), and tabu search (TS) are the three well known meta-heuristics for combinatorial optimization problems. In this paper, single-machine total weighted tardiness problems with sequence-dependent setup times are solved by SA, GA, and TS approaches. A random swap and insertion search is applied in SA, and a mutation operator performed by a greedy local search is used in a GA. Similarly, a swap and an insertion tabu list are adopted in TS. To verify these proposed approaches, computational experiments were conducted on benchmark problem sets. The experimental results show that these approaches find new upper bound values for most benchmark problems within reasonable computational expenses.