A heuristic model for dynamic flexible job shop scheduling problem considering variable processing times

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed algorithm.     

Robust scheduling of a two-machine flow shop with uncertain processing times

This paper focuses on manufacturing environments where job processing times are uncertain. In these settings, scheduling decision makers are exposed to the risk that an optimal schedule with respect to a deterministic or stochastic model will perform poorly when evaluated relative to actual processing times. Since the quality of scheduling decisions is frequently judged as if processing times were known a priori, robust scheduling, i.e., determining a schedule whose performance (compared to the associated optimal schedule) is relatively insensitive to the potential realizations of job processing times, provides a reasonable mechanism for hedging against the prevailing processing time uncertainty. In this paper we focus on a two-machine flow shop environment in which the processing times of jobs are uncertain and the performance measure of interest is system makespan. We present a measure of schedule robustness that explicitly considers the risk of poor system performance over all potential realizations of job processing times. We discuss two alternative frameworks for structuring processing time uncertainty. For each case, we define the robust scheduling problem, establish problem complexity, discuss properties of robust schedules, and develop exact and heuristic solution approaches. Computational results indicate that robust schedules provide effective hedges against processing time uncertainty while maintaining excellent expected makespan performance     

Single machine scheduling problem with stochastic sequence-dependent setup times

In this study, we consider stochastic single machine scheduling problem. We assume that setup times are both sequence dependent and uncertain while processing times and due dates are deterministic. In the literature, most of the studies consider the uncertainty on processing times or due dates. However, in the real-world applications (i.e. plastic moulding industry, appliance assembly, etc.), it is common to see varying setup times due to labour or setup tools availability. In order to cover this fact in machine scheduling, we set our objective as to minimise the total expected tardiness under uncertain sequence-dependent setup times. For the solution of this NP-hard problem, several heuristics and some dynamic programming algorithms have been developed. However, none of these approaches provide an exact solution for the problem. In this study, a two-stage stochastic-programming method is utilised for the optimal solution of the problem. In addition, a Genetic Algorithm approach is proposed to solve the large-size problems approximately. Finally, the results of the stochastic approach are compared with the deterministic one to demonstrate the value of the stochastic solution.     

Robust makespan minimisation in identical parallel machine scheduling problem with interval data

Parallel machine scheduling problems are commonly encountered in a wide variety of manufacturing environments and have been extensively studied. This paper addresses a makespan minimisation scheduling problem on identical parallel machines, in which the specific processing time of each job is uncertain, and its probability distribution is unknown because of limited information. In this case, the deterministic or stochastic scheduling model may be unsuitable. We propose a robust (min–max regret) scheduling model for identifying a robust schedule with minimal maximal deviation from the corresponding optimal schedule across all possible job-processing times (called scenarios). These scenarios are specified as closed intervals. To solve the robust scheduling problem, which is NP-hard, we first prove that a regret-maximising scenario for any schedule belongs to a finite set of extreme point scenarios. We then derive two exact algorithms to optimise this problem using a general iterative relaxation procedure. Moreover, a good initial solution (optimal schedule under a mid-point scenario) for the aforementioned algorithms is discussed. Several heuristics are developed to solve large-scale problems. Finally, computational experiments are conducted to evaluate the performance of the proposed methods.     

Flow-line scheduling problem with controllable processing times

In this paper we address the simultaneous scheduling and optimal-processing-times selection problem in a multi-product deterministic flow line operated under a cyclic scheduling approach. The selection of processing times plays an important role in achieving the desired production rate with the least possible operating cost. We first formulate the important subproblem of optimal-processing-times selection for different objectives, when the sequence of jobs is fixed, and then develop an efficient solution procedure for it. The fast solution of the fixed sequence problem is necessary for the development of efficient approximate solution procedures for the simultaneous scheduling and optimal-processing-times problem. A computational study on the effectiveness of the proposed solution procedure is presented. For the solution of the simultaneous scheduling and optimal-processing-times problem we suggest an iterative solution procedure, and report our computational experience with this procedure. For the solution of large problems we present a genetic algorithm. The effectiveness of the algorithm is demonstrated through computational results and by evaluating the performance of the obtained solutions against lower bounds that we developed for the problem.     

A heuristic algorithm for master production scheduling problem with controllable processing times and scenario-based demands

Master production scheduling (MPS) is widely used by manufacturing industries in order to handle the production scheduling decisions in the production planning hierarchy. The classical approach to MPS assumes infinite capacity, fixed (i.e. non-controllable) processing times and a single pre-determined scenario for the demand forecasts. However, the deterministic optimisation approaches are sometimes not suitable for addressing the real-world problems with high uncertainty and flexibility. Accordingly, in this paper, we propose a new practical model for designing an optimal MPS for the environments in which processing times may be controllable by allocating resources such as facilities, energy or manpower. Due to the NP-hardness of our model, an efficient heuristic algorithm using local search technique and theory of constraints is developed and analysed. The computational results especially for large-sized test problems show that the average optimality gap of proposed algorithm is four times lower than that of exact solution using GAMS while it consumes also significantly smaller run times. Also, the analysis of computational results confirms that considering the controllable processing times may improve the solution space and help to more efficiently utilise the available resources. According to the model structure and performance of the algorithm, it may be proposed for solving large and complex real-world problems particularly the machining and steel industries.     

A branch and bound algorithm for optimal cyclic scheduling in a robotic cell with processing time windows

A branch and bound algorithm is described for optimal cyclic scheduling in a robotic cell with processing time windows. The objective is to minimise the cycle time by determining the exact processing time on each machine which is limited within a time window. The problem is formulated as a set of prohibited intervals of the cycle time, which is usually applied in the robotic cyclic scheduling problem with fixed processing times. Since both bounds of these prohibited intervals are linear expressions of the processing times, we divide these prohibited intervals into a series of the subsets and transform the problem into enumerating the non-prohibited intervals of cycle time in each subset. This enumeration procedure is completed by an efficient branch and bound algorithm, which could find an optimal solution by enumerating partial non-prohibited intervals. Computational results on the benchmark instances and randomly generated test instances indicate that the algorithm is effective.     

Scheduling trucks in container terminals using a genetic algorithm

Trucks are the most popular transport equipment in most mega-terminals, and scheduling them to minimize makespan is a challenge that this article addresses and attempts to resolve. Specifically, the problem of scheduling a fleet of trucks to perform a set of transportation jobs with sequence-dependent processing times and different ready times is investigated, and the use of a genetic algorithm (GA) to address the scheduling problem is proposed. The scheduling problem is formulated as a mixed integer program. It is noted that the scheduling problem is NP-hard and the computational effort required to solve even small-scale test problems is prohibitively large. A crossover scheme has been developed for the proposed GA. Computational experiments are carried out to compare the performance of the proposed GA with that of GAs using six popular crossover schemes. Computational results show that the proposed GA performs best, with its solutions on average 4.05% better than the best solutions found by the other six GAs.     

Cultural algorithms,an alternative heuristic to solve the job shop scheduling problem

In this work, an approach for solving the job shop scheduling problem using a cultural algorithm is proposed. Cultural algorithms are evolutionary computation methods that extract domain knowledge during the evolutionary process. Additional to this extracted knowledge, the proposed approach also uses domain knowledge given a priori (based on specific domain knowledge available for the job shop scheduling problem). The proposed approach is compared with respect to a Greedy Randomized Adaptive Search Procedure (GRASP), a Parallel GRASP, a Genetic Algorithm, a Hybrid Genetic Algorithm, and a deterministic method called shifting bottleneck. The cultural algorithm proposed in this article is able to produce competitive results with respect to the two approaches previously indicated at a significantly lower computational cost than at least one of them and without using any sort of parallel processing.     

Minimising makespan on parallel batch processing machines with non-identical ready time and arbitrary job sizes

This paper considers the parallel batch processing machine scheduling problem which involves the constraints of unequal ready times, non-identical job sizes, and batch dependent processing times in order to sequence batches on identical parallel batch processing machines with capacity restrictions. This scheduling problem is a practical generalisation of the classical parallel batch processing machine scheduling problem, which has many real-world applications, particularly, in the aging test operation of the module assembly stage in the manufacture of thin film transistor liquid crystal displays (TFT-LCD). The objective of this paper is to seek a schedule with a minimum total completion time for the parallel batch processing machine scheduling problem. A mixed integer linear programming (MILP) model is proposed to optimise the scheduling problem. In addition, to solve the MILP model more efficiently, an effective compound algorithm is proposed to determine the number of batches and to apply this number as one parameter in the MILP model in order to reduce the complexity of the problem. Finally, three efficient heuristic algorithms for solving the large-scale parallel batch processing machine scheduling problem are also provided.     

An immune algorithm for scheduling a hybrid flow shop with sequence-dependent setup times and machines with random breakdowns

Much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. Furthermore, most scheduling problems that have been discussed in the literature are under the assumption that machines are continuously available. Nevertheless, in most real-life industries a machine can be unavailable for many reasons, such as unanticipated breakdowns (stochastic unavailability), or due to scheduled preventive maintenance where the periods of unavailability are known in advance (deterministic unavailability). This paper deals with hybrid flow shop scheduling problems in which there are sequence-dependent setup times (SDSTs), and machines suffer stochastic breakdowns, to optimise objectives based on the expected makespan. With the increase in manufacturing complexity, conventional scheduling techniques for generating a reasonable manufacturing schedule have become ineffective. An immune algorithm (IA) can be used to tackle complex problems and produce a reasonable manufacturing schedule within an acceptable time. In this research, a computational method based on a clonal selection principle and an affinity maturation mechanism of the immune response is used. This paper describes how we can incorporate simulation into an immune algorithm for the scheduling of a SDST hybrid flow shop with machines that suffer stochastic breakdowns. The results obtained are analysed using a Taguchi experimental design.     

Bi-criteria SDST hybrid flow shop scheduling with learning effect of setup times: water flow-like algorithm approach

In studies on automatic scheduling problems, processing times do not differ according to repetition of job or process sequences so it may also be necessary to consider processing times independent from setup times. While considering setup times, the human factor has an important effect on setup, so by the processing of similar tasks frequently worker skills improve and they are able to perform setup at a greater pace. This fact is known as the ‘learning effect’ in the literature. This paper deals with sequence-dependent setup times (SDSTs) hybrid flow shop scheduling with learning effect of setup times for minimising weighted sum of makespan and total tardiness. A mathematical programming model that incorporates these aspects of the problem is developed which belongs to the NP-hard class. Thus, because of the intensive computation, we propose a novel meta-heuristic approach called water flow-like algorithm (WFA) which has the feature of multiple and dynamic numbers of solution agents. Various parameters of the problem and the WFA are reviewed by means of Taguchi experimental design. For the evaluation of the proposed WFA, problem data was generated to compare it against a random key genetic algorithm (RKGA). The results demonstrate the high performance of the WFA with respect to the RKGA.     

A new Nawaz–Enscore–Ham-based heuristic for permutation flow-shop problems with bicriteria of makespan and machine idle time

A new heuristic based on the Nawaz–Enscore–Ham algorithm is proposed in this article for solving a permutation flow-shop scheduling problem. A new priority rule is proposed by accounting for the average, mean absolute deviation, skewness and kurtosis, in order to fully describe the distribution style of processing times. A new tie-breaking rule is also introduced for achieving effective job insertion with the objective of minimizing both makespan and machine idle time. Statistical tests illustrate better solution quality of the proposed algorithm compared to existing benchmark heuristics.     

Modelling and scheduling analysis of multi-cluster tools with residency constraints based on time constraint sets

This paper is dedicated to the scheduling problem of multi-cluster tools with process module residency constraints and multiple wafer product types. The problem is formulated as a non-linear programming model based on a set of time constraint sets. An effective algorithm called the time constraint sets based (TCSB) algorithm is presented as a new method to schedule the transport modules to minimise the makespan of a number of wafers. In approach, time constraint sets are maintained for all the resources and necessary operations to exploit the remaining production capacities during the scheduling process. To validate the proposed algorithm on a broader basis, a series of simulation experiments are designed to compare our TCSB algorithm with the benchmark with regard to cluster factor, configuration flexibilities and the variation of the processing times and residency constraint times. The results indicate that the proposed TCSB algorithm gives optimal or near optimal scheduling solutions in most cases.     

Multi-objective fuzzy parallel machine scheduling problems under fuzzy job deterioration and learning effects

This paper investigates a multi-objective parallel machine scheduling problem under fully fuzzy environment with fuzzy job deterioration effect, fuzzy learning effect and fuzzy processing times. Due dates are decision variables for the problem and objective functions are to minimise total tardiness penalty cost, to minimise earliness penalty cost and to minimise cost of setting due dates. Due date assignment problems are significant for Just-in-Time (JIT) thought. A JIT company may want to have optimum schedule by minimising cost combination of earliness, tardiness and setting due dates. In this paper, we compare different approaches for modelling fuzzy mathematical programming models with a local search algorithm based on expected values of fuzzy parameters such as job deterioration effect, learning effect and processing times.     

Workload allocation in multi-product, multi-facility production systems with setup times

In this article, we model the problem of assigning work to M heterogeneous servers (machines), which arises from exogenous demands for N products, in the presence of nonzero setup times. We seek a workload allocation which minimizes the total expected Work-in-Progress (WIP) inventory. Demands are assumed to arrive according to independent Poisson processes, but the setup and the processing times can have arbitrary distributions. Whenever a machine produces more than one product type, production batch sizes are determined by a group scheduling policy; which is also known as the cyclic-exhaustive polling policy. We formulate the workload allocation problem as a nonlinear optimization problem and then provide several insights gleaned from first order necessary conditions, from numerical examples, and from a close examination of the objective function. For example, we show that increasing either the load or the number of products assigned to a machine, or both, does not necessarily increase its contribution to total WIP. These insights are then used to devise a heuristic workload allocation as well as a lower bound. The heuristic allocation is further refined using a nonlinear optimization algorithm.     

A new approach to two-machine flow shop problem with uncertain processing times

This paper deals with the problem of optimization of job sequence in a two-machine flow shop problem in the presence of uncertainty. It is assumed that the processing times of jobs on the machines are described by triangular fuzzy sets. A new optimization algorithm based on Johnson”s algorithm for deterministic processing times and on an improvement of McCahon and Lee”s algorithm is developed and presented. In order to compare fuzzy processing times, McCahon and Lee use mean values of their corresponding fuzzy sets. It is shown that this approach cannot fully explore possible relationships between fuzzy sets. In order to overcome this drawback we consider different fuzzy sets determined by λ-cuts of the fuzzy processing times. Extensive experiments show that the new algorithm gives better solutions with respect to makespan than existing McCahon and Lee's algorithm.     

A scheduling problem in glass manufacturing

In this paper, a production scheduling problem in glass manufacturing is studied. The production facility consists of multiple identical production lines and each production line includes a number of serially arranged machines. The production is characterized by semi-ordered processing times in each product family, and the last machine in each production line is a bottleneck machine. Significant changeover times are required when products of different families are produced on a production line. The scheduling problem was modeled as a parallel no-delay flowshop scheduling problem (PNDFSP). The PNDFSP combines the parallel machine scheduling problem (PMSP) with the no-delay flowshop scheduling problem (NDFSP). While PMSP and NDFSP have received considerable attention in the literature, PNDFSP has not been well studied. A mixed-integer programming formulation is developed and an efficient heuristic algorithm is proposed. The sequential heuristic algorithm considers simultaneously the line changeover time, no-delay effect, and line utilization in assigning product families to the production lines. The computational results are reported.     

Hedge against total flow time uncertainty of the uniform parallel machine scheduling problem with interval data

We consider a total flow time minimisation problem of uniform parallel machine scheduling when job processing times are only known to be bounded within certain given intervals. A minmax regret model is proposed to identify a robust schedule that minimises the maximum deviation from the optimal total flow time over all possible realisations of the job processing times. To solve this problem, we first prove that the maximal regret for any schedule can be obtained in polynomial time. Then, we derive a mixed-integer linear programming (MILP) formulation of our problem by exploiting its structural properties. To reduce the computational time, we further transform our problem into a robust single-machine scheduling problem and derive another MILP formulation with fewer variables and constraints. Moreover, we prove that the optimal schedule under the midpoint scenario is a 2-approximation for our minmax regret problem. Finally, computational experiments are conducted to evaluate the performance of the proposed methods.     

Scheduling of machines and automated guided vehicles in FMS using differential evolution

This paper addresses the problem of simultaneous scheduling of machines and two identical automated guided vehicles (AGVs) in a flexible manufacturing system (FMS). For solving this problem, a new meta-heuristic differential evolution (DE) algorithm is proposed. The problem consists of two interrelated problems, scheduling of machines and scheduling of AGVs. A simultaneous scheduling of these, in order to minimise the makespan will result in a FMS being able to complete all the jobs assigned to it at the earliest time possible, thus saving resources. An increase in the performance of the FMS under consideration would be expected as a result of making the scheduling of AGVs as an integral part of the overall scheduling activity. The algorithm is tested by using problems generated by various researchers and the makespan obtained by the algorithm is compared with that obtained by other researchers and analysed.