Quantum annealing heuristics for the job shop scheduling problem with availability constraints

Scheduling machine-dependent jobs to minimize lateness on machines with identical speed under availability constraints

Optimization of the integrated problem of employee timetabling and job shop scheduling

Classical scheduling problem assumes that machines are available during the scheduling horizon. This assumption may be justified in some situations but it does not apply if maintenance requirements, machine breakdowns or other availability constraints have to be considered. In this paper, we treat a two-machine job shop scheduling problem with one availability constraint on each machine to minimise the maximum completion time (makespan). The unavailability periods are known in advance and the processing of an operation cannot be interrupted by an unavailability period (non-preemptive case). We present in our approach properties dealing with permutation dominance and the optimality of Jackson's rule under availability constraints. In order to evaluate the effectiveness of the proposed approach, we develop two mixed integer linear programming models and two schemes for a branch and bound method to solve the tackled problem. Computational results validate the proposed approach and prove the efficiency of the developed methods.

Fuzzy job shop scheduling problem with availability constraints

In this paper we consider a multiobjective job shop scheduling problem. The machines are subject to availability constraints that are due to preventive maintenance, machine breakdowns or tool replacement. Two optimization criteria were considered; the makespan for the jobs and the total cost for the maintenance activities. The job shop scheduling problem without considering the availability constraints is known to be NP-Hard. Because of the complexity of the problem, we develop a two-phase genetic algorithm based heuristic to solve the addressed problem. A set of pareto optimal solutions is obtained in the first phase containing relatively large number of solutions. This makes difficult the choice of the most suitable solution. For this reason the second phase will filter the obtained set so as to reduce its size. Performance of the proposed heuristic is evaluated through computational experiments on the benchmark of Muth & Thomson mt06 of 6×6 and 10 different sizes benchmarks of Lawrence. The results show that the heuristic gives solutions close to those obtained in the classic job shop scheduling problem.

Two-machine job shop problem under availability constraints on one machine: Makespan minimization

Heuristic algorithms for two-machine job shop problem under availability constraints on one machine: makespan minimization

In this paper we deal with variants of traditional cases of unavailability constraints in scheduling problems. In the literature, two main approaches are usually found. In the first one, operations can be interrupted by unavailability periods and in the second one, operations cannot be interrupted. The context we consider is more general; some operations can be interrupted, the others cannot. Moreover, we assume that information can be related to operations as well as to unavailability periods. Consequently an unavailability period can make possible or not the interruption of an operation. As an application to this new problem, the single machine problem with heads and tails and the job-shop scheduling problem are tackled. All combinations of possible cases are studied and after a review of the state-of-the-art, branch-and-bound algorithms are proposed to solve these problems. Finally, computational experiments are conducted and discussed.

Article history: Received April 17, 2012 Accepted 11 June 2012 Available online June 14 2012 In this paper, we consider job shop scheduling and machine location problem, simultaneously. Processing, transportation, and setup times are defined as deterministic parameters. The purpose of this paper is to determine machine location and job scheduling such that the make span and transportation cost is minimized. Therefore, the proposed model is a multi-objective problem one, where the first objective function minimizes make span and another minimizes the transportation cost. To solve the multi-objective problem, two methods are evaluated. Considering combination of job shop scheduling problem and machine location problem makes the proposed model more complex than job shop scheduling problem, which is an NP-hard problem. Therefore, to solve the proposed model, genetic algorithm as a meta-heuristic algorithm is implemented. To show the efficiency of the proposed genetic algorithm, 6×6 job shop scheduling problems are considered. © 2012 Growing Science Ltd. All rights reserved.

<p>Job shop scheduling (JSS) problems are difficult combinatorial optimisation problems that have been studied over the past 60 years. The goal of a JSS problem is to schedule the arriving jobs as effectively as possible on the limited machine resources on the shop floor. Each job has a sequence of operations that need to be processed on specific machines, but the machines can only process one job at a time. JSS and other types of scheduling are important problems in manufacturing systems, such as semiconductor manufacturing. In particular, this thesis focuses on dynamic JSS (DJSS) problems, where unforeseen events occur during processing that needs to be handled by the manufacturer. Examples of dynamic events that occur in DJSS problems are dynamic or unforeseen job arrivals, machine breakdowns, uncertain job processing times, and so on. A prominent method of handling DJSS problems is to design effective dispatching rules for the DJSS problem handled by the manufacturer. Dispatching rules are local decision makers that determine what job is processed by a machine when the machine finishes processing the previous job and becomes available. Dispatching rules have been investigated extensively by both academics and industry experts due to their simplicity, interpretability, low computational cost and their ability to cope effectively in dynamic environments. However, dispatching rules are designed for a specific DJSS problem and have no guarantee that they retain their effectiveness on other DJSS problems. In a real-world scenario, the properties of a manufacturing system can change over time, meaning that previously effective dispatching rule may longer be effective. Therefore, a manufacturer may need to redesign a dispatching rule to maintain a competitive edge on the market. However, designing an effective dispatching rule for a specific DJSS problem is expensive, and typically requires a human expert and extensive trial-and-error process to verify their effectiveness. To circumvent the manual design of dispatching rules, researchers have proposed hyper-heuristic approaches to automate the design of dispatching rules. In particular, various genetic programming based hyper-heuristic (GP-HH) approaches have been proposed in the literature to evolve effective dispatching rules for scheduling problems, including DJSS problems. However, there are many potential directions that have not been fully investigated. The overall goal of this thesis is to develop new and effective GP-HH approaches to designing high-quality dispatching rules for DJSS problems that aims to improve beyond the standard GP approach while maintaining computational efficiency. The focus will be on developing approaches which can decompose complex JSS problems down to simpler subcomponents, evolving multiple heuristics to handle the subcomponents, and developing GP-HH approaches that can handle complex DJSS problems by exploiting the problem properties. This thesis is the first to develop ensemble GP approaches that evolve ensembles of dispatching rules using cooperative coevolution. In addition, the thesis also investigates different combination schemes for one of the ensemble GP approaches to combine the ensemble member outputs effectively. The results show that ensemble GP approach evolves rules that perform significantly better than the rules evolved by the benchmark GP approach. This thesis provides the first investigation into applying GP-HH to a DJSS problem with dynamic job arrivals and machine breakdowns. In addition, the thesis also develops machine breakdown GP approach to the DJSS problem by incorporating machine breakdown GP terminals. The results show that the standard GP do not generalise well over the DJSS problem. The best rules from the machine breakdown GP approach do perform better than the best rule from the standard GP approach, and the analysis shows that the rules behaviour is similar to the shortest processing time rule in certain decision situations. This thesis is the first to develop a multitask GP approach to evolve a portfolio of dispatching rules for a DJSS problem with dynamic job arrivals and machine breakdowns. The multitask GP approach improve on the standard GP approach either in terms of the effectiveness of the output rules or the computation time required to evolve the rules. The analysis shows that the difference between DJSS problem having no machine breakdowns and having machine breakdowns is a more significant factor than the difference between two DJSS problems with different frequencies of machine breakdown investigated.</p>

<p>Job shop scheduling (JSS) problems are difficult combinatorial optimisation problems that have been studied over the past 60 years. The goal of a JSS problem is to schedule the arriving jobs as effectively as possible on the limited machine resources on the shop floor. Each job has a sequence of operations that need to be processed on specific machines, but the machines can only process one job at a time. JSS and other types of scheduling are important problems in manufacturing systems, such as semiconductor manufacturing. In particular, this thesis focuses on dynamic JSS (DJSS) problems, where unforeseen events occur during processing that needs to be handled by the manufacturer. Examples of dynamic events that occur in DJSS problems are dynamic or unforeseen job arrivals, machine breakdowns, uncertain job processing times, and so on. A prominent method of handling DJSS problems is to design effective dispatching rules for the DJSS problem handled by the manufacturer. Dispatching rules are local decision makers that determine what job is processed by a machine when the machine finishes processing the previous job and becomes available. Dispatching rules have been investigated extensively by both academics and industry experts due to their simplicity, interpretability, low computational cost and their ability to cope effectively in dynamic environments. However, dispatching rules are designed for a specific DJSS problem and have no guarantee that they retain their effectiveness on other DJSS problems. In a real-world scenario, the properties of a manufacturing system can change over time, meaning that previously effective dispatching rule may longer be effective. Therefore, a manufacturer may need to redesign a dispatching rule to maintain a competitive edge on the market. However, designing an effective dispatching rule for a specific DJSS problem is expensive, and typically requires a human expert and extensive trial-and-error process to verify their effectiveness. To circumvent the manual design of dispatching rules, researchers have proposed hyper-heuristic approaches to automate the design of dispatching rules. In particular, various genetic programming based hyper-heuristic (GP-HH) approaches have been proposed in the literature to evolve effective dispatching rules for scheduling problems, including DJSS problems. However, there are many potential directions that have not been fully investigated. The overall goal of this thesis is to develop new and effective GP-HH approaches to designing high-quality dispatching rules for DJSS problems that aims to improve beyond the standard GP approach while maintaining computational efficiency. The focus will be on developing approaches which can decompose complex JSS problems down to simpler subcomponents, evolving multiple heuristics to handle the subcomponents, and developing GP-HH approaches that can handle complex DJSS problems by exploiting the problem properties. This thesis is the first to develop ensemble GP approaches that evolve ensembles of dispatching rules using cooperative coevolution. In addition, the thesis also investigates different combination schemes for one of the ensemble GP approaches to combine the ensemble member outputs effectively. The results show that ensemble GP approach evolves rules that perform significantly better than the rules evolved by the benchmark GP approach. This thesis provides the first investigation into applying GP-HH to a DJSS problem with dynamic job arrivals and machine breakdowns. In addition, the thesis also develops machine breakdown GP approach to the DJSS problem by incorporating machine breakdown GP terminals. The results show that the standard GP do not generalise well over the DJSS problem. The best rules from the machine breakdown GP approach do perform better than the best rule from the standard GP approach, and the analysis shows that the rules behaviour is similar to the shortest processing time rule in certain decision situations. This thesis is the first to develop a multitask GP approach to evolve a portfolio of dispatching rules for a DJSS problem with dynamic job arrivals and machine breakdowns. The multitask GP approach improve on the standard GP approach either in terms of the effectiveness of the output rules or the computation time required to evolve the rules. The analysis shows that the difference between DJSS problem having no machine breakdowns and having machine breakdowns is a more significant factor than the difference between two DJSS problems with different frequencies of machine breakdown investigated.</p>

In many scheduling problems, machines can face availability constraints and as a result, they may stop for a while. In this paper, a novel definition for single machine scheduling problem with flexible periodic availability constraints has been provided. According to this definition, in each period, the duration of unavailability corresponding to the continuous working time of the machine changes in a discrete manner and it can adopt two different values. Therefore, such availability constraints are called bimodal availability constraints. The objective has been to minimise the total completion time. By considering the complexity issues through a mathematical model, a heuristic algorithm with the time complexity of and a branch-and-bound algorithm accompanied with several lemmas and efficient dominance rules are proposed in order to solve the problems optimally. Computational results for 1680 sample problems are employed to demonstrate that the branch-and-bound algorithm is able to solve problems up to 22 jobs and the mean average error for the heuristic algorithm is 1.05%.

In today’s world, the manufacturing systems are growing day by day and capable to produce the products on time as per the customers’ requirement. However, the energy consumption by these manufacturing systems has been ignored, and a higher amount of energy is consuming to increase the production rate. Therefore, it is must to consider the criteria of energy consumption along with other traditional objectives of performance measures. Thus, in the present work, energy consumption has been considered with other measures to solve the flexible job shop scheduling (JSS) problem. It is a non-polynomial (NP) hard problem, and this problem belongs to the class of combinatorial optimization, so it is difficult to solve with a simple and exact mathematical formulation. Thus, this article presents the modified genetic algorithm (GA)-based methodology to deal with flexible JSS problem. The GA has been modified in order to increase local search using variable neighbourhood search (VNS)-based mutation operator in order to avoid premature convergence of regular GA. The proposed approach considers multiple objectives in order to produce an optimized solution for flexible JSS problem such as makespan, processing cost as well as the energy consumption. In present work, an alternative (flexible) manufacturing process has been considered to extend the JSS problem. A suitable chromosome has been designed to code the schedule (solution) for JSS problem having additional processing flexibility. A case study (of 6 jobs and 15 machines) has been presented in order to assess the effectiveness of projected modified GA method. Results reveal that the proposed VNS-based approach in GA is effective enough to reduce makespan, processing cost as well as energy consumption performance measures.

Job shop scheduling (JSS) problems have been studied for over six decades. Many of them are proved to be non-deterministic polynomial-time (NP) hard, which means that they are intractable and the computation time increases exponentially with the problem size goes up. Some assumptions have been made in the previous studies about JSS problems in order to simplify the model and solve it. One of those assumption is that the transferring times of jobs between different machines are negligible. However, it is highly not practical not to model the material handling activities in a typical shop floor scheduling problems in reality, especially when the movements of jobs on shop floor are completely relying on the material handling equipment and the transferring times are comparable to the production times. Omitting the transferring times will make the result of scheduling impossible to be implemented. Therefore, many recent studies have been done about Job shop scheduling with material handling (JSPMH/JSSMH). The problem has been defined into two different categories: offline and online scheduling problems. Offline scheduling means solving JSSMH problem as static scheduling problem that is solved before shop floor starts its production with known or predicted information of orders, while online scheduling is dynamic scheduling problem that is solved to generate schedules in real time as orders arrive on the shop floor. In both methods, the simulation modeling tool has been widely used with its ability of efficiently searching for optimal solution as well as evaluating the results. In articles that study the JSSMH problems as the dynamic scheduling, simulation method has been popularly used to factor in various scenarios of production. Our review will comprehensively summarize how JSSMH problems are solved in dynamic and static problem settings, as well as how simulation models play a useful role in solving this type of problems.

The n-job, m-machine Job shop scheduling (JSP) problem is one of the general production scheduling problems. The JSP problem is a scheduling problem, where a set of ‘n’ jobs must be processed or assembled on a set of ‘m’ dedicated machines. Each job consists of a specific set of operations, which have to be processed according to a given technical precedence order. Job shop scheduling problem is a NP-hard combinatorial optimization problem.  In this paper, optimization of three practical performance measures mean job flow time, mean job tardiness and makespan are considered. The hybrid approach of Sheep Flocks Heredity Model Algorithm (SFHM) is used for finding optimal makespan, mean flow time, mean tardiness. The hybrid SFHM approach is tested with multi objective job shop scheduling problems. Initial sequences are generated with Artificial Immune System (AIS) algorithm and results are refined using SFHM algorithm. The results show that the hybrid SFHM algorithm is an efficient and effective algorithm that gives better results than SFHM Algorithm, Genetic Algorithm (GA). The proposed hybrid SFHM algorithm is a good problem-solving technique for job shop scheduling problem with multi criteria.