Fuzzy job shop scheduling problem with availability constraints

This chapter first presents job shop scheduling problems (JSSP) with fuzzy processing time and fuzzy trapezoid or doublet due-date. An efficient random key genetic algorithm (RKGA) is suggested, in which a random key representation and a new decoding strategy are proposed and two-point or discrete crossover are used. Performance analyses on random key representation are done and RKGA is compared with other algorithm. Computations results validate the effectiveness of random key representation and the promising advantage of RKGA on fuzzy scheduling.

There are many uncertain factors in job shop scheduling problems. However, those uncertainties are critical for the scheduling procedures. The imprecise processing times are modeled as triangular fuzzy numbers (TFNs) and the due dates are modeled as trapezium fuzzy numbers in this paper. A multi-objective genetic algorithm is proposed to solve fuzzy job shop scheduling problems, in which the objective functions are conflicting. Agreement index (AI) is used to show the satisfaction of client which is defined as value of the area of processing time membership function intersection divided by the area of the due date membership function. The multi-objective function is composed of maximize both the minimum agreement and maximize the average agreement index. Two benchmark problems were used to show the effectiveness of the proposed approach. Experimental results demonstrate that the multi-objective genetic algorithm does not get stuck at a local optimum easily, and it can solve job-shop scheduling problems with fuzzy processing time and fuzzy due date effectively.

Job-shop scheduling is a difficult problem, both theoretically and practically. The theoretical problems stem from the search for optimal schedules subject to a limited number of constraints, while the complexity of practical problems is due to the number and variety of constraints that are not rigid in the actual situations. Indeed, in real world descriptions there are many vaguely formulated relations and imprecise data. Although the job-shop scheduling problem has often been investigated, very little of this research is concerned with the uncertainty characterized by the imprecision in problem variables. In this paper, we consider a fuzzy job-shop scheduling problem with imprecise processing times. We use fuzzy numbers and level (/spl lambda/, 1) interval-valued fuzzy numbers for the representation of vague processing times. This problem is similar to a fuzzy multiple criteria optimization problem. The primary results obtained from this research are: (1) signed distance ranking fuzzy numbers used to obtain a job-shop scheduling problem in the fuzzy sense and (2) signed distance ranking level (/spl lambda/, 1) interval-valued fuzzy numbers used to obtain another such problem.

The environmental concerns are having a significant impact on the operation of power systems. The traditional Unit Commitment problem, which to minimizes the fuel cost is inadequate when environmental emissions are also considered in the operation of power plants. This paper presents a Biased Random Key Genetic Algorithm (BRKGA) approach combined with non-dominated sorting procedure to find solutions for the unit commitment multiobjective optimization problem. In the first stage, the BRKGA solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0,1]. In the subsequent stage, a nondominated sorting procedure similar to NSGA II is employed to approximate the set of Pareto solution through an evolutionary optimization process. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as, in the crossover strategy. Test results with the existent benchmark systems of 10 units and 24 hours scheduling horizon are presented. The comparison of the obtained results with those of other Unit Commitment (UC) multiobjective optimization methods reveal the effectiveness of the proposed method.

The Fuzzy Job-Shop Scheduling Problems (FJJSP) are NP-hard and several meta-heuristic optimization algorithms were considered to solve them. Since there are human errors and the possibility of system failure, the due date of each job cannot be crisp. So, the FJSSP with fuzzy due date created to consider the real-world realities. In this paper, two objects such as minimizing the maximum of the makespan and maximizing the minimum of the satisfaction degree are considered to solve the FJSSP with fuzzy due date. To achieve to this aim, a modified draft of multi-objective particle swarm optimization (MOPSO) are designed to obtain the optimal Pareto solutions. A technical preprocessing and dynamic management repository of non-dominated solutions are proposed to enhance the MOPSO. The comparison of the experimental results, based on a set of benchmark datasets, with the results of the non-dominated sorting genetic algorithm (NSGA-II) proves the advantages.

A hybrid algorithm combining chemical-reaction optimization and tabu search(CROTS) for solving the fuzzy job-shop scheduling problem(FJSSP) is investigated. The objective is to minimize the fuzzy makespan, i.e., the maximum fuzzy completion time. In the hybrid algorithm, encoding mechanism is realized through an operation sequence based way. Four improved Chemical-reaction optimization(CRO) collisions are embedded in the proposed algorithm, i.e., on-wall collision, inter-molecule collision, synthesis, and decomposition. An efficient crossover operator is designed and applied into the three elementary collisions, i.e., inter-molecule collision, synthesis, and decomposition. TS based local search is embedded to perform exploitation for the best molecule, which enhances the search ability of the algorithm. The proposed algorithm is tested on the sixteen well-known benchmark instances. Through the comparisons with other three present algorithms, the highly effective performance in exploration and exploitation capability of the proposed CROTS algorithm is concluded. Through the tests on eighteen randomly generated instances, the capability of CROTS for solving large scale problems is verified.

The problem of scheduling stochastic job shop subject to breakdown is seldom considered. This paper proposes an efficient genetic algorithm (GA) for the problem with exponential processing time and non-resumable jobs. The objective is to minimize the stochastic makespan itself. In the proposed GA, a novel random key representation is suggested to represent the schedule of the problem and a discrete event-driven decoding method is applied to build the schedule and handle breakdown. Probability stochastic order and the addition operation of exponential random variables are also used to calculate the objective value. The proposed GA is applied to some test problems and compared with a simulated annealing and a particle swarm optimization. The computational results show the effectiveness of the GA and its promising advantage on stochastic scheduling.

This paper proposes a methodology to design production strategy based on risk analysis using an integrated organization and process simulation. A process simulator is developed to evaluate the risk emerging from the integration of an organization model, a production model, feasibility constraints of factory, and teams' production strategies. The process simulation iterates with the following procedure: (1) extract the class of available workers, facilities, and activities in a time horizon, (2) prioritize the work using parameters of production strategy, (3) allocate workers and facilities to activities under the constraints of simulation, (4) determine if each worker can work or not based on an uncertainty ratio, (5) renew the condition of all activities, workers, facilities and time. Better production strategies are searched using a random key based genetic algorithm which minimizes the average total labor cost. The designer selects a production strategy considering average total labor cost and standard deviation of total labor cost. The proposed methodology is applied to case studies of the block assembly process in a shipbuilding company. Results show that the proposed methodology can evaluate organizational performance based on total labor cost including risk. Furthermore, the case studies confirm that an adequate production strategy can be selected given the constraints of a specific factory.

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

This paper presents a two-stage genetic algorithm (2S-GA) for multi-objective Job Shop scheduling problems. The 2S-GA is proposed with three criteria: Minimize makespan, Minimize total weighted earliness, and Minimize total weighted tardiness. The proposed algorithm is composed of two Stages: Stage 1 applies parallel GA to find the best solution of each individual objective function with migration among populations. In Stage 2 the populations are combined. The evolution process of Stage 2 is based on Steady-State GA using the weighted aggregating objective function. The algorithm developed can be used with one or two objectives without modification. The genetic algorithm is designed and implemented with the GALIB object library. The random keys representation is applied to the problem. The schedules are constructed using a permutation with m-repetitions of job numbers. Performance of the proposed algorithm is tested on published benchmark instances and compared with results from other published approaches for both the single objective and multi-objective cases. The experimental results show that 2S-GA is effective and efficient to solve job shop scheduling problem in term of solution quality.

Production scheduling is a critical requirement in today’s production systems. The production scheduling problem focuses on the rational allocation of production resources, determining the processing order of production tasks and operations, satisfying production constraints arising from the production environment such as the number of machines and task duration, and achieving optimal production goals, such as completing all tasks in the fastest way possible. The Flexible Job Shop Scheduling (FJSP) problem is a classical production scheduling issue, an extension of the Job Shop Scheduling (JSP) problem. The JSP problem involves allocating a set of jobs to a set of machines, where each job consists of multiple operations that must adhere to a precedence order. Each machine can process only one operation at a time for each job, and the time required for each operation on the corresponding machine is predetermined. The challenge in the JSP problem is to determine an appropriate order for processing operations or assignments, based on the production objective. FJSP represents a more complex and flexible variant of this problem, where at least one operation of a task can be performed on a set of alternative machines. Given that FJSP problems are NP-hard, solutions tend to be complex, varied, and often have limited applicability. Many FJSP scenarios require targeted modeling. In this paper, I propose a modeling approach for the static scheduling problem of job shops, considering low flexibility and demonstrating its usability by comparing it with other scheduling approaches, such as those based on genetic algorithm modeling. The paper is organized as follows:The first part of this paper offers a brief introduction to the FJSP problem, including background, research motivation, and main contributions, the second part provides a literature review,including a brief review and introduction of recent solutions to the FJSP problem, the third part describes a specific modeling approach, the fourth part details the test experiments and results of the modeling approach and includes comparisons with some other approaches, the fifth part analyzes the results from the fourth part and discusses the advantages and disadvantages of the modeling approach relative to others, and the sixth part concludes with a summary of findings and recommendations.

A single-machine scheduling problem with maintenance activities to minimize makespan

In this paper we consider the single machine scheduling problem with availability constraints in order to minimize the total completion times of jobs. We propose two exact approaches to solve the problem: a dynamic programming and a branch and bound method. The study of these approaches is carried out in this article and a concluding analysis based on several experimental results allows us to select the most suitable method according to the studied instance.

This paper incorporates the preventive maintenance activities into the two-stage assembly flow-shop scheduling problem, which has m machines at the production stage and an assembly machine at the second one. In this paper, three maintenance policies are employed based on the maximization of machine’s reliability and availability. This problem is NP-hard. So, two hybrid optimization methods, namely variable neighborhood search together with simulated annealing algorithm, and variable neighborhood search along with tabu search algorithm, are used to find the proper job sequencing. Statistical methods are conducted based on the hypothetical testing and analysis of variance to determine the better solution method and sensitivity analysis. Also, the performances of the presented algorithms on the problems of different sizes are analyzed. Results have shown that variable neighborhood search with simulated annealing outperforms another algorithm in the quality of solutions and computational time.

This paper presents a feasible optimal solution to the maintenance-scheduling problem of medical equipment. The proposed approach is based on the exponential survival model developed by the authors. Based on the data analysis obtained for Infusion Pumps and the associated survival function, the problem of preventive maintenance scheduling is formulated as a Mixed-Integer Mathematical Linear Programming (MILP) problem. The overall problem was solved using MATLAB and CPLEX. The obtained results that correspond to the maintenance scheduling plan was compared to the results obtained using a Greedy Algorithm (GA) by analysing both the survival index of each equipment and the availability constraint. Simulations results show that the Greedy Algorithm gives the same optimal solution to the scheduling plan problem as the MILP.