A memetic algorithm for job shop scheduling using a critical-path-based local search heuristic

In this article, a new memetic algorithm has been proposed to solve job shop scheduling problems (JSSPs). The proposed method is a genetic-algorithm-based approach combined with a local search heuristic. The proposed local search heuristic is based on critical operations. It removes the critical operations and reassigns them to a new position to improve the fitness value of the schedule. Moreover, in this article, a new fitness function is introduced for JSSPs. The new fitness function called priority-based fitness function is defined in three priority levels to improve the selection procedure. To show the generality of our proposed method, we apply it to three different types of job scheduling problems including classical, flexible and multi-objective flexible JSSPs. The experiment results show the efficiency of the proposed fitness function. In addition, the results show that incorporating local search not only offers better solutions but also improves the convergence rate. Compared to the state-of-the-art algorithms, the proposed method outperforms the existing methods in classical JSSPs and offers competitive solutions in other types of scheduling problems.     

Local search algorithms for the multiprocessor flow shop scheduling problem

The multiprocessor flow shop scheduling problem is a generalization of the ordinary flow shop scheduling problem. The problem consists of both assigning operations to machines and scheduling the operations assigned to the same machine. We review the literature on local search methods for flow shop and job shop scheduling and adapt them to the multiprocessor flow shop scheduling problem. Other local search approaches we consider are variable-depth search and simulated annealing. We show that tabu search and variable-depth search with a neighborhood originated by Nowicki and Smutnicki outperform the other algorithms.     

Multifleet routing and multistop flight scheduling for schedule perturbation

Efficient and effective incidental scheduling techniques for schedule perturbation are essential to an airline carrier's operations. This research aims at developing a framework to assist carriers in fleet routing and flight scheduling for schedule perturbations in the operations of multifleet and multistop flights. The framework is based on a basic multifleet schedule perturbation model constructed as a timespace network from which strategic models are developed to research incidental scheduling. These network models are formulated as multiple commodity network flow problems. Lagrangian relaxation with subgradient methods accompanied by the network simplex method, a Lagrangian heuristic and a modified subgradient method are developed to solve the problems. A case study regarding the international operations of a major Taiwan airline carrier is presented.     

An Improved Genetic Algorithm for the Distributed and Flexible Job-shop Scheduling problem

The Distributed and Flexible Job-shop Scheduling problem (DFJS) considers the scheduling of distributed manufacturing environments, where jobs are processed by a system of several Flexible Manufacturing Units (FMUs). Distributed scheduling problems deal with the assignment of jobs to FMUs and with determining the scheduling of each FMU, in terms of assignment of each job operation to one of the machines able to work it (job-routing flexibility) and sequence of operations on each machine. The objective is to minimize the global makespan over all the FMUs. This paper proposes an Improved Genetic Algorithm to solve the Distributed and Flexible Job-shop Scheduling problem. With respect to the solution representation for non-distributed job-shop scheduling, gene encoding is extended to include information on job-to-FMU assignment, and a greedy decoding procedure exploits flexibility and determines the job routings. Besides traditional crossover and mutation operators, a new local search based operator is used to improve available solutions by refining the most promising individuals of each generation. The proposed approach has been compared with other algorithms for distributed scheduling and evaluated with satisfactory results on a large set of distributed-and-flexible scheduling problems derived from classical job-shop scheduling benchmarks.     

具有可变配送费用和固定配送时刻的单机排序问题

研究了单机环境下生产与配送的协同排序问题.有多个工件需要在一台机器上进行加工,加工完的工件需要分批配送到一个客户.每批工件只能在固定的几个配送时刻出发,不同的配送时刻对应着不同的配送费用.我们的目标是找到生产与配送的协同排序,极小化排序的时间费用与配送费用的加权和.研究了排序理论中主要的四个目标函数,构建了单机情况下的具体模型,分析了问题的复杂性,对于配送费用单调非增的情况给出了它们的最优算法.     

A genetic algorithm for resource investment project scheduling problem,tardiness permitted with penalty

In this paper a genetic algorithm for solving a class of project scheduling problems, called Resource Investment Problem, is presented. Tardiness of project is permitted with defined penalty. Elements of algorithm such as chromosome structure, unfitness function, crossover, mutation, immigration and local search operations are explained.     

A dynamic edge covering and scheduling problem: complexity results and approximation algorithms

We consider a new dynamic edge covering and scheduling problem that focuses on assigning resources to nodes in a network to minimize the amount of time required to process all edges in it. Resources need to be co-located at the endpoints of an edge for it to be processed and, therefore, this problem contains both edge covering and scheduling decisions. These new problems have motivating applications in traffic systems and military intelligence operations. We provide complexity results for the dynamic edge covering and scheduling problem over different types of networks. We then show that existing approximation algorithms for parallel machine scheduling problems can be leveraged to provide approximation algorithms for this new class of problems over certain types of networks.     

Statistical process control for monitoring scheduling performance—addressing the problem of correlated data

In both manufacturing and service operations effective scheduling plays an important role in achieving delivery performance and in utilizing resources economically. Classical scheduling theory takes a narrow, static view of performance. In reality the assessment of scheduling performance is a particularly difficult task. Typically scheduling is an activity that takes place repeatedly over time in the context of an overall planning and control architecture. Scheduling may be viewed as an activity within a process. Statistical Process Control (SPC) provides an attractive option for monitoring performance. In this paper we investigate the potential of applying SPC control charts in this context. The feasibility of monitoring flow time in a single processor model using control charts is studied using simulation. The application of control charts to monitor time-related measures in operational systems raises fundamental statistical problems. The need for approaches that are robust with respect to data correlation and lack of normality is shown to be an essential requirement. Residual-based approaches and the Exponentially Weighted Moving Average (EWMA) chart are shown to be reasonably effective in avoiding false alarms and in detecting process shifts. The applicability of the single processor model to more complex operational systems is discussed. The implications of the work for the design of performance monitoring and continuous improvement systems for time-related measures in manufacturing and service operations are considered. A number of areas are highlighted for further theoretical and practical studies.     

Algorithms for single machine total tardiness scheduling with sequence dependent setups

We consider the problem of scheduling a single machine to minimize total tardiness with sequence dependent setup times. We present two algorithms, a problem space-based local search heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP) for this problem. With respect to GRASP, our main contributions are—a new cost function in the construction phase, a new variation of Variable Neighborhood Search in the improvement phase, and Path Relinking using three different search neighborhoods. The problem space-based local search heuristic incorporates local search with respect to both the problem space and the solution space. We compare our algorithms with Simulated Annealing, Genetic Search, Pairwise Interchange, Branch and Bound and Ant Colony Search on a set of test problems from literature, showing that the algorithms perform very competitively.     

Analysis of the temporal decomposition procedure for scheduling with release and due dates

This paper first presents an improved method of temporal decomposition for minimising the searching space of scheduling problems. Next, the effects of the temporal decomposition procedure in scheduling problems are analysed. It is theoretically shown that the complexity of a scheduling algorithm using decomposed subsets varies inversely with that of the decomposition procedure. Therefore, the efficiency of the overall scheduling algorithm is strongly related to the decomposability of the set of operations to be processed on each machine. This decomposability is evaluated using a probabilistic approach where the probability distributions of the scheduling parameters are obtained from historical workshop data. The average number of decomposed subsets and the average size of these subsets are estimated. Both theoretical analysis and simulation results have revealed that the decomposition procedure leads to optimal effects when some conditions on scheduling parameters are met.     

Scheduling alternative operations in two-machine flow-shops

Most of the previous studies on scheduling problems assume that each machine is used exclusively for one operation although it has, in practice, potential to carry out some others. This paper studies two-machine flow-shop scheduling problems in which either or both machines are versatile so that alternative operations are possible. Branch-and-bound algorithms are developed to minimize the makespan of jobs for these problems and computational experiments are conducted to illustrate the effectiveness of these algorithms.     

Airline crew scheduling from planning to operations

Crew scheduling problems at the planning level are typically solved in two steps: first, creating working patterns, and then assigning these to individual crew. The first step is solved with a set covering model, and the second with a set-partitioning model. At the operational level, the (re) planning period is considerably smaller than during the strategic planning phase. We integrate both models to solve time critical crew recovery problems arising on the day of operations. We describe how pairing construction and pairing assignment are done in a single step, and provide solution techniques based on simple tree search and more sophisticated column generation and shortest-path algorithms.     

A note on scheduling alternative operations in two-machine flowshops

In this note, we consider a class of problems for scheduling a set of jobs each of which consists of two consecutive operations. The jobs are to be processed in a two-machine flowshop in which either or both machines are versatile. A versatile machine can perform both operations of a job. The objective is to minimise the makespan. While the whole class of problems has been shown to be NP-complete, we provide a general pseudopolynomial dynamic programming scheme which solves the problems analytically. This also establishes that the problems are only NP-complete in the ordinary sense. The solution scheme can be modified to solve another class of similar two-machine flowshop scheduling problems.     

Maximization of solution flexibility for robust shop scheduling

We consider the problem of introducing flexibility in the schedule determination phase, for shop scheduling problems with release dates and deadlines. The flexibility is provided by generating a family of schedules, instead of a unique one. We represent a family of schedules by an ordered group assignment defining for each machine a sequence of groups where the operations within a group are totally permutable. We propose a polynomial time algorithm to evaluate the worst case completion time of operations in an ordered group assignment. We then consider the single machine problem with heads and deadlines associated to operations, as a sub-problem of the job shop problem. We propose polynomial time dynamic programming algorithms for minimizing the number of groups and for maximizing the number of characterized sequences, under specific constraints. Finally, computational experiences on job shop benchmarks, show the impact of grouping operations on the solution makespan value.     

A note on “A mixed integer programming model for advanced planning and scheduling (APS)”

In a recent paper, Chen and Ji [Chen, K., Ji, P., 2007. A mixed integer programming model for advanced planning and scheduling (APS). European Journal of Operational Research 181, 515–522] develop a mixed integer programming model for advanced planning and scheduling problem that considers capacity constraints and precedence relations between the operations. The orders require processing of several operations on eligible machines. The model presented in the above paper works for the case where each operation can be processed on only one machine. However, machine eligibility means that only a subset of machines are capable of processing a job and this subset may include more than one machine. We provide a general model for advanced planning and scheduling problems with machine eligibility. Our model can be used for problems where there are alternative machines that an operation can be assigned to.     

A general model for cyclic machine scheduling problems

A general framework for modeling and solving cyclic scheduling problems is presented. The objective is to minimize the cycle time. The model covers different cyclic versions of the job-shop problem found in the literature, robotic cell problems, the single hoist scheduling problem and tool transportation between the machines.It is shown that all these problems can be formulated as mixed integer linear programs which have a common structure. Small instances are solved with CPLEX. For larger instances tabu search procedures have been developed. The main ideas of these methods are indicated.     

Integrating Interval Estimates of Global Optima and Local Search Methods for Combinatorial Optimization Problems

The problem of estimating the global optimal values of intractable combinatorial optimization problems is of interest to researchers developing and evaluating heuristics for these problems. In this paper we present a method for combining statistical optimum prediction techniques with local search methods such as simulated annealing and tabu search and illustrate the approach on a single machine scheduling problem. Computational experiments show that the approach yields useful estimates of optimal values with very reasonable computational effort.     

Single-machine time-dependent scheduling problems with fixed rate-modifying activities and resumable jobs

In this paper, we deal with single machine scheduling problems subject to time dependent effects. The main point in our models is that we do not assume a constant processing rate during job processing time. Rather, processing rate changes according to a fixed schedule of activities, such as replacing a human operator by a less skilled operator. The contribution of this paper is threefold. First, we devise a time-dependent piecewise constant processing rate model and show how to compute processing time for a resumable job. Second, we prove that any time-dependent continuous piecewise linear processing time model can be generated by the proposed rate model. Finally, we propose polynomial-time algorithms for some single machine problems with job independent rate function. In these procedures the job-independent rate effect does not imply any restriction on the number of breakpoints for the corresponding continuous piecewise linear processing time model. This is a clear element of novelty with respect to the polynomial-time algorithms proposed in previous contributions for time-dependent scheduling problems.     

Evaluation of mathematical models for flexible job-shop scheduling problems

With the rapid development in computer technologies, mathematical programming-based technique to solve scheduling problems is significantly receiving attention from researchers. Although, it is not efficient solution method due to the NP-hard structure of these problems, mathematical programming formulation is the first step to develop an effective heuristic. Numerous comparative studies for variety scheduling problems have appeared over the years. But in our search in literature there is not an entirely review for mathematical formulations of flexible job shop scheduling problems (FJSP). In this paper, four the most widely used formulations of the FJSP are compiled from literature and a time-indexed model for FJSP is proposed. These formulations are evaluated under three categories that are distinguished by the type of binary variable that they rely on for using of sequencing operations on machines. All five formulations compared and results are presented.