Showing papers on "Job shop scheduling published in 1995"

Speed is as Powerful as Clairvoyance.

Abstract: We introduce resource augmentation as a method for analyzing online scheduling problems. In resource augmentation analysis the on-line scheduler is given more resources, say faster processors or more processors, than the adversary. We apply this analysis to two well-known on-line scheduling problems, the classic uniprocessor CPU scheduling problem 1 |ri, pmtn|S Fi, and the best-effort firm real-time scheduling problem 1|ri, pmtn| S wi( 1- Ui). It is known that there are no constant competitive nonclairvoyant on-line algorithms for these problems. We show that there are simple on-line scheduling algorithms for these problems that are constant competitive if the online scheduler is equipped with a slightly faster processor than the adversary. Thus, a moderate increase in processor speed effectively gives the on-line scheduler the power of clairvoyance. Furthermore, the on-line scheduler can be constant competitive on all inputs that are not closely correlated with processor speed. We also show that the performance of an on-line scheduler is best-effort real time scheduling can be significantly improved if the system is designed in such a way that the laxity of every job is proportional to its length.

A reinforcement learning approach to job-shop scheduling

Abstract: We apply reinforcement learning methods to learn domain-specific heuristics for job shop scheduling. A repair-based scheduler starts with a critical-path schedule and incrementally repairs constraint violations with the goal of finding a short conflict-free schedule. The temporal difference algorithm TD(λ) is applied to tram a neural network to learn a heuristic evaluation function over states. This evaluation function is used by a one-step lookahead search procedure to find good solutions to new scheduling problems. We evaluate this approach on synthetic problems and on problems from a NASA space shuttle pay load processing task. The evaluation function is trained on problems involving a small number of jobs and then tested on larger problems. The TD scheduler performs better than the best known existing algorithm for this task--Zwehen's iterative repair method based on simulated annealing. The results suggest that reinforcement learning can provide a new method for constructing high-performance scheduling systems.

A GENETIC ALGORITHM FOR THE JOB SHOP PROBLEMf

Abstract: Scope and Purpoee--Job shop scheduling is a strongly NP-hard problem of combinatorial optimization and one of the most well-known machine scheduling problems. Scope of this paper is to present some improvements obtained in dealing with this problem using a heuristic technique based on Genetic Algorithms.

Implications of classical scheduling results for real-time systems

Abstract: Knowledge of complexity, fundamental limits and performance bounds-well known for many scheduling problems-helps real time designers choose a good design and algorithm and avoid poor ones. The scheduling problem has so many dimensions that it has no accepted taxonomy. We divide scheduling theory between uniprocessor and multiprocessor results. In the uniprocessor section, we begin with independent tasks and then consider shared resources and overload. In the multiprocessor section, we divide the work between static and dynamic algorithms. >

Robust scheduling to hedge against processing time uncertainty in single-stage production

Abstract: Schedulers confronted with significant processing time uncertainty often discover that a schedule which is optimal with respect to a deterministic or stochastic scheduling model yields quite poor performance when evaluated relative to the actual processing times. In these environments, the notion of schedule robustness, i.e., determining the schedule with the best worst-case performance compared to the corresponding optimal solution over all potential realizations of job processing times, is a more appropriate guide to schedule selection. In this paper, we formalize the robust scheduling concept for scheduling situations with uncertain or variable processing times. To illustrate the development of solution approaches for a robust scheduling problem, we consider a single-machine environment where the performance criterion of interest is the total flow time over all jobs. We define two measures of schedule robustness, formulate the robust scheduling problem, establish its complexity, describe properties of the optimal schedule, and present exact and heuristic solution procedures. Extensive computational results are reported to demonstrate the efficiency and effectiveness of the proposed solution procedures.

A heuristic algorithm for a dial-a-ride problem with time windows, multiple capacities, and multiple objectives

Abstract: The paper describes a system for the solution of a static dial-a-ride routing and scheduling problem with time windows (DARPTW). The problem statement and initialization of the development project was made by the Copenhagen Fire-Fighting Service (CFFS). The CFFS needed a new system for scheduling elderly and disabled persons, involving about 50.000 requests per year. The problem is characterized by, among other things, multiple capacities and multiple objectives. The capacities refer to the fact that a vehicle may be equipped with e.g. normal seats, children seats or wheel chair places. The objectives relate to a number of concerns such as e.g. short driving time, high vehicle utilization or low costs. A solution algorithm REBUS based on an insertion heuristics was developed. The algorithm permits in a flexible way weighting of the various goals such that the solution reflects the user's preferences. The algorithm is implemented in a dynamic environment intended for on-line scheduling. Thus, a new request for service is treated in less than 1 second, permitting an interactive user interface.

A generalized permutation approach to job shop scheduling with genetic algorithms

Abstract: In order to sequence the tasks of a job shop problem (JSP) on a number of machines related to the technological machine order of jobs, a new representation technique — mathematically known as “permutation with repetition” is presented. The main advantage of this single chromosome representation is — in analogy to the permutation scheme of the traveling salesman problem (TSP) — that it cannot produce illegal operation sequences. As a consequence of the representation scheme a new crossover operator preserving the initial scheme structure of permutations with repetition will be sketched. Its behavior is similar to the well known Order-Crossover for simple permutation schemes. Actually theGOX operator for permutations with repetition arises from aGeneralisation ofOX. Computational experiments show, that GOX passes the information from a couple of parent solutions efficiently to offspring solutions. Together, the new representation and GOX support the cooperative aspect of genetic search for scheduling problems strongly.

Hybrid Heuristics for the Vehicle Routing Problem with Time Windows

Abstract: This paper addresses the development of effective heuristics for solving the vehicle routing and scheduling problem with time window constraints. Both tour construction and local search tour improvement heuristics are developed. A major premise of the paper is that embedding global tour improvement procedures within the tour construction process can lead to improved solutions. Computational results are reported on test problems from the literature as well as real world applications. The hybrid construction/improvement heuristic is more effective in reducing vehicle fleet size requirements than previously reported heuristics.

The Two-Stage Assembly Scheduling Problem: Complexity and Approximation

Abstract: This paper introduces a new two-stage assembly scheduling problem. There are m machines at the first stage, each of which produces a component of a job. When all m components are available, a single assembly machine at the second stage completes the job. The objective is to schedule jobs on the machines so that the makespan is minimized. We show that the search for an optimal solution may be restricted to permutation schedules. The problem is proved to be NP-hard in the strong sense even when m = 2. A schedule associated with an arbitrary permutation of jobs is shown to provide a worst-case ratio bound of two, and a heuristic with a worst-case ratio bound of 2-1/m is presented. The compact vector summation technique is applied for finding approximation solutions with worst-case absolute performance guarantees.

A Time Window Approach to Simultaneous Scheduling of Machines and Material Handling System in an FMS

Abstract: This paper exploits the interactions between the machine scheduling and the scheduling of the material handling system in an FMS by addressing them simultaneously. The material transfer between machines is done by a number of identical automated guided vehicles (AGVs) which are not allowed to return to the load/unload station after each delivery. This operating policy introduces an additional complexity to the problem because it results in sequence-dependent travel times for the deadheading trips between successive loaded trips of the AGVs. The problem is formulated as a nonlinear mixed integer programming model. Its objective is makespan minimization. The formulation consists of constraint sets of a machine scheduling subproblem and a vehicle scheduling subproblem which interact through a set of time window constraints for the material handling trip starting times. An iterative procedure is developed where, at each iteration, a new machine schedule is generated by a heuristic procedure, the operation com...

Scheduling batch processing machines with incompatible job families

Abstract: The problem of scheduling a single batch processing machine with incompatible job families was studied, where jobs of different families cannot be processed together in the same batch. First static problems where all jobs are available simultaneously were considered and showed that for a regular performance measure there will be no unnecessary partial batches. This allowed us to develop efficient optimal algorithms to minimize makespan (Cmax), maximum lateness (Lmax) and total weighted completion time and apply some of these results to problems with parallel identical batch processing machines. Then problems withdynamic job arrivals were considered and an efficient optimal algorithm for minimizing Cmax and several heuristics to minimize Lmax were provided. Computational experiments showed that the heuristics developed for the latter problem consistently improve on dispatching solutions in very reasonable CPU times.

Scheduling algorithm of data sampling times in the integrated communication and control systems

Abstract: Integrated communication and control systems (ICCS) consist of several distributed control processes which share a network medium. Performance of several feedback control loops in the ICCS is subject to the network-induced delays from sensor to controller and from controller to actuator. The network-induced delays are directly dependent upon the data sampling times of the control components which share a network medium. In this study, a scheduling algorithm of determining data sampling times is developed using the window concept, where the sampled data from the control components in the ICCS share a limited number of windows, so that the performance requirement of each control loop is satisfied as well as the utilization of network resources is considerably increased. The scheduling algorithm is verified by discrete-event/continuous-time simulation model of an example of ICCS. >

Fuzzy constraints in job-shop scheduling

Abstract: This paper proposes an extension of the constraint-based approach to job-shop scheduling, that accounts for the flexibility of temporal constraints and the uncertainty of operation durations. The set of solutions to a problem is viewed as a fuzzy set whose membership function reflects preference. This membership function is obtained by an egalitarist aggregation of local constraint-satisfaction levels. Uncertainty is qualitatively described in terms of possibility distributions. The paper formulates a simple mathematical model of job-shop scheduling under preference and uncertainty, relating it to the formal framework of constraint-satisfaction problems in artificial intelligence. A combinatorial search method that solves the problem is outlined, including fuzzy extensions of well-known look-ahead schemes.

Task scheduling in multiprocessing systems

Abstract: The complex problem of assigning tasks to processing elements in order to optimize a performance measure has resulted in numerous heuristics aimed at approximating an optimal solution. This article addresses the task scheduling problem in many of its variations and surveys the major solutions. The scheduling techniques we discuss might be used by a compiler writer to optimize the code that comes out of a parallelizing compiler. The compiler would produce grains of sequential code, and the optimizer would schedule these grains such that the program runs in the shortest time.

Rolling horizon procedures for dynamic parallel machine scheduling with sequence-dependent setup times.

Abstract: SUMMARY We present a family of rolling horizon heuristics for minimizing maximum lateness on parallel identical machines in the presence of sequence dependent setup times and dynamic job arrivals. This problem arises as a subproblem in a decomposition procedure for more complex job shop scheduling problems. The procedures solve a series of single machine subproblems to optimality and implement only part of the solution. Extensive computational experiments show that these methods significantly outperform dispatching rules combined with local search methods, both on average and in the worst case. Their performance advantage is particularly pronounced when there is high competition for machine capacity.

Field Development Planning Using Simulated Annealing - Optimal Economic Well Scheduling and Placement

Abstract: A method for optimizing the net present value of a full field development by varying the placement and sequence of production wells is presented. This approach is automated and combines an economics package and Mobil's in-house simulator, PEGASUS, within a simulated annealing optimization engine. A novel framing of the well placement and scheduling problem as a classic travelling salesman problem is required before optimization via simulated annealing can be applied practically. An example of a full field development using this technique shows that non-uniform well spacings are optimal (from an NPV standpoint) when the effects of well interference and variable reservoir properties are considered. Examples of optimizing field NPV with variable well costs also show that non-uniform wells spacings are optimal. Project NPV increases of 25 to 30 million dollars were shown using the optimal, non-uniform development versus reasonable, uniform developments. The ability of this technology to deduce these non-uniform well spacings opens up many potential applications that should materially impact the economic performance of field developments.

The one-machine problem with delayed precedence constraints and its use in job shop scheduling

Abstract: We study the one machine scheduling problem with release and delivery times and the minimum makespan objective, in the presence of constraints that for certain pairs of jobs require a delay between the completion of the first job and the start of the second (delayed precedence constraints). This problem arises naturally in the context of the Shifting Bottleneck Procedure for the general job shop scheduling problem, as a relaxation of the latter, tighter than the standard one-machine relaxation. The paper first highlights the difference between the two relaxations through some relevant complexity results. Then it introduces a modified Longest Tail Heuristic whose analysis identifies those situations that permit efficient branching. As a result, an optimization algorithm is developed whose performance is comparable to that of the best algorithms for the standard one-machine problem. Embedding this algorithm into a modified version of the Shifting Bottleneck Procedure that uses the tighter one-machine relaxa...

Solving the job shop scheduling problem with tabu search

Abstract: In the job shop scheduling problem we desire to minimize the makespan where a set of machines perform technologically ordered operations unique to each member of a set of jobs. Each operation has a fixed time duration, no machine can perform more than one operation at a time, and preemption is not allowed. In this paper, an effective tabu search approach to the job shop scheduling problem is presented. The procedure starts from the best solution rendered by a set of 14 heuristic dispatching solutions. It then makes use of the classical disjunctive network representation of the problem and iteratively moves to another feasible solution by reversing the order of two adjacent critical path operations performed by the same machine. The concepts of historical generators and search restart are used in conjunction with a contiguous spectrum of short term memory values to enhance the overall exploration strategy. Computational results are presented and areas for future investigation are suggested.

An Evolutionary Tabu Search Algorithm And The NHL Scheduling Problem

Abstract: We present in this paper a new evolutionary procedure for solving general optimization problems that combines efficiently the mechanisms of genetic algorithms and tabu search. In order to explore the solution space properly interaction phases are interspersed with periods of optimization in the algorithm. An adaptation of this search principle to the National Hockey League (NHL) problem is discussed. The hybrid method developed in this paper is well suited for Open Shop Scheduling problems (OSSP). The results obtained appear to be quite satisfactory.

Optimal Scheduling of Urban Transit Systems Using Genetic Algorithms

Abstract: Scheduling of urban transit network can be formulated as an optimization problem of minimizing the overall transfer time (TT) of transferring passengers and initial waiting time (IWT) of the passengers waiting to board a bus/train at their point of origin. In this paper, a mathematical programming (MP) formulation of the scheduling problem at one transfer station is presented. The MP problem is large and nonlinear in terms of the decision variables, thereby making it difficult for classical programming techniques to solve the problem. We apply genetic algorithms (GAs)-search and optimization methods based on natural genetics and selection-to solve the scheduling problem. The main advantage of using GAs is that the problem can be reformulated in a manner that is computationally more efficient than the original problem. Further, the coding aspect of GAs inherently takes care of most of the constraints associated with the scheduling problem. Results from a number of test problems demonstrate that the GAs are able to find optimal schedules with a reasonable computational resource. The paper concludes by presenting a number of extensions to the present problem and discusses plausible solution techniques using GAs. The success of GAs in this paper suggests their efficacy as a solution tool for similar optimization problems arising in transportation systems.