Showing papers on "Job shop scheduling published in 1997"

Scheduling to minimize average completion time: off-line and on-line approximation algorithms

Abstract: In this paper we introduce two general techniques for the design and analysis of approximation algorithms for NP-hard scheduling problems in which the objective is to minimize the weighted sum of the job completion times. For a variety of scheduling models, these techniques yield the first algorithms that are guaranteed to find schedules that have objective function value within a constant factor of the optimum. In the first approach, we use an optimal solution to a linear programming relaxation in order to guide a simple list-scheduling rule. Consequently, we also obtain results about the strength of the relaxation. Our second approach yields on-line algorithms for these problems: in this setting, we are scheduling jobs that continually arrive to be processed and, for each time t, we must construct the schedule until time t without any knowledge of the jobs that will arrive afterwards. Our on-line technique yields constant performance guarantees for a variety of scheduling environments, and in some cases essentially matches the performance of our off-line LP-based algorithms.

An integrated approach for modeling and solving the general multiprocessor job-shop scheduling problem using tabu search

Abstract: The problem considered in this paper is an important extension of the classical job-shop scheduling problem, where the same operation can be performed on more than one machine. The problem is to assign each operation to a machine and to sequence the operations on the machines, such that the makespan of a set of jobs is minimized. We introduce an extended version of the disjunctive graph model, that is able to take into account the fact that operations have to be assigned to machines. This allows us to present an integrated approach, by defining a neighborhood structure for the problem where there is no distinction between reassigning or resequencing an operation. This neighborhood is proved to be connected. A tabu search procedure is proposed and computational results are provided.

Energy minimization using multiple supply voltages

Abstract: We present a dynamic programming technique for solving the multiple supply voltage scheduling problem in both nonpipelined and functionally pipelined data-paths. The scheduling problem refers to the assignment of a supply voltage level (selected from a fixed and known number of voltage levels) to each operation in a data flow graph so as to minimize the average energy consumption for given computation time or throughput constraints or both. The energy model is accurate and accounts for the input pattern dependencies, re-convergent fanout induced dependencies, and the energy cost of level shifters. Experimental results show that using three supply voltage levels on a number of standard benchmarks, an average energy saving of 40.19% (with a computation time constraint of 1.5 times the critical path delay) can be obtained compared to using a single supply voltage level.

Performance analysis of embedded software using implicit path enumeration

Abstract: Embedded computer systems are characterized by the presence of a processor running application-specific dedicated software. A large number of these systems must satisfy real-time constraints. This paper examines the problem of determining the extreme (best and worst) case bounds on the running time of a given program on a given processor. This has several applications in the design of embedded systems with real-time constraints. An important aspect of this problem is determining which paths in the program are exercised in the extreme cases. The state-of-the-art solution here relies on an explicit enumeration of program paths. This solution runs out of steam rather quickly since the number of feasible program paths is typically exponential in the size of the program. We present a solution for this problem that does not require an explicit enumeration of program paths, i.e., the paths are considered implicitly. This solution is implemented in the program cinderella (in recognition of her hard real-time constraint-she had to be back home at the stroke of midnight), which currently targets a popular embedded processor-the Intel i960. The preliminary results of using this tool are also presented here.

A heuristic to minimize the total weighted tardiness with sequence-dependent setups

Abstract: We propose a three-phase heuristic for the problem of minimizing the total weighted tardiness on a single machine in the presence of sequence-dependent setup times. In the first phase a number of parameters characterizing the problem instance at hand are calculated. In the second phase we develop a schedule by using a new priority rule whose parameters are calculated based on the results of the first phase. Computational experiments show that this rule significantly outperforms the only other rule so far developed in the literature. The third phase consists of a local improvement procedure to improve the schedule obtained in the second phase. The procedure we suggest has been successfully implemented in an industrial scheduling system.

Current trends in deterministic scheduling

Abstract: Scheduling is concerned with allocating limited resources to tasks to optimize certain objective functions. Due to the popularity of the Total Quality Management concept, on-time delivery of jobs has become one of the crucial factors for customer satisfaction. Scheduling plays an important role in achieving this goal. Recent developments in scheduling theory have focused on extending the models to include more practical constraints. Furthermore, due to the complexity studies conducted during the last two decades, it is now widely understood that most practical problems are NP-hard. This is one of the reasons why local search methods have been studied so extensively during the last decade. In this paper, we review briefly some of the recent extensions of scheduling theory, the recent developments in local search techniques and the new developments of scheduling in practice. Particularly, we survey two recent extensions of theory: scheduling with a 1-job-on-r-machine pattern and machine scheduling with availability constraints. We also review several local search techniques, including simulated annealing, tabu search, genetic algorithms and constraint guided heuristic search. Finally, we study the robotic cell scheduling problem, the auto-mated guided vehicles scheduling problem, and the hoist scheduling problem.

A Reactive Tabu Search Metaheuristic for the Vehicle Routing Problem with Time Windows

Abstract: This article develops a reactive tabu search metaheuristic for the vehicle routing and scheduling problem with time window constraints. Reactive tabu search dynamically varies the size of the list of forbidden moves to avoid cycles as well as an overly constrained search path. Intensification and diversification strategies are examined as ways to achieve higher quality solutions. The λ-interchange mechanism of Osman is used as the neighborhood structure for the search process. Computational results on test problems from the literature as well as large-scale real-world problems are reported. The metaheuristic achieves solutions that compare favorably with previously reported results.

Short Shop Schedules

Abstract: We consider the open shop, job shop, and flow shop scheduling problems with integral processing times. We give polynomial-time algorithms to determine if an instance has a schedule of length at most 3, and show that deciding if there is a schedule of length at most 4 is 𝒩𝒫-complete. The latter result implies that, unless 𝒫 = 𝒩𝒫, there does not exist a polynomial-time approximation algorithm for any of these problems that constructs a schedule with length guaranteed to be strictly less than 5/4 times the optimal length. This work constitutes the first nontrivial theoretical evidence that shop scheduling problems are hard to solve even approximately.

Daily Aircraft Routing and Scheduling

Abstract: In this paper we consider the daily aircraft routing and scheduling problem DARSP. It consists of determining daily schedules which maximize the anticipated profits derived from the aircraft of a heterogeneous fleet. This fleet must cover a set of operational flight legs with known departure time windows, durations and profits according to the aircraft type. We present two models for this problem: a Set Partitioning type formulation and a time constrained multicommodity network flow formulation. We describe the network structure of the subproblem when a column generation technique is applied to solve the linear relaxation of the first model and when a Dantzig-Wolfe decomposition approach is used to solve the linear relaxation of the second model. The linear relaxation of the first model provides upper bounds. Integer solutions to the overall problem are derived through branch-and-bound. By exploiting the equivalence between the two formulations, we propose various optimal branching strategies compatible with the column generation technique. Finally we report computational results obtained on data provided by two different airlines. These results show that significant profit improvement can be generated by solving the DARSP using our approach and that this can be obtained in a reasonable amount of CPU time.

Approximating total flow time on parallel machines

Abstract: We consider the problem of optimizing the total flow time of a stream of jobs that are released over time in a multiprocessor setting. This problem is NP-hard even when there are only two machines and preemption is allowed. Although the total (or average) flow time is widely accepted as a good measurement of the overall quality of service, no approximation algorithms were known for this basic scheduling problem. This paper contains two main results. We first prove that when preemption is allowed, Shortest Remaining Processing Time (SRPT) is an O(log(min{nm,P})) approximation algorithm for the total flow time, where n is the number of jobs, m is the number of machines, and P is the ratio between the maximum and the minimum processing time of a job. We also provide an @W(log(nm+P)) lower bound on the (worst case) competitive ratio of any randomized algorithm for the on-line problem in which jobs are known at their release times. Thus, we show that up to a constant factor SRPT is an optimal on-line algorithm. Our second main result addresses the non-preemptive case. We present a general technique that allows to transform any preemptive solution into a non-preemptive solution at the expense of an O(nm) factor in the approximation ratio of the total flow time. Combining this technique with our previous result yields an O(nmlognm) approximation algorithm for this case. We also show an @W(n^1^3^-^@e) lower bound on the approximability of this problem (assuming P NP).

Local search for nonpreemptive multi-mode resource-constrained project scheduling

Abstract: This paper addresses a general class of nonpreemptive resource-constrained project scheduling problems in which activity durations are discrete functions of committed renewable and nonrenewable resources. We provide a well known 0–1 problem formulation and stress the importance of the model by giving applications within production and operations management. Furthermore, we prove that the feasibility problem is already NP-complete. Solution procedures proposed so far have the following shortcomings: exact methods can solve only very small instances to optimality; heuristic solution approaches fail to generate feasible solutions when problems become highly resource-constrained. Hence, we propose a new local search method that first tries to find a feasible solution and secondly performs a single-neighborhood search on the set of feasible mode assignments. To evaluate the new procedure we perform a rigorous computational study on two benchmark sets. The experiment includes a comparison of our procedure with other heuristics.

Optimal broadcast scheduling in packet radio networks using mean field annealing

Abstract: We present an efficient broadcast scheduling algorithm based on mean field annealing (MFA) neural networks Packet radio (PR) is a technology that applies the packet switching technique to the broadcast radio environment In a PR network, a single high-speed wideband channel is shared by all PR stations When a time-division multi-access protocol is used, the access to the channel by the stations' transmissions must be properly scheduled in both the time and space domains in order to avoid collisions or interferences It is proven that such a scheduling problem is NP-complete Therefore, an efficient polynomial algorithm rarely exists, and a mean field annealing-based algorithm is proposed to schedule the stations' transmissions in a frame consisting of certain number of time slots Numerical examples and comparisons with some existing scheduling algorithms have shown that the proposed scheme can find near-optimal solutions with reasonable computational complexity Both time delay and channel utilization are calculated based on the found schedules

Job shop scheduling with a genetic algorithm and machine learning

Abstract: Dynamic job shop scheduling has been proven to be an intractable problem for analytical procedures. Recent advances in computing technology, especially in artificial intelligence, have alleviated this problem by intelligently restricting the search space considered, thus opening the possibility of obtaining better results. Researchers have used various techniques that were developed under the general rubric of artificial intelligence to solve job shop scheduling problems. The most common of these have been expert systems, genetic algorithms and machine learning. Of these, we identify machine learning and genetic algorithms to be promising for scheduling applications in a job shop. In this paper, we propose to combine complementarily the strengths of genetic algorithms and induced decision trees, a machine learning technique, to develop a job shop scheduling system. Empirical results, using machine learning for releasing jobs into the shop floor and a genetic algorithm to dispatch jobs at each machine, are...

Better bounds for online scheduling

Abstract: We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal et al. (J. Comput. System Sci., 51 (1995), pp. 359{366) gave a deterministic online algorithm that is 1.986-competitive. Karger, Phillips, and Torng (J. Algorithms, 20 (1996), pp. 400{430) generalized the algorithm and proved an upper bound of 1.945. The best lower bound currently known on the competitive ratio that can be achieved by deterministic online algorithms is equal to 1.837. In this paper we present an improved deterministic online scheduling algorithm that is 1.923-competitive; for all m 2. The algorithm is based on a new scheduling strategy, i.e., it is not a generalization of the approach by Bartal et al. Also, the algorithm has a simple structure. Furthermore, we develop a better lower bound. We prove that, for general m, no deterministic online scheduling algorithm can be better than 1.852-competitive.

Integrated generation and transmission maintenance scheduling with network constraints

Abstract: Most unit maintenance scheduling packages consider preventive maintenance schedule of generating units over a one or two year operational planning period in order to minimize the total operating cost while satisfying system energy requirements and maintenance constraints. In a global maintenance scheduling problem, the authors propose to consider transmission line maintenance scheduling and line capacity limits along with generation and line outages. The inclusion of transmission and network constraints in generating unit maintenance will increase the complexity of the problem, so they propose to decompose the global generator/transmission scheduling problem into a master problem and sub-problems using Benders decomposition. In the first stage, a master problem is solved to determine a solution for maintenance schedule decision variables. In the second stage, sub-problems are solved to minimize operating costs while satisfying the network constraints. Benders cuts based on the solution of the sub-problem are introduced to the master problem for improving the existing solution. The iterative procedure continues until an optimal or near optimal solution is found.

Short-term resource scheduling with ramp constraints [power generation scheduling]

Abstract: This paper describes a Lagrangian relaxation-based method to solve the short-term resource scheduling (STRS) problem with ramp constraints. Instead of discretizing the generation levels, the ramp rate constraints are relaxed with the system demand constraints using Lagrange multipliers. Three kinds of ramp constraints, startup, operating and shutdown ramp constraints are considered. The proposed method has been applied to solve the hydro-thermal generation scheduling problem at PG&E. An example alone with numerical results is also presented.

β-Robust scheduling for single-machine systems with uncertain processing times

Abstract: In scheduling environments with processing time uncertainty, system performance is determined by both the sequence in which jobs are ordered and the actual processing times of jobs. For these situations, the risk of achieving substandard system performance can be an important measure of scheduling effectiveness. To hedge this risk requires an explicit consideration of both the mean and the variance of system performance associated with alternative schedules, and motivates a β-robustness objective to capture the likelihood that a schedule yields actual performance no worse than a given target level. In this paper we focus on β-robust scheduling issues in single-stage production environments with uncertain processing times. We define a general β-robust scheduling objective, formulate the β-robust scheduling problem that results when job processing times are independent random variables and the performance measure of interest is the total flow time across all jobs, establish problem complexity, and develop e...

Job shop scheduling

Abstract: Scheduling is the allocation of shared resources over time to competing activities, and has been the subject of a significant amount of literature in the operations research field. Emphasis has been on investigating machine scheduling problems where jobs represent activities and machines represent resources; each machine can process at most one job at a time. This chapter reviews a variety of GA applications to the JSSP. We begin our discussion by formulating the JSSP by a disjunctive graph. We then look at domain independent binary and permutation representations, followed by an active schedule representation with GT crossover and the genetic enumeration method. Section 7.7 discusses a method for integrating local optimisation directly into GAs. Section 7.8 discusses performance comparison using the well known Muth and Thompson benchmark and the more difficult ten tough problems.

Scheduling Semiconductor Burn-In Operations to Minimize Total Flowtime

Abstract: This paper addresses a problem of batch scheduling which arises in the burn-in stage of semiconductor manufacturing. Burn-in ovens are modeled as batch-processing machines which can handle up to B jobs simultaneously. The processing time of a batch is equal to the longest processing time among the jobs in the batch. The scheduling problem involves assigning jobs to batches and determining the batch sequence so as to minimize the total flowtime. In practice, there is a small number m of distinct job types. Previously, the only solution techniques known for the single-machine version of this problem were an O(m23Bm+1) pseudopolynomial algorithm, and a branch-and-bound procedure. We present an algorithm with a running time of O(m23m), which is independent of B, the maximum batch size. We also present a polynomial heuristic for the general problem (when m is not fixed), which is a two-approximation algorithm. For any problem instance, this heuristic provides a solution at least as good as that given by previo...

An algorithm for thermal unit maintenance scheduling through combined use of GA, SA and TS

Abstract: This paper describes a method of solving a large scale long-term thermal generating unit maintenance scheduling problem. In the solution algorithm, the genetic algorithm (GA), simulated annealing (SA) and the tabu search (TS) method are used cooperatively. The solution algorithm keeps the advantages of the individual algorithms and shows a reasonable combination of local and global searches. The method takes the maintenance class and several consecutive years scheduling into consideration. Several real-scale numerical examples demonstrate the effectiveness of the proposed method.

A Mixed-Integer Linear Programming Model for Short-Term Scheduling of Single-Stage Multiproduct Batch Plants with Parallel Lines

Abstract: An important industrial problem is the short-term scheduling of batch multiproduct facilities where a wide range of products are manufactured in small amounts that must be satisfied at certain due dates during the given time horizon. This paper presents a new MILP mathematical formulation for the batch scheduling problem involving a single processing stage for every product to be delivered. Based on a continuous representation of the time domain and the concept of job predecessor and successor to effectively handle changeovers, the proposed model is able to determine the optimal allocation of jobs to lines/units, the sequence of jobs on every line/unit, and their starting and completion times so as to minimize one of the following problem objectives: the overall tardiness, the schedule makespan, or the number of tardy orders. Facilities having nonidentical parallel units/lines, sequence-dependent changeovers, finite release times for units and orders, and restrictions on the types of orders that can be m...

Scheduling a two-stage hybrid flow shop with parallel machines at the first stage

Abstract: This paper considers a non-preemptive two-stage hybrid flow shop problem in which the first stage contains several identical machines, and the second stage contains a single machine Each job is to be processed on one of the first-stage machines, and then on the second-stage machine The objective is to find a schedule which minimizes the maximum completion time or makespan The problem is NP-hard in the strong sense, even when there are two machines at the first stage Several lower bounds are derived and are tested in a branch and bound algorithm Also, constructive heuristics are presented, and a descent algorithm is proposed Extensive computational tests with up to 250 jobs, and up to 10 machines in the first stage, indicate that some of the heuristics consistently generate optimal or near-optimal solutions

Approximation schemes for scheduling

Abstract: We consider the classic scheduling/load balancing problems where there are m identical machines and n jobs, and each job should be assigned to some machine. Traditionally, the assignment of jobs to machines is measured by the makespan (maximum load) i.e., the L{sub {infinity}} norm of the assignment. An {epsilon}-approximation scheme was given by Hochbaum and Shmoys for minimizing the L{sub {infinity}} norm. In several applications, such as in storage allocation, a more appropriate measure is the sum of the squares of the loads (which is equivalent to the L{sub 2} norm). This problem was considered in who showed how to approximate the optimum value by a factor of about 1.04. In fact, a more general measure, which is the L, norm (for any p {ge} 1) t can also be approximated to some constant which may be as large as 3/2. We improve e these results by providing an c-approximation scheme for the general L{sub p} norm (and in particular for the L{sub 2} norm). We also consider the case of restricted assignment of unit jobs where we show how to find in polynomial time, a solution a which is optimal for all norms.