Showing papers on "Single-machine scheduling published in 2003"

Daily imaging scheduling of an Earth observation satellite

Abstract: This work presents the development of a daily imaging scheduling system for a low-orbit, Earth observation satellite. The daily imaging scheduling problem of satellite considers various imaging requests with different reward opportunities, changeover efforts between two consecutive imaging tasks, cloud-coverage effects, and the availability of the spacecraft resource. It belongs to a class of single-machine scheduling problems with salient features of sequence-dependent setup, job assembly, and the constraint of operating time windows. The scheduling problem is formulated as an integer-programming problem, which is NP-hard in computational complexity. Lagrangian relaxation and linear search techniques are adopted to solve this problem. In order to demonstrate the efficiency and effectiveness of our solution methodology, a Tabu search-based algorithm is implemented, which is modified from the algorithm in Vasquez and Hao, 2001. Numerical results indicate that the approach is very effective to generate a near-optimal, feasible schedule for the imaging operations of the satellite. It is efficient in applications to the real problems. The Lagrangian-relaxation approach is superior to the Tabu search one in both optimality and computation time.

An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times

Abstract: In this paper, we consider a simplified real-life identical parallel machine scheduling problem with sequence-dependent setup times and job splitting to minimize makespan. We propose a heuristic to solve this problem. Our method is composed of two parts. The problem is first reduced into a single machine scheduling problem with sequence-dependent setup times. This reduced problem can be transformed into a Traveling Salesman Problem (TSP), which can be efficiently solved using Little's method. In the second part, a feasible initial solution to the original problem is obtained by exploiting the results of the first part. This initial solution is then improved in a step by step manner, taking into account the setup times and job splitting. We develop a lower bound and evaluate the performances of our heuristic on a large number of randomly generated instances. The solution given by our heuristic is less than 4.88% from the lower bound.

Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine

Abstract: This paper tackles the general single machine scheduling problem, where jobs have different release and due dates and the objective is to minimize the weighted number of late jobs. The notion of master sequence is first introduced, i.e., a sequence that contains at least an optimal sequence of jobs on time. This master sequence is used to derive an original mixed-integer linear programming formulation. By relaxing some constraints, a Lagrangean relaxation algorithm is designed which gives both lower and upper bounds. The special case where jobs have equal weights is analyzed. Computational results are presented and, although the duality gap becomes larger with the number of jobs, it is possible to solve problems of more than 100 jobs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 50: 2003

Decompositions, Network Flows, and a Precedence Constrained Single-Machine Scheduling Problem

Abstract: We present an in-depth theoretical, algorithmic, and computational study of a linear programming (LP) relaxation to the precedence constrained single-machine scheduling problem 1|prec|S jw jC jto minimize a weighted sum of job completion times. On the theoretical side, we study the structure of tight parallel inequalities in theLP relaxation and show thatevery permutation schedule that is consistent with Sidney's decomposition has total cost no more than twice the optimum. On the algorithmic side, we provide a parametric extension to Sidney's decomposition and show that a finest decomposition can be obtained by essentially solving a parametric minimum-cut problem. Finally, we report results obtained by an algorithm based on these developments on randomly generated instances with up to 2,000 jobs.

MILP formulation and polynomial time algorithm for an aircraft scheduling problem

Abstract: This paper presents a polynomial time algorithm used for solving a mixed integer linear program (MILP) formulation of a scheduling problem applicable to air traffic control. We first relate the general MILP (which we believe to be NP-hard) to the air traffic control problem, which consists of performing maneuver assignments to achieve scheduling constraints for airport arrival traffic. This MILP can be solved with CPLEX, yet there is no guarantee on the running time. We show that a specific case of this air traffic control problem, which is of interest in its own right, may be solved using an exact polynomial-time algorithm. The case of interest consists of finding the largest achievable time separation between aircraft upon arrival, compatible with airspace restrictions and aircraft performance. Our algorithm transforms the problem to a single machine scheduling problem, and then embeds its solution into a bisection algorithm. We establish the polynomial complexity of the resulting algorithm by proving an algebraic property of its optimal solution. We compare the running times of CPLEX and our algorithm for 1800 cases with up to 20 aircraft. The results show numerical evidence of the guaranteed running time of our algorithm, by contrast with CPLEX whose average performance is good, but also shows a significant number of instances with unpredictably large computational time. We perform 8100 additional runs of our algorithm with up to 100 aircraft, to numerically confirm the predicted worst case running time of our algorithm.

Learning single-machine scheduling heuristics subject to machine breakdowns with genetic programming

Abstract: Genetic programming (GP) has been rarely applied to scheduling problems. In this paper the use of GP to learn single-machine predictive scheduling (PS) heuristics with stochastic breakdowns is investigated, where both tardiness and stability objectives in face of machine failures are considered. The proposed bi-tree structured representation scheme makes it possible to search sequencing and idle time inserting programs integratedly. Empirical results in different uncertain environments show that GP can evolve high quality PS heuristics effectively. The roles of inserted idle time are then analysed with respect to various weighting objectives. Finally some guides are supplied for PS design based on GP-evolved heuristics.

Scheduling Problems under Linear Deterioration

Abstract: This paper considers the scheduling problem under linear deterioration. It is assumed that the deterioration function is a linear function. Optimal algorithms are presented respectively for single machine scheduling problems of minimizing the makespan, weighted sum of completion times, maximum lateness and maximum cost. For two machine flow shop scheduling problem to minimize the makespan, it is proved that the optimal schedule can be obtained by Johnson′s rule. If the processing times of operations are equal for each job, flow shop scheduling problems can be transformed into single machine scheduling problems.

Single machine scheduling with maximum earliness and number tardy

Abstract: In this paper, we study the bicriteria scheduling problem of minimizing the maximum earliness and the number of tardy jobs on a single machine. We assume idle time insertion is not allowed. We first examine the problem of minimizing maximum earliness while keeping the number of tardy jobs to its minimum value. We then propose a general procedure for generating all efficient schedules for bicriteria problems. We also develop a general procedure to find the efficient schedule that minimizes a composite function of the two criteria by evaluating only a small fraction of the efficient solutions. We adapt the general procedures for the bicriteria problem of minimizing maximum earliness and the number of tardy jobs.

New Results On Sequencing With Rate Modification

Abstract: In many production systems a time period is scheduled for machine maintenance, during which the machine is idle. After the maintenance activity is completed the production rate may be affected. The decisions under consideration are (i) when to schedule this rate-modifying activity, and (ii) how to sequence the jobs. We study three single machine scheduling problems with a rate-modifying activity: minimum makespan with precedence constraints, minimum makespan with a learning effect and minimum number of tardy jobs. We introduce a polynomial time solution for each of the three problems.

An investigation on single machine total weighted tardiness scheduling problems

Abstract: The urge to produce products in the production line at a faster rate with no compromise in quality has led to scheduling gaining greater importance in the modern day industries. Scheduling is concerned with the allocation of limited resources to tasks over time. The investigations on various scheduling problems have been of constant interest to researchers worldwide. This paper deals with an investigation on the total weighted tardiness of the single machine scheduling problems. The problems are solved by a heuristic procedure, namely backward forward heuristics. The different methods of formulating the problem instances are discussed. The benchmark problems and their best known values available in the OR library are used for the comparison to find out the influence of Relative Due Date (RDD) and Tardiness Factor (TF) used to generate the problem instances.

Evolutionary programming for minimizing the average flow time in the presence of non-zero ready times

Abstract: In this paper, first manufacturing scheduling is briefly discussed and later the problem studied is introduced. The optimal solution to minimizing the average flow time in single machine scheduling is obtained by the Shortest Processing Time rule if ready times are zero for all jobs. In the case of non-zero ready times, preemption plays a key role in the solution. Preemption allowed version is solved optimally by using the Shortest Remaining Processing Time procedure. However, the version of preemption not allowed is known as NP-hard and delay and nondelay strategies might be used in a hybrid fashion. This paper focuses on minimizing the average flow time in the presence of non-zero times and when preemption is not allowed. The proposed method is evolutionary programming (EP). The results indicate that EP produces near optimal and consistent results in a short period of time.

Optimal Online Algorithms for Minimax Resource Scheduling

Abstract: We consider a very general online scheduling problem with an objective to minimize the maximum level of resource allocated. We find a simple characterization of an optimal deterministic online algorithm. We develop further results for the two, more specific problems of single resource scheduling and hierarchical line balancing. We determine how to compute optimal online algorithms for both problems using linear programming and integer programming, respectively. We show that randomized algorithms can outperform deterministic algorithms, but only if the amount of work done is a nonconcave function of resource allocation.

Single Machine Scheduling of Unit-time Jobs with Controllable Release Dates

Abstract: The paper presents a bicriterion approach to solve the single-machine scheduling problem in which the job release dates can be compressed while incurring additional costs. The two criteria are the makespan and the compression cost. For the case of equal job processing times, an O(n4) algorithm is developed to construct integer Pareto optimal points. We discuss how the algorithm developed can be modified to construct an e-approximation of noninteger Pareto optimal points. The complexity status of the problem with total weighted completion time criterion is also established.

A branch-and-bound algorithm for the single-machine weighted earliness-tardiness scheduling problem with job independent weights

Abstract: In this paper we propose a branch-and-bound algorithm for the single-machine earliness-tardiness scheduling problem where weights for earliness and tardiness are independent of jobs. Here, machine idle times are allowed. In our branch-and-bound algorithm, the search tree is generated by fixing the processing order of jobs from the first to the last, or, from the last to the first. To improve the efficiency of the algorithm, we propose new lower bounds. We also show dominance properties that are utilized both for reducing branches in the search tree and for improving the lower bounds. Then, we show the effectiveness of our algorithm by numerical experiments.

Some Single Machine Scheduling Problems with Learning Effect under Consistent Condition

Abstract: n Jobs are to be processed on the same machine, the basic processing time for job j is Pj,j= 1,2,..., n. In a given sequence, if job j is in position r, then the actual processing time for it is Pjrα, in which a (?) 0 is a given constant learning effect. We are asked to schedule the n jobs in such a way that some objective functions are minimized. For the following three objective functions: the total weighted completion time, the maximum lateness and the number of tardy job, this paper proves that the WSPT rule, the EDD rule and the modified Moore-Hodgson algorithm can construct the optimal sequence under corresponding consistent condition, respectively. This paper givers also the error estimation for these three rules in general cases.

Efficient polynomial algorithms for special cases of weighted early/tardy scheduling with release dates and a common due date

Abstract: In this paper we consider a single machine scheduling problem with integer release dates and a common due date. The objective is to minimise the weighted sum of the jobs' earliness and tardiness costs. We present an efficient polynomial algorithm for the unit processing time case. We also show how to calculate, for the general case, the minimum non-restrictive due date.