Showing papers on "Single-machine scheduling published in 2001"
TL;DR: A new memetic algorithm for the total tardiness single machine scheduling (SMS) problem with due dates and sequence-dependent setup times is proposed and several neighborhood reduction schemes are developed and proved to be effective when compared to the complete neighborhood.
186 citations
TL;DR: The purpose here is to simultaneously sequence jobs and schedule maintenance activity to optimize regular performance measures and study problems with objective functions such as expected makespan, total expected completion time, maximum expected lateness, and expected maximum lateness.
105 citations
TL;DR: A scheduling model in which each task has a normal processing time which deteriorates as a step function if its starting time is beyond a given deteriorating date is studied, which shows that the flow time problem is NP-complete and suggests a pseudo-polynomial algorithm for the makespan problem.
81 citations
TL;DR: Polynomial time algorithms are presented to find an optimal batch sequence and resource values such that either the total weighted resource consumption is minimized, subject to meeting job deadlines, or the maximum job lateness is minimized; subject to an upper bound on the total Weighted resource consumption.
70 citations
TL;DR: A tabu search-based solution procedure designed specifically for a certain class of single-machine scheduling problems with a non-regular performance measure is developed and found to perform better than the simulated annealing approach for the variance minimization problem.
54 citations
TL;DR: A constructive heuristic, which determines the sequence of jobs and simultaneously inserts idle times, is proposed, and the heuristic solutions are compared to optimal solutions.
49 citations
TL;DR: Identifying the computational complexity of the problems, developing dynamic programming algorithms to optimally solve them, and providing efficient and exact polynomial algorithms for the special cases are provided.
48 citations
TL;DR: The paper investigates the authors' most recent branch and bound algorithm and discovers the following paradoxes and develops a very fast branch algorithm that handles instances with up to 500 jobs.
Abstract: The paper deals with the single-machine total tardiness problem. It investigates the authors' most recent branch and bound algorithm and discovers the following paradoxes. Deleting a lower bound drastically improves the performance of the algorithm, while adding a stronger component, like a better decomposition rule, negatively affects its performance. Guided by those paradoxes it develops a very fast branch algorithm that handles instances with up to 500 jobs. It also shows that the powerful recent result of Chang et al. (Operations Research Letters 1995; 17:221–229) can be further improved. Copyright © 2001 John Wiley & Sons, Ltd.
48 citations
TL;DR: A new algorithm that can output optimal solutions even when available memory is limited is presented and it has been found to run faster than dynamic programming and depth-first branch-and-bound formulations and can solve much larger instances of the problem in reasonable time.
37 citations
TL;DR: A positive answer to this conjecture is given, showing that this problem to minimize total compression plus weighted flow cost is NP-hard.
35 citations
TL;DR: The problem is NP-complete in the ordinary sense and a dynamic programming based pseudo-polynomial algorithm is developed that minimizes the weighted number of early and tardy jobs and the location penalty.
Abstract: This paper studies a single machine scheduling problem to minimize the weighted number of early and tardy jobs with a common due window. There are n non-preemptive and simultaneously available jobs. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. The window size is a given parameter but the window location is a decision variable. The objective of the problem is to find a schedule that minimizes the weighted number of early and tardy jobs and the location penalty. We show that the problem is NP-complete in the ordinary sense and develop a dynamic programming based pseudo-polynomial algorithm. We conduct computational experiments, the results of which show that the performance of the dynamic algorithm is very good in terms of memory requirement and CPU time. We also provide polynomial time algorithms for two special cases.
TL;DR: This paper is concerned with scheduling of a marketing-production system in which the demand rate changes in accordance with marketing actions, and the structure of the hedging-point policy is fully analyzed.
Abstract: This paper is concerned with scheduling of a marketing-production system in which the demand rate changes in accordance with marketing actions. Our goal is to provide illuminating descriptions and insight on the optimal control policies. A basic building-block model involving a single machine is developed. The objective is to choose the rates of production and marketing to maximize the overall profit. Consisting of a pair of hedging points, the optimal policy is attractive in practice because of its simplicity and can be computed by solving algebraic equations. Aiming at obtaining analytic solutions, various control regions of the optimal policy are depicted; the structure of the hedging-point policy is fully analyzed.
TL;DR: In this paper a local search approach for a single-machine scheduling problem with positive and negative time-lags and the objective to minimize the makespan is presented and infeasible solutions are incorporated into the search process.
TL;DR: This paper considers a single machine scheduling problem with random processing times to minimize the expected total weighted deviations of completion times from a random common due date and shows the optimal schedules to be @L-shaped.
29 May 2001
TL;DR: A scheduling system, based on genetic algorithms, is proposed, for the resolution of the dynamic version of the same problem, which takes into account dynamic occurrences in a system and adapts the current population to a new regenerated population.
Abstract: The paper starts by studying the performance of two interrelated genetic algorithms (GA) for the static single machine scheduling problem (SMSP). One is a single start GA, the other, called MetaGA, is a multi-start version GA. The performance is evaluated, for total weighted tardiness, on the basis of the quality of scheduling solutions obtained for a limit on computation time. Then, a scheduling system, based on genetic algorithms is proposed, for the resolution of the dynamic version of the same problem. The approach used adapts the resolution of the static problem to the dynamic one in which changes may occur continually. This takes into account dynamic occurrences in a system and adapts the current population to a new regenerated population.
TL;DR: The problem of scheduling the production and delivery of a supplier to feed the production of F manufacturers is studied and is proved to be NP-hard.
Abstract: The problem of scheduling the production and delivery of a supplier to feed the production of F manufacturers is studied The orders fulfilled by the supplier are delivered to the manufacturers in batches of the same size The supplier's production line has to be set up whenever it switches from processing an order of one manufacturer to an order of another manufacturer The objective is to minimize the total setup cost, subject to maintaining continuous production for all manufacturers The problem is proved to be NP-hard It is reduced to a single machine scheduling problem with deadlines and jobs belonging to F part types An O(Nlog F) algorithm, where N is the number of delivery batches, is presented to find a feasible schedule A dynamic programming algorithm with O(N
F
/F
F−2) running time is presented to find an optimal schedule If F=2 and setup costs are unit, an O(N) time algorithm is derived
TL;DR: A polynomial time algorithm to minimize maximum tardiness on a single machine in the presence of deadlines can be extended only when deadlines and due dates are compatible and all job release times are equal.
Journal Article•
TL;DR: In this paper, the authors provide lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weighted and uncounted total flow time.
Abstract: The problem of scheduling jobs that arrive over time on a single machine is well-studied. We study the preemptive model and the model with restarts. We provide lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weighted and unweighted total flow time. By using new techniques, we provide the first lower bounds for several of these problems, and we significantly improve the bounds that were known.
TL;DR: This work addresses the single-machine problem of scheduling n independent jobs subject to target start times and shows that in case of a linear objective function the problem is solvable in O(n4) time if preemption is allowed or if total completion time outweighs maximum promptness.
01 Jan 2001
TL;DR: The ordinaryNP-completeness of the considered problem is proved by reducing to it the ordinary NP-complete Partition Problem by giving also some properties of the optimal resource allocation.
Abstract: The paper deals with a single machine scheduling problem for the maximum completion time (makespan) minimization subject to the constraint on the total amount of available resources. The job processing times are given by non-decreasing linear functions simultaneously dependent on the starting moment of their execution and on the amount of allocated resources. We prove the ordinary NP-completeness of the considered problem by reducing to it the ordinary NP-complete Partition Problem. We give also some properties of the optimal resource allocation. The optimal solutions for some special cases of the latter problem are also presented.
TL;DR: A nonpreemptive single-machine scheduling model with time-dependent multiple criteria and a dynamic programming (DP)-based algorithm to finding all efficient schedules is introduced.
04 Dec 2001
TL;DR: This work considers a setup scheduling problem for a manufacturing system with finite buffers, which comprises a non-perfect, reliable single machine processing two part types, modeled by means of a fluid approximation.
Abstract: We consider a setup scheduling problem for a manufacturing system with finite buffers. Some analytical results for the infinite capacity case are also included. The system comprises a non-perfect, reliable single machine processing two part types, modeled by means of a fluid approximation. The objective of the control is to minimize an index cost under steady and transient conditions. Dynamic programming is used to derive the structure of the optimal policy and some initial analytical results are given. A symmetry assumption on part types is considered to simplify the problem.
01 Jan 2001
TL;DR: An approach based on GA for solving dynamic scheduling problems, where the products (jobs) to be processed have due dates, and the approach used adapts the resolution of the static problem to the dynamic one in which changes may occur continually.
Abstract: Due to their dynamic nature, real scheduling problems have an additional complexity in relation to static ones. In many situations these problems, even for apparently simple situations, are hard to solve, i.e. the time required to compute an optimal solution increases exponentially with the size of the problem [1]. GAs have been extensively used in the context of Job-Shop Scheduling Problems (JSSP). If all jobs are known before processing starts the JSSP is called static, while if job release times are not fixed at a single point in time, i.e. jobs arrive to the system at different times, the problem is called dynamic. Scheduling problems can also be classified as deterministic, when processing times and all other parameters are known and fixed, and stochastic, when some or all parameters are uncertain [7]. The proposed approach deals with these two cases of dynamic scheduling: deterministic and stochastic. For such class of problems, the goal is no longer to find a single optimum, but rather to continuously adapt the solution to the changing environment. The purpose of this paper is to describe an approach based on GA for solving dynamic scheduling problems, where the products (jobs) to be processed have due dates. This paper starts by presenting a scheduling system, based on Genetic Algorithms for the resolution of the dynamic version of Single Machine Scheduling Problem (SMSP). The approach used adapts the resolution of the static problem to the dynamic one in which changes may occur continually. This takes into account dynamic occurrences in a system and adapts the current population to a new regenerated population. Then, it is proposed an approach for the resolution of the Job-Shop Scheduling Problem (JSSP) in dynamic environments. The paper is structured as follows: section 2 provides a description of the considered scheduling problem. Section 3 summarises an approach for the resolution of the Dynamic Single Machine Scheduling Problem. The proposed approach for dynamic scheduling is presented in section 4. Finally, the paper concludes with a summary and some ideas for future work.
TL;DR: This paper considers a single-machine scheduling problem in which jobs are classified into classes and a setup is required between jobs of different classes, called a sequence-independent class setup problem, which is NP-complete.
01 Jan 2001
TL;DR: The main result is that the solution of the ‖C‖1— problem with the actuallyrecognized O(2 n ) complexity ((1991)) can be approximated in terms of the l p —norm-based criteria ‖ C‖ r merely with the complexity O(n log n), where 1 < r 1 ≤r ≤ +∞ and r 1 is large enough.
Abstract: In the paper we consider an approximate O(n log n) time solution of theproblem of a single machine scheduling with time dependentprocessing times, where α j ≥ 0.The main result of the paper is that in view of the inequality‖C‖1 ≤ ω(n,r)‖C‖ r , where‖C‖ r = (n + l)1-1/r and1 ≤ r ≤ +∞, the solution of the ‖C‖1— problem with the actuallyrecognized O(2 n ) complexity ((1991)) can beapproximated in terms of the l p —norm-based criteria ‖C‖ r merely with the complexity O(n log n), where 1 < r 1 ≤r ≤ +∞and r 1 is large enough. Relations to some more general problems are also indicated.
04 Dec 2001
TL;DR: The optimisation problem with quadratic cost function and nonlinear constraints is stated and formalised as a multi-stage optimal control problem; the optimal closed-loop control laws at each stage are obtained.
Abstract: The problem of optimally defining and controlling the behaviour of a single machine processing a certain number of jobs and modelled as a discrete event dynamic system is addressed. The number of jobs, their sizes, and their service sequence are fixed, whereas their timing is the matter of the optimisation problem. The objective function to be optimised is a weighted sum of the inventory cost of the quadratic deviations from the due-dates of jobs and their completion times, and the quadratic deviations between the unitary processing times of jobs and those specified by the regular system functioning. An optimisation problem with quadratic cost function and nonlinear constraints is stated and formalised as a multi-stage optimal control problem. The control problem is solved by a procedure making use of dynamic programming techniques; the optimal closed-loop control laws at each stage are thus obtained.
15 Oct 2001
TL;DR: This work considers single machine scheduling problems in which due dates are assigned according to the CON (common due date) rule to find an optimal value of the due date and the related optimal schedule in order to optimize a given criterion based on the due Date and the completion times of jobs.
Abstract: We consider single machine scheduling problems in which due dates are assigned according to the CON (common due date) rule. The objective in this problem is to find an optimal value of the due date and the related optimal schedule in order to optimize a given criterion based on the due date and the completion times of jobs.
01 Jan 2001
TL;DR: A single machine scheduling problem with set-up times and job processing times given as linear functions dependent on some continuously divisible resources is considered and polynomial time solution algorithms are presented.
Abstract: In the paper, we consider a single machine scheduling problem with set-up times and job processing times given as linear functions dependent on some continuously divisible resources The scheduling objective is to find the optimal sequence of the jobs and the allocation of limited resources, which minimize the maximum completion time (makespan) A dual problem is also considered, ie the problem, in which the objective is to find a sequence of jobs and an allocation of resources, which minimize the total resource consumption, under a given constraint on maximum completion time Based on the problems properties, we present polynomial time solution algorithms We conclude the paper by outlining some possible directions for future research
TL;DR: An O(n logn ) algorithm (where n is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights.
Abstract: This paper is devoted to the following version of the single machine preemptive scheduling problem of minimizing the weighted number of late jobs. A processing time, a release date, a due date and a weight of each job are given. Certain jobs are specified to be completed in time, i.e. , their due dates are assigned to be deadlines, while the other jobs are allowed to be completed after their due dates. The release/due date intervals are nested, i.e. , no two of them overlap (either they have at most one common point or one covers the other). Necessary and sufficient conditions for the completion of all jobs in time are considered, and an O(n logn ) algorithm (where n is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights.
27 Aug 2001
TL;DR: By using new techniques, this work provides the first lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weights of total flow time.
Abstract: The problem of scheduling jobs that arrive over time on a single machine is well-studied. We study the preemptive model and the model with restarts. We provide lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weighted and unweighted total flow time. By using new techniques, we provide the first lower bounds for several of these problems, and we significantly improve the bounds that were known.