Showing papers on "Single-machine scheduling published in 2000"

Single Machine Scheduling with Learning Effect Considerations

Abstract: In this paper we study a single machine scheduling problem in which the job processing times will decrease as a result of learning. A volume-dependent piecewise linear processing time function is used to model the learning effects. The objective is to minimize the maximum lateness. We first show that the problem is NP-hard in the strong sense and then identify two special cases which are polynomially solvable. We also propose two heuristics and analyse their worst-case performance.

Scheduling under Fuzziness

Abstract: Fuzzy Knowledge Representation in Scheduling: I.B. Turksen, M.H.F. Zarandi, M. Dudzic: Caster Scheduling System Analysis with Fuzzy Technology.- M. Litoiu, R. Tadei: Dynamic Scheduling on Distributed Real-Time Systems by Self-Learning Fuzzy Algorithms.- Fuzzy Constraints in Scheduling: H. Fagier, C. Thierry: The Use of Possibilistic Decision Theory in Manufacturing, Planning and Control: Recent Results in Fuzzy Master Production Scheduling.- P. Fortemps: Introducing Flexibility in Scheduling: The Preference Approach.- H. Ishii: Scheduling Problems with Fuzzy Constraints.- H. Ishibuchi, T. Murata: Flowshop Scheduling with Fuzzy Duedate and Fuzzy Processing Time.- Fuzzy Uncertainty in Scheduling: G. Adamopoulos, C.P. Pappis, N.I. Karacapilidis: A Methodology for Solving a Range of Scheduling Problems under Uncertainty.- S. Chanas, A. Kasperski, D. Kuchta: Two Approaches to Fuzzy Flow Shop Problem.- M. Hapke, R. Slowinski: Fuzzy Set Approach to Multi-Objective and Multi-Mode Project Scheduling under Uncertainty.- M. Vlach: Single Machine Scheduling under Fuzziness.- L. Geneste, B. Grabot, P. Moutarlier: Scheduling of Heterogeneous Data Using Fuzzy Logic in a Customer-Subcontractor Context.- N. Kubota, T. Fukuda: Virus-Evolutionary Genetic Algorithm for Sequencing Jobs in Fuzzy Environment.- N.I. Karacapilidis, C.P. Pappis, G. Adamopulos: Fuzzy Set Approaches to Lot Sizing.

A Best Possible Deterministic On-Line Algorithm for Minimizing Maximum Delivery Time on a Single Machine

Abstract: We consider a single-machine on-line scheduling problem where jobs arrive over time A set of independent jobs has to be scheduled on the machine, where preemption is not allowed and the number of jobs is unknown in advance Each job becomes available at its release date, which is not known in advance, and its characteristics, ie, processing requirement and delivery time, become known at its arrival The objective is to minimize the time by which all jobs have been delivered We propose and analyze an on-line algorithm based on the following idea: As soon as the machine becomes available for processing, choose an available job with highest priority, and schedule it if its processing requirement is not too large Otherwise, postpone the start of this job We prove that our algorithm has performance bound $(\sqrt{5}+1)/2 \approx 161803$, and we show that there cannot exist a deterministic on-line algorithm with a better performance ratio for this problem

Scheduling with generalized batch delivery dates and earliness penalties

Abstract: In this paper, we study some single machine scheduling problems with generalized batch delivery dates and earliness penalties. The generalized delivery dates are given a-priori before any jobs are processed. They are unrelated to the jobs and the processing order. Each specific delivery batch contains jobs completed but undelivered until the specific delivery date. We consider scheduling problems to minimize two types of earliness penalties: one is the total earliness; the other is the maximum earliness. For these two problems, first we show that they are NP-hard in the strong sense for general cases; then we prove that they are still NP-hard even if there are only two generalized batch dates. We also prove that they are solved in polynomial time for general earliness penalty function if all processing times are equal, and give an O(n log(n)) algorithm to solve the weighted earliness cases.

A genetic algorithm for scheduling on a single machine with set-up times and due dates

Abstract: This paper presents a genetic algorithm for a single machine-scheduling problem with the objective of minimizing total tardiness. Each job has its own due date and the set-up times are sequence dependent. The parameters of the genetic algorithm are determined by a statistical method. For small problems, the solutions given by the proposed method are compared with solutions provided by a commercial package, and for larger problems, with those obtained by a heuristic proposed in the literature.

Single machine scheduling with deadlines and increasing rates of processing times

Abstract: The makespan, flow time and maximum lateness problems of scheduling a set of tasks with deadlines and increasing rates of processing times on a single machine are considered in this paper. We first show that, when the increasing rates of processing time are identical, the makespan problem is equivalent to the corresponding flow time problem. Both problems are solvable in $O(n^5)$ time by a dynamic programming algorithm. As an application of the dynamic programming algorithm, we demonstrate that the corresponding maximum lateness problem can be solved in $O(n^6\log n)$ time. We then show that the general makespan problem is strongly NP-complete. Thus, both the corresponding flow time problem and maximum lateness problem are also strongly NP-complete.

A Simulated Annealing Approach to Bicriteria Scheduling Problems on a Single Machine

Abstract: In this paper, we apply a simulated annealing approach to two bicriteria scheduling problems on a single machine. The first problem is the strongly NP-hard problem of minimizing total flowtime and maximum earliness. The second one is the NP-hard problem of minimizing total flowtime and number of tardy jobs. We experiment on different neighbourhood structures as well as other parameters of the simulated annealing approach to improve its performance. Our computational experiments show that the developed approach yields solutions that are very close to lower bounds and hence very close to the optimal solutions of their corresponding problems for the minimization of total flowtime and maximum earliness. For the minimization of total flowtime and number tardy, our experiments show that the simulated annealing approach yields results that are superior to randomly generated schedules.

Restarts can help in the on-line minimization of the maximum delivery time on a single machine

Abstract: We consider a single-machine on-line scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on a single machine. Each job becomes available at its release date, which is not known in advance, and its characteristics, i.e. processing requirement and delivery time, become known at its arrival. The objective is to minimize the time by which all jobs have been delivered. In our model preemption is not allowed, but we are allowed to restart a job, that is, the processing of a job can be broken off to have the machine available to process an urgent job, but the time already spent on processing this interrupted job is considered to be lost. We propose an on-line algorithm and show that its performance bound is equal to 1.5, which matches a known lower bound due to Vestjens. For the same problem without restarts the optimal worst-case bound is known to be equal to (\sqrt{5}+1)/2 \thickapprox 1.61803; this is the first example of a situation in which the possibility of applying restarts reduces the worst-case performance bound, even though the processing times are known. Copyright © 2000 John Wiley & Sons, Ltd.

Single–machine scheduling with random machine breakdowns and randomly compressible processing times

Abstract: This work presents a model of single-machine scheduling problem. The machine is failure-prone and subject to random breakdowns. The processing time is a deterministic sequence that is randomly compressible, which may be from the introduction of new technology or addition of new equipment. Taking into account the cost for the random breakdowns and the random compressible processing time, our objective is to find the optimal scheduling policy to minimize an objective function. Under simple conditions, it is shown that the optimal sequence possesses a V-shape property.

Dynamic single-machine scheduling under distributed decision-making

Abstract: This paper presents a deterministic dynamic model for the single-machine scheduling problem The model uses forecasts of future job arrivals with the current data to extract job interactions over time, updating the information on rolling basis The model is implemented in a distributed structure with both the machine and the jobs involved in decision-making to create a schedule The decision-making is modelled similar to an auction with a theoretical basis for problem decomposition, bid construction and bid evaluation Numerical results indicate that the model outperforms other distributed implementations in both static and dynamic implementations for a wide range of single-machine scheduling problems

Lower bounds and algorithms for flowtime minimization on a single machine with set-up times

Abstract: SUMMARY A recent trend in the analysis of scheduling models integrates batching decisions with sequencing decisions. The interplay between batching and sequencing reects the realities of the small-volume, high-variety manufacturing environment and adds a new feature to traditional scheduling problems. Practical interest in this topic has given rise to new research eorts, and there has been a series of articles in the research literature surveying the rapidly developing state of knowledge. Exam- ples include Ghosh (1), Liaee and Emmons (2), Potts and Van Wassenhove (3), and Webster and Baker (4). This paper deals with an important theoretical and practical problem in this area. We examine the single-machine model with family (or group) set-up times and a criterion of minimizing total weighted job completion time (weighted owtime). We propose new lower bounds for this problem, and then turn our attention to renement of a previously proposed branch-and-bound algorithm. The benets of our renements are illustrated by computational experiments.

Stability of real-time lot-scheduling and machine replacement policies with quality levels

Abstract: We consider a single machine, multiproduct manufacturing system which can operate at finitely many quality levels. The quality of the machine deteriorates according to a continuous-time Markov process and the only way to improve the quality is by replacing the machine by a new one. In this framework we derive conditions for the stability of the system under a simple class of real-time scheduling/replacement policies. The stability notion that we employ is the recurrence of the total work backlog.

Scheduling a single machine where setup times are sequence dependent using an ant colony heuristic

Abstract: This paper presents an ant-colony heuristic for the solution of an industrial scheduling problem in an aluminum casting center. The authors first show how the ant-colony heuristic proposed in [1] can be adapted to the single machine scheduling problem with sequence dependent setup times. In this illustrations we minimize the total tardiness. It will be shown that this heuristic performs better, in most cases, than other recent heuristics on the published problem set of Rubin and Ragatz [2]. We then show how this heuristic can be adapted to the particular conditions found in aluminum production. We present an efficient representation of a continuous horizontal casting process which allows us to take account of multiple objectives. We have incorporated the methods proposed in software that has been implemented in the plant. 1 Problem Description We treat a scheduling problem encountered in an Alcan aluminium foundry located in Quebec. In this foundry, two holding furnaces are charged with molten metal from a transfer crucible coming from the refiners. These furnaces continuously feed liquid metal to the horizontal casting rig. A customer's alloy specification is produced by adding the required ingredients and grain refiners to the molten aluminium in the holding furnaces. Molten aluminum is poured into channels leading to a basin and a mold having the crossection of the desired ingots. The aluminum flows through the mold taking the proper crossectional shape and, at the same time, fuses. Since the casting is continuous, a large automated circular saw cuts the fused aluminum into the required ingot lengths as it is produced. If the crossection must be changed, then casting must be stopped and the mold changed. A change in the alloy being produced may also require a draining and cleaning to prevent contamination of the alloy to be cast next. Stoppages on the casting rig can be avoided if, while one holding furnace supplies metal for the pour, the second is prepared and loaded. The speed of a pour depends on the alloy type and on the number of pieces in the mold. The preparation time of a holding furnace is a function of the quantity of molten metal used, the quantity of solid metal used, and of any draining and cleaning required. A change of alloy will also affect the holding furnace preparation time. The metallurgical composition of the new alloy may require that the holding furnace be drained and cleaned before the pour. The basin is a holding chamber that retains a small amount of molten metal just before the mold and the availability of basins constitutes a further technological constraint. Molds may be attached only to specific basins and the one required may be undergoing cleaning from a previous usage. A feasible sequence of orders is one that ensures that sufficient pure metal is available for all pours, that basins and molds are available when required for each order and that draining and cleaning of the rig is done when required. A desirable feasible sequence takes into account the objectives of customer service and efficiency. We model the objectives of the scheduler by treating the minimization of unweighted total tardiness for all orders, the minimization of unused production capacity over the planning horizon, the minimization of the total number of drainings for the furnaces and we include a penalty function encouraging efficient transportation of the product. This function favors sequences where orders for the same destination are consecutive and penalizes sequences where this is not the case. In its general form, we see this problem as one of scheduling of n orders with sequence dependent setup times on one machine while taking into account the technological and logical constraints on equipment and the management of the supply of liquid metal. In the literature, we find that this problem has been classed as NP-hard ([3], [4], [5]) and is more complex than many described in the survey paper of MacCarthy & Liu [6]. In our work, we have chosen the minimization of total tardiness as a basis for comparison with other methods. 2 Solution Algorithm: Ant Colony Optimization The ant-colony metaheuristic was introduced in the doctoral thesis of Dorigo [7] and was inspired by studies of the behavior of ants ([8], [9], [10]). The works of Colorni, Dorigo & Maniezzo [11], Dorigo, Maniezzo & Colorni [12], Dorigo, Maniezzo & Colorni [13], Dorigo, Gambardella [1], Dorigo & Di Caro [14] offer detailed information on the workings of the algorithm and the choice of the various parameters. The present authors have constructed an ant-colony heuristic to address the scheduling problem described. The basic approach described in [1] was used as a basis for our heuristic. Our version of this heuristic includes the state-transition rule, the global updating rule, the local updating rule, and closely follows the parameter settings recommended by Dorigo and Gambardella. A modification, which we consider major was made to accommodate the nature of the problem at hand. In calculating the state transition probabilities, two distance matrices are used. The first is derived from the setup times in the usual manner for the TSP. The second is derived from computations of the tardiness that would result from the various state transitions. Both are used in a greedy manner and are combined in the state transition rule.

A genetic algorithm for the dynamic single machine scheduling problem

Abstract: This 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

Restarts Can Help in the On-Line Minimization of the Maximum Delivery Time on a Single Machine

Abstract: We consider a single-machine on-line scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on a single machine. Each job becomes available at its release date, which is not known in advance, and its characteristics, i.e., processing requirement and delivery time, become known at its arrival. The objective is to minimize the time by which all jobs have been delivered. In our model preemption is not allowed, but we are allowed to restart a job, that is, the processing of a job can be broken off to have the machine available to process an urgent job, but the time already spent on processing this interrupted job is considered to be lost. We propose an on-line algorithm and show that its performance bound is equal to 1.5, which matches a known lower bound due to Vestjens. For the same problem without restarts the optimal worst-case bound is known to be equal to (√5 + 1)/2 ≈ 1.61803; this is the first example of a situation in which the possibility of applying restarts reduces the worst-case performance bound, even though the processing times are known.

Trade-off solutions in a single-machine scheduling problem for minimizing total earliness and maximum tardiness

Abstract: This paper considers a single-machine scheduling problem involving minimization of the total earliness and the maximum tardiness. Four dominant properties for the precedence relationship between jobs in a search for an optimal solution are proposed. The lower bounds of the total earliness and the maximum tardiness of a subproblem are derived. The dominance properties and the lower bounds are implemented in the branchand-bound algorithm to facilitate the search for an optimal schedule. A heuristic algorithm is then developed to overcome the inefficiency of the branch-and-bound algorithm. Computational performance of the two algorithms is also investigated.

Scheduling Deteriorating Jobs with Ready Times

Abstract: The paper deals with a single machine scheduling problem, where the job processing time is start time and ready time dependent. The problem is to find such a schedule (the job processing order) which minimizes the maximum schedule length (makespan). We show that the problem is NP-complete and present some heuristic algorithm basing on the proved problem properties. Some computational analysis of the proposed algorithm is also given.

Evolutionary approaches with multirecombination for the parallel machine scheduling problem

Abstract: Parallel machine scheduling, also known as parallel task scheduling, involves the assignment of multiple tasks onto the system architecture's processing components (a bank of machines in parallel). Parallel machine scheduling is important from both the theoretical and practical points of view. From the theoretical viewpoint, it is a generalization of the single machine scheduling problem. From the practical point of view it permits to take full advantage of the processing power provided by resources in parallel. Two basic models involving m machines and n jobs are the foundations of more complex models. In the first problem the jobs are allocated according to resource availability following some allocation rule. In the second one, besides that, jobs are subject to precedence constraints. The completion time of the last job to leave the system, known as the makespan (C/sub max/), is one of the most important objective functions to be minimized, because it usually implies high utilization of resources. These problems, minimizing the makespan, are known in the literature (Pinedo, 1995) as the unrestricted parallel machine scheduling (Pm|C/sub max/) and the parallel machine scheduling with job precedence constraints (Pm|prec|C/sub max/). Evolutionary algorithms (EAs) have also been used to solve scheduling problems. This paper proposes a multirecombination scheme to solve both parallel machine scheduling problems.

GA-Based Approach to Single Machine Scheduling with General Early Tardy Penalty Weights

Abstract: It is accordance with Just In Time (JIT) philosophy to penalize early/tardy jobs. A genetic algorithm based optimal method of solving single machine scheduling problem with general early tardy penalty weights is presented in the paper,which is composed of sequencing optimization and timing optimization algorithms. A new crossover operator is constructed for optimal sequencing search and an effective optimal timing algorithm proposed based on the characteristic analyses of penalty function. For different scale of scheduling problems, a lot of comparative computational experiments were done and the results manifested the method effectiveness.

Single machine scheduling with two job classes : minimizing maximum lateness

Abstract: In this paper a single machine scheduling problem with two job classes is considered. In this problem, if two adjacent jobs in a schedule belong to the same class no set up time is required. Howeve...

Scheduling based on earliness and tardiness criteria in assembly job shops

Abstract: In this research, the following four scheduling problems have been studied; (1) single machine problem with earliness cost minimization, (2) single machine problem with the sum of the weighted earliness and weighted tardiness cost minimization, (3) assembly job shop problem with earliness cost minimization, and (4) assembly job shop problem with the sum of weighted earliness and weighted tardiness cost minimization. Four mathematical models based on these four scheduling problems were developed in an effort to obtain optimal solutions. Six heuristic algorithms have been developed to solve the problems. The performances of the heuristic algorithms were demonstrated on some sample test problems. Quality of solutions and CPU time of solutions were the factors of interest. Several properties of optimal solutions for the single machine scheduling problem with the objective of minimizing the weighted earliness penalty have been identified In the research. Algorithms I, III, V, and VI were developed based on these identified properties while the algorithms II and IV were developed based on the tabu search concept. Algorithms I and 11 were developed to solve the first case (1) problem. The results indicate that these two algorithms are able to produce solutions close to optimal in small size problems. The results also show that algorithm I is relatively better than algorithm 11 in large size problem. Algorithms III and IV were developed to solve the second case (2) problem. Both algorithms obtained a small average deviation solutions (i.e.. less than 2%) from optimal in small size test problems. For all problems tested, the algorithm IV is the best algorithm for solving the eariiness/tardiness problems compared to algorithm III and the Ow & Morton algorithm. Algorithm V was developed to solve the third case (3) problem. It obtained an average deviation solutions less than 1% from the optimal. Algorithm VI was developed to solve the fourth case (4) problem. Algorithm VI obtained an average deviation solutions of 2.53% from the optimal.