Heuristics Based on Partial Enumeration for the Unrelated Parallel Processor Scheduling Problem

The classical deterministic scheduling problem of minimizing the makespan on unrelated parallel processors is known to be NP-hard in the strong sense. Given the mixed integer linear model with binary decision variables, this paper presents heuristic algorithms based on partial enumeration. Basically, they consist in the construction of mixed integer subproblems, considering the integrality of some subset of variables, formulated using the information obtained from the solution of the linear relaxed problem. Computational experiments are reported for a collection of test problems, showing that some of the proposed algorithms achieve better solutions than other relevant approximation algorithms published up to now.     

A new approach for scheduling independent tasks with multiple modes

Heuristic algorithms for scheduling tasks with multiple modes and minimizing the schedule length involve in general two distinct phases, task mode assignment and then task scheduling. We propose a novel approach where these two features are managed in an integrated mechanism with mode assignment embedded in scheduling. The problem is first reformulated as a special single-mode task scheduling problem, and then is modeled as a graph interval T-coloring. Finally, a tabu-like metaheuristic is proposed for this latter graph coloring problem, and the performance of our approach is compared to known multi-mode scheduling heuristics.     

The project scheduling problem with production and consumption of resources: A list-scheduling based algorithm

The paper deals with algorithms for applying classical list scheduling to a project scheduling problem where the units of resources are produced or consumed at the occurrence of precedence-related events. It is shown that the feasibility variant of the project scheduling problem is NP-complete. Moreover, polynomial-time scheduling algorithms are devised for the three cases where the occurrence time sequence of all events or the consuming events or the producing events is given in advance. By enumerating these sequences (called linear orders), one obtains a list-scheduling based algorithm for minimizing the makespan of a project scheduling problem with production and consumption of resources.     

Thek-partitioning problem

Thek-partitioning problem is defined as follows: Given a set of items {I ₁,I ₂,...,I _n} where itemIj is of weightwj 0, find a partitionS ₁,S ₂,...,S _m of this set with ¦S _i ¦ =k such that the maximum weight of all subsetsS _i is minimal,k-partitioning is strongly related to the classical multiprocessor scheduling problem of minimizing the makespan on identical machines. This paper provides suitable tools for the construction of algorithms which solve exactly the problem. Several approximation algorithms are presented for this NP-hard problem. The worst-case behavior of the algorithms is analyzed. The best of these algorithms achieves a performance bound of 4/3.     

An effective mathematical formulation for the unidirectional cluster-based quay crane scheduling problem

The quay crane scheduling problem plays an important role in the paradigm of port container terminal management, due to the fact that it closely relates to vessel berthing time. In this paper, we focus on the study of a special strategy for the cluster-based quay crane scheduling problem that forces quay cranes to move unidirectionally during the scheduling. The scheduling problem arising when this strategy is applied is called the unidirectional quay crane scheduling problem in the literature. Different from other researches attempting to construct more sophisticated searching algorithms, in this paper, we seek for a more compact mathematical formulation of the unidirectional cluster-based quay crane scheduling problem that can be easily solved by a standard optimization solver. To assess the performance of the proposed model, commonly accepted benchmark suites are used and the results indicate that the proposed model outperforms the state-of-the-art algorithms designed for the unidirectional cluster-based quay crane scheduling problem.     

Simulated annealing and genetic algorithms for minimizing mean flow time in an open shop

This paper considers the problem of scheduling n jobs on m machines in an open shop environment so that the sum of completion times or mean flow time becomes minimal. It continues recent work by Bräsel et al. [H. Bräsel, A. Herms, M. Mörig, T. Tautenhahn, T. Tusch, F. Werner, Heuristic constructive algorithms for open shop scheduling to minmize mean flow time, European J. Oper. Res., in press (doi.10.1016/j.ejor.2007.02.057)] on constructive algorithms. For this strongly NP-hard problem, we present two iterative algorithms, namely a simulated annealing and a genetic algorithm. For the simulated annealing algorithm, several neighborhoods are suggested and tested together with the control parameters of the algorithm. For the genetic algorithm, new genetic operators are suggested based on the representation of a solution by the rank matrix describing the job and machine orders. Extensive computational results are presented for problems with up to 50 jobs and 50 machines, respectively. The algorithms are compared relative to each other, and the quality of the results is also estimated partially by a lower bound for the corresponding preemptive open shop problem. For most of the problems, the genetic algorithm is superior when fixing the same number of 30 000 generated solutions for each algorithm. However, in contrast to makespan minimization problems, where the focus is on problems with an equal number of jobs and machines, it turns out that problems with a larger number of jobs than machines are the hardest problems.     

LP-based online scheduling: from single to parallel machines

We study classic machine sequencing problems in an online setting. Specifically, we look at deterministic and randomized algorithms for the problem of scheduling jobs with release dates on identical parallel machines, to minimize the sum of weighted completion times: Both preemptive and non-preemptive versions of the problem are analyzed. Using linear programming techniques, borrowed from the single machine case, we are able to design a 2.62-competitive deterministic algorithm for the non-preemptive version of the problem, improving upon the 3.28-competitive algorithm of Megow and Schulz. Additionally, we show how to combine randomization techniques with the linear programming approach to obtain randomized algorithms for both versions of the problem with competitive ratio strictly smaller than 2 for any number of machines (but approaching two as the number of machines grows). Our algorithms naturally extend several approaches for single and parallel machine scheduling. We also present a brief computational study, for randomly generated problem instances, which suggests that our algorithms perform very well in practice. A preliminary version of this work appears in the Proceedings of the 11th conference on integer programming and combinatorial optimization (IPCO), Berlin, 8–10 June 2005.     

Rollout Algorithms for Stochastic Scheduling Problems

Stochastic scheduling problems are difficult stochastic control problems with combinatorial decision spaces. In this paper we focus on a class of stochastic scheduling problems, the quiz problem and its variations. We discuss the use of heuristics for their solution, and we propose rollout algorithms based on these heuristics which approximate the stochastic dynamic programming algorithm. We show how the rollout algorithms can be implemented efficiently, with considerable savings in computation over optimal algorithms. We delineate circumstances under which the rollout algorithms are guaranteed to perform better than the heuristics on which they are based. We also show computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better than the performance of their underlying heuristics.     

Semi-on-line problems on two identical machines with combined partial information

This paper considers the semi-on-line versions of scheduling problem P2||C_max. We study the semi-on-line problems with combination of two types of information. Five basic types of partial information are considered. For two kinds of pairwise combination, we present their respective optimal semi-on-line algorithms which show that combination can admit to construct better algorithms.     

Hybrid Rollout Approaches for the Job Shop Scheduling Problem

In this paper, we focus on heuristic approaches for solving the deterministic job shop scheduling problem. More specifically, a new priority dispatch rule and hybrid rollout algorithms are developed for approaching the problem under consideration. The proposed solution algorithms are tested on a set of instances taken from the literature and compared with other methods. The computational results validate the effectiveness of the developed solution approaches and show that the proposed rollout algorithms are competitive with respect to several state-of-art heuristics for solving the job shop scheduling problem. The author thanks Dr. Marco Mancini and Dr. Alessandro Tarasio for valuable suggestions about computational issues.     

A disjunctive graph model and framework for constructing new train schedules

Train scheduling is a complex and time consuming task of vital importance in many countries. To create completely new train schedules that are more accurate and efficient than permitted by current techniques, a novel “hybrid” job shop approach is proposed and implemented in this paper. Unique characteristics of train scheduling are firstly incorporated into a disjunctive graph representation of the solution. Dedicated “stand-alone” constructive algorithms that utilise this representation are then developed. The modelling approach and the constructive algorithms are essential as they provide the basis for which meta-heuristics and other iterative refinement algorithms can be applied. A numerical investigation and case study is provided and demonstrates the viability of the modelling approach. Furthermore it is demonstrated that good quality solutions are provided with reasonable computational effort.     

求解带组换装时间单机调度问题的禁忌搜索算法

以包头某钢铁线材企业生产实际调度问题为背景,研究了一类带组换装时间的单机调度问题.由于该问题是NP难的,本文提出了一类适合该问题的禁忌搜索算法.此外,本文将问题性质引入了禁忌搜索算法以进一步提高算法寻优性能,降低算法运行时间.本文提出的算法在随机问题和实际问题上均进行了测试,实验结果表明,本文提出的算法能在不到10秒的时间内获得实际问题的一个近似最优解.     

The k-Client Problem

Virtually all previous research in online algorithms has focused on single-threaded systems where only a single sequence of requests compete for system resources. To model multithreaded online systems, we define and analyze the k-client problem, a dual of the well-studied k-server problem. In the basic k-client problem, there is a single server and k clients, each of which generates a sequence of requests for service in a metric space. The crux of the problem is deciding which client's request the single server should service rather than which server should be used to service the current request. We also consider variations where requests have nonzero processing times and where there are multiple servers as well as multiple clients.We evaluate the performance of algorithms using several cost functions including maximum completion time and average completion time. Two of the main results we derive are tight bounds on the performance of several commonly studied disk scheduling algorithms and lower bounds of on the competitive ratio of any online algorithm for the maximum completion time and average completion time cost functions when k is a power of 2. Most of our results are essentially identical for the maximum completion time and average completion time cost functions.     

Minimizing average completion time in the presence of release dates

A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of schedulingn jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when all jobs are available at time 0, all the problems that we consider are NP-hard, and essentially nothing was known about constructing good approximations in polynomial time. We give the first constant-factor approximation algorithms for several variants of the single and parallel machine models. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of averageweighted completion time as well. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.This work was performed under US Department of Energy contract number DE-AC04-76AL85000.Research partly supported by NSF Award CCR-9308701, a Walter Burke Research Initiation Award and a Dartmouth College Research Initiation Award.Research partially supported by NSF Research Initiation Award CCR-9211494 and a grant from the New York State Science and Technology Foundation, through its Center for Advanced Technology in Telecommunications.     

Resolution approach for multi-objective problems with uncertain demands

The job-shop scheduling problem (JSP) is one of the hardest problems (NP-complete problem). In a lot of cases, the combination of goals and resource exponentially increases search space. The objective of resolution of such a problem is generally, to maximize the production with a lower cost and makespan. In this paper, we explain how to modify the objective function of genetic algorithms to treat the multi-objective problem and to generate a set of diversified “optimal” solutions in order to help decision maker. We are interested in one of the problems occurring in the production workshops where the list of demands is split into firm (certain) jobs and predicted jobs. One wishes to maximize the produced quantity, while minimizing as well as possible the makespan and the production costs. Genetic algorithms are used to find the scheduling solution of the firm jobs because they are well adapted to the treatment of the multi-objective optimization problems. The predicted jobs will be inserted in the real solutions (given by genetic algorithms). The solutions proposed by our approach are compared to the lower bound of the cost and makespan in order to prove the quality and robustness of our proposed approach.     

A scatter search algorithm for the distributed permutation flowshop scheduling problem

The distributed permutation flowshop problem has been recently proposed as a generalization of the regular flowshop setting where more than one factory is available to process jobs. Distributed manufacturing is a common situation for large enterprises that compete in a globalized market. The problem has two dimensions: assigning jobs to factories and scheduling the jobs assigned to each factory. Despite being recently introduced, this interesting scheduling problem has attracted attention and several heuristic and metaheuristic methods have been proposed in the literature. In this paper we present a scatter search (SS) method for this problem to optimize makespan. SS has seldom been explored for flowshop settings. In the proposed algorithm we employ some advanced techniques like a reference set made up of complete and partial solutions along with other features like restarts and local search. A comprehensive computational campaign including 10 existing algorithms, together with statistical analyses, shows that the proposed scatter search algorithm produces better results than existing algorithms by a significant margin. Moreover all 720 known best solutions for this problem are improved.     

Mixed-integer programming models for an employee scheduling problem with multiple shifts and work locations

This paper is concerned with the problem of assigning employees to gas stations owned by the Kuwait National Petroleum Corporation (KNPC), which hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. Although similar employee scheduling problems have been addressed in the literature, certain peculiarities of the problem require novel mathematical models and algorithms to deal with the specific nature and size of this problem. The problem is modeled as a mixed-integer program, and a problem size analysis based on real data reveals that the formulation is too complex to solve directly. Hence, a two-stage approach is proposed, where the first stage assigns employees to stations, and the second stage specifies shifts and off-days for each employee. Computational results related to solving the two-stage models directly via CPLEX and by specialized heuristics are reported. The two-stage approach provides daily schedules for employees for a given time horizon in a timely fashion, taking into consideration the employees’ expressed preferences. This proposed modeling approach can be incorporated within a decision support system to replace the current manual scheduling practice that is often chaotic and has led to feelings of bias and job dissatisfaction among employees.     

On the geometry,preemptions and complexity of multiprocessor and shop scheduling

In this paper we study multiprocessor and open shop scheduling problems from several points of view. We explore a tight dependence of the polynomial solvability/intractability on the number of allowed preemptions. For an exhaustive interrelation, we address the geometry of problems by means of a novel graphical representation. We use the so-called preemption and machine-dependency graphs for preemptive multiprocessor and shop scheduling problems, respectively. In a natural manner, we call a scheduling problem acyclic if the corresponding graph is acyclic. There is a substantial interrelation between the structure of these graphs and the complexity of the problems. Acyclic scheduling problems are quite restrictive; at the same time, many of them still remain NP-hard. We believe that an exhaustive study of acyclic scheduling problems can lead to a better understanding and give a better insight of general scheduling problems. We show that not only acyclic but also a special non-acyclic version of periodic job-shop scheduling can be solved in polynomial (linear) time. In that version, the corresponding machine dependency graph is allowed to have a special type of the so-called parti-colored cycles. We show that trivial extensions of this problem become NP-hard. Then we suggest a linear-time algorithm for the acyclic open-shop problem in which at most m−2 preemptions are allowed, where m is the number of machines. This result is also tight, as we show that if we allow one less preemption, then this strongly restricted version of the classical open-shop scheduling problem becomes NP-hard. In general, we show that very simple acyclic shop scheduling problems are NP-hard. As an example, any flow-shop problem with a single job with three operations and the rest of the jobs with a single non-zero length operation is NP-hard. We suggest linear-time approximation algorithm with the worst-case performance of ( , respectively) for acyclic job-shop (open-shop, respectively), where (‖ℳ‖, respectively) is the maximal job length (machine load, respectively). We show that no algorithm for scheduling acyclic job-shop can guarantee a better worst-case performance than . We consider two special cases of the acyclic job-shop with the so-called short jobs and short operations (restricting the maximal job and operation length) and solve them optimally in linear time. We show that scheduling m identical processors with at most m−2 preemptions is NP-hard, whereas a venerable early linear-time algorithm by McNaughton yields m−1 preemptions. Another multiprocessor scheduling problem we consider is that of scheduling m unrelated processors with an additional restriction that the processing time of any job on any machine is no more than the optimal schedule makespan C _max^*. We show that the (2m−3)-preemptive version of this problem is polynomially solvable, whereas the (2m−4)-preemptive version becomes NP-hard. For general unrelated processors, we guarantee near-optimal (2m−3)-preemptive schedules. The makespan of such a schedule is no more than either the corresponding non-preemptive schedule makespan or max {C _max^*,p _max}, where C _max^* is the optimal (preemptive) schedule makespan and p _max is the maximal job processing time. E.V. Shchepin was partially supported by the program “Algebraical and combinatorial methods of mathematical cybernetics” of the Russian Academy of Sciences. N. Vakhania was partially supported by CONACyT grant No. 48433.     

A tabu search algorithm for solving economic lot scheduling problem

The economic lot scheduling problem has driven considerable amount of research. The problem is NP-hard and recent research is focused on finding heuristic solutions rather than searching for optimal solutions. This paper introduces a heuristic method using a tabu search algorithm to solve the economic lot scheduling problem. Diversification and intensification schemes are employed to improve the efficiency of the proposed Tabu search algorithm. Experimental design is conducted to determine the best operating parameters for the Tabu search. Results show that the tabu search algorithm proposed in this paper outperforms two well known benchmark algorithms.     

New solution methods for single machine bicriteria scheduling problem: Minimization of average flowtime and number of tardy jobs

We consider the bicriteria scheduling problem of minimizing the number of tardy jobs and average flowtime on a single machine. This problem, which is known to be NP-hard, is important in practice, as the former criterion conveys the customer’s position, and the latter reflects the manufacturer’s perspective in the supply chain. We propose four new heuristics to solve this multiobjective scheduling problem. Two of these heuristics are constructive algorithms based on beam search methodology. The other two are metaheuristic approaches using a genetic algorithm and tabu-search. Our computational experiments indicate that the proposed beam search heuristics find efficient schedules optimally in most cases and perform better than the existing heuristics in the literature.