scispace - formally typeset
Search or ask a question

Showing papers in "Journal of Scheduling in 2009"


Journal ArticleDOI
TL;DR: The paper defines the problem of dynamic scheduling and provides a review of the state-of-the-art of currently developing research on dynamic scheduling, and the principles of several dynamic scheduling techniques, namely, heuristics, meta-heuristic, multi-agent systems, and other artificial intelligence techniques are described in detail.
Abstract: In most real-world environments, scheduling is an ongoing reactive process where the presence of a variety of unexpected disruptions is usually inevitable, and continually forces reconsideration and revision of pre-established schedules. Many of the approaches developed to solve the problem of static scheduling are often impractical in real-world environments, and the near-optimal schedules with respect to the estimated data may become obsolete when they are released to the shop floor. This paper outlines the limitations of the static approaches to scheduling in the presence of real-time information and presents a number of issues that have come up in recent years on dynamic scheduling. The paper defines the problem of dynamic scheduling and provides a review of the state-of-the-art of currently developing research on dynamic scheduling. The principles of several dynamic scheduling techniques, namely, heuristics, meta-heuristics, multi-agent systems, and other artificial intelligence techniques are described in detail, followed by a discussion and comparison of their potential.

786 citations


Journal ArticleDOI
TL;DR: A critical discussion of the research on exam timetabling which has taken place in the last decade or so is presented and a range of relevant important research issues and challenges that have been generated by this body of work are outlined.
Abstract: Examination timetabling is one of the most important administrative activities that takes place in all academic institutions. In this paper, we present a critical discussion of the research on exam timetabling which has taken place in the last decade or so. This last ten years has seen a significantly increased level of research attention for this important area. There has been a range of insightful contributions to the scientific literature both in terms of theoretical issues and practical aspects. The main aim of this survey is to highlight the new trends and key research achievements that have been carried out in the last decade. We also aim to outline a range of relevant important research issues and challenges that have been generated by this body of work. We first define the problem and discuss previous survey papers. Within our presentation of the state-of-the-art methodologies, we highlight recent research trends including hybridisations of search methodologies and the development of techniques which are motivated by raising the level of generality at which search methodologies can operate. Summarising tables are presented to provide an overall view of these techniques. We also present and discuss some important issues which have come to light concerning the public benchmark exam timetabling data. Different versions of problem datasets with the same name have been circulating in the scientific community for the last ten years and this has generated a significant amount of confusion. We clarify the situation and present a re-naming of the widely studied datasets to avoid future confusion. We also highlight which research papers have dealt with which dataset. Finally, we draw upon our discussion of the literature to present a (non-exhaustive) range of potential future research directions and open issues in exam timetabling research.

370 citations


Journal ArticleDOI
TL;DR: A decision support system for cyclic master surgery scheduling that relies on mixed integer programming techniques involving the solution of multi-objective linear and quadratic optimization problems, and on a simulated annealing metaheuristic is presented.
Abstract: This paper presents a decision support system for cyclic master surgery scheduling and describes the results of an extensive case study applied in a medium-sized Belgian hospital. Three objectives are taken into account when building the master surgery schedule. First of all, the resulting bed occupancy at the hospitalization units should be leveled as much as possible. Second, a particular operating room is best allocated exclusively to one group of surgeons having the same speciality; i.e., operating rooms should be shared as little as possible between different surgeon groups. Third, the master surgery schedule is preferred to be as simple and repetitive as possible, with few changes from week to week. The system relies on mixed integer programming techniques involving the solution of multi-objective linear and quadratic optimization problems, and on a simulated annealing metaheuristic.

175 citations


Journal ArticleDOI
TL;DR: A revised optimization model for the scheduling of quay cranes is presented and a heuristic solution procedure is proposed for searching a subset of above average quality schedules which produces much better solutions in considerably shorter run times than all algorithms known from the literature.
Abstract: This paper considers the problem of scheduling quay cranes which are used at sea port container terminals to load and unload containers. This problem is studied intensively in a recent stream of research but still lacks a correct treatment of crane interference constraints. We present a revised optimization model for the scheduling of quay cranes and propose a heuristic solution procedure. At its core a Branch-and-Bound algorithm is applied for searching a subset of above average quality schedules. The heuristic takes advantage from efficient criteria for branching and bounding the search with respect to the impact of crane interference. Although the used techniques are quite standard, the new heuristic produces much better solutions in considerably shorter run times than all algorithms known from the literature.

174 citations


Journal ArticleDOI
TL;DR: A model is presented that includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of vehicles for making the deliveries and uses an allocation model in the form of a mixed integer program to find good feasible solutions that serve as starting points for the tabu search.
Abstract: The integration of production and distribution decisions presents a challenging problem for manufacturers trying to optimize their supply chain. At the planning level, the immediate goal is to coordinate production, inventory, and delivery to meet customer demand so that the corresponding costs are minimized. Achieving this goal provides the foundations for streamlining the logistics network and for integrating other operational and financial components of the system. In this paper, a model is presented that includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of vehicles for making the deliveries. Demand can be satisfied from either inventory held at the customer sites or from daily product distribution. In the most restrictive case, a vehicle routing problem must be solved for each time period. The decision to visit a customer on a particular day could be to restock inventory, meet that day's demand or both. In a less restrictive case, the routing component of the model is replaced with an allocation component only. A procedure centering on reactive tabu search is developed for solving the full problem. After a solution is found, path relinking is applied to improve the results. A novel feature of the methodology is the use of an allocation model in the form of a mixed integer program to find good feasible solutions that serve as starting points for the tabu search. Lower bounds on the optimum are obtained by solving a modified version of the allocation model. Computational testing on a set of 90 benchmark instances with up to 200 customers and 20 time periods demonstrates the effectiveness of the approach. In all cases, improvements ranging from 10---20% were realized when compared to those obtained from an existing greedy randomized adaptive search procedure (GRASP). This often came at a three- to five-fold increase in runtime, however.

164 citations


Journal ArticleDOI
TL;DR: A hybrid Benders decomposition (HBD) algorithm is developed that combines the complimentary strengths of both mixed-integer linear programming (MILP) and constraint programming (CP) to solve this NP-hard optimization problem.
Abstract: We study an assignment type resource-con- strained project scheduling problem with resources being multi-skilled personnel to minimize the total staffing costs. We develop a hybrid Benders decomposition (HBD) algorithm that combines the complimentary strengths of both mixed-integer linear programming (MILP) and constraint programming (CP) to solve this NP-hard optimization problem. An effective cut-generating scheme based on temporal analysis in project scheduling is devised for resolving resource conflicts. The computational study shows that our hybrid MILP/CP algorithm is both effective and efficient compared to the pure MILP or CP method alone.

154 citations


Journal ArticleDOI
TL;DR: In this article, the authors compare the performance of five different heuristics for multi-depot vehicle scheduling problem, namely, a truncated branch-and-cut method, a Lagrangian heuristic, the truncated column generation method, the large neighborhood search heuristic (LNS), a truncation column generation for neighborhood evaluation, and a tabu search algorithm, and show that column generation heuristic performs the best when enough computational time is available and stability is required.
Abstract: Given a set of timetabled tasks, the multi-depot vehicle scheduling problem consists of determining least-cost schedules for vehicles assigned to several depots such that each task is accomplished exactly once by a vehicle. In this paper, we propose to compare the performance of five different heuristics for this well-known problem, namely, a truncated branch-and-cut method, a Lagrangian heuristic, a truncated column generation method, a large neighborhood search heuristic using truncated column generation for neighborhood evaluation, and a tabu search heuristic. The first three methods are adaptations of existing methods, while the last two are new in the context of this problem. Computational results on randomly generated instances show that the column generation heuristic performs the best when enough computational time is available and stability is required, while the large neighborhood search method is the best alternative when looking for good quality solutions in relatively fast computational times.

123 citations


Journal ArticleDOI
David P. Bunde1
TL;DR: It is shown that the optimal flow corresponding to a particular energy budget cannot be exactly computed on a machine supporting exact real arithmetic, including the extraction of roots, as well as total flow, which is NP-hard.
Abstract: We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give a linear-time algorithm to compute all non-dominated solutions for the general uniprocessor problem and a fast arbitrarily-good approximation for multiprocessor problems when every job requires the same amount of work. We also show that the multiprocessor problem becomes NP-hard when jobs can require different amounts of work. For total flow, we show that the optimal flow corresponding to a particular energy budget cannot be exactly computed on a machine supporting exact real arithmetic, including the extraction of roots. This hardness result holds even when scheduling equal-work jobs on a uniprocessor. We do, however, extend previous work by Pruhs et al. to give an arbitrarily-good approximation for scheduling equal-work jobs on a multiprocessor.

91 citations


Journal ArticleDOI
TL;DR: A typology is proposed that distinguishes between proactive, progressive, and revision approaches, and a theoretic model integrating those three approaches is defined, focusing on scheduling and schedule execution.
Abstract: There are many systems and techniques that address stochastic planning and scheduling problems, based on distinct and sometimes opposite approaches, especially in terms of how generation and execution of the plan, or the schedule, are combined, and if and when knowledge about the uncertainties is taken into account. In many real-life problems, it appears that many of these approaches are needed and should be combined, which to our knowledge has never been done. In this paper, we propose a typology that distinguishes between proactive, progressive, and revision approaches. Then, focusing on scheduling and schedule execution, a theoretic model integrating those three approaches is defined. This model serves as a general template to implement a system that will fit specific application needs: we introduce and discuss our experimental prototypes which validate our model in part, and suggest how this framework could be extended to more general planning systems.

90 citations


Journal ArticleDOI
TL;DR: Numerical experiments show that the proposed algorithm can optimally solve 300 jobs instances of the total weighted tardiness problem and thetotal weighted earliness-tardness problem, and that it outperforms the previous algorithms specialized for these problems.
Abstract: This study proposes an exact algorithm for the general single-machine scheduling problem without machine idle time to minimize the total job completion cost. Our algorithm is based on the Successive Sublimation Dynamic Programming (SSDP) method. Its major drawback is heavy memory usage to store dynamic programming states, although unnecessary states are eliminated in the course of the algorithm. To reduce both memory usage and computational efforts, several improvements to the previous algorithm based on the SSDP method are proposed. Numerical experiments show that our algorithm can optimally solve 300 jobs instances of the total weighted tardiness problem and the total weighted earliness-tardiness problem, and that it outperforms the previous algorithms specialized for these problems.

88 citations


Journal ArticleDOI
TL;DR: In this article, a branch-and-bound algorithm for hard two-agent scheduling problems is proposed, where each agent has an objective function which depends on the completion times of its jobs only.
Abstract: In this paper, we develop branch-and-bound algorithms for several hard, two-agent scheduling problems, i.e., problems in which each agent has an objective function which depends on the completion times of its jobs only. Our bounding approach is based on the fact that, for all problems considered, the Lagrangian dual gives a good bound and can be solved exactly in strongly polynomial time. The problems addressed here consist in minimizing the total weighted completion time of the jobs of agent A, subject to a bound on the cost function of agent B, which may be: (i) total weighted completion time, (ii) maximum lateness, (iii) maximum completion time. An extensive computational experience shows the effectiveness of the approach.

Journal ArticleDOI
TL;DR: A novel memetic algorithm is proposed which evolves good quality sequences of repairs generated by CABAROST, which was tested on instances of the real-world nurse rostering problem at the Queens Medical Centre NHS Trust in Nottingham.
Abstract: In this paper we present a novel Case-Based Reasoning (CBR) system called CABAROST (CAsed-BAsed ROSTering) which was developed for personnel scheduling problems. CBR is used to capture and store examples of personnel manager behaviour which are then used to solve future problems. Previous examples of constraint violations in schedules and the repairs that were used to solve the violations are stored as cases. The sequence in which violations are repaired can have a great impact on schedule quality. A novel memetic algorithm is proposed which evolves good quality sequences of repairs generated by CABAROST. The algorithm was tested on instances of the real-world nurse rostering problem at the Queens Medical Centre NHS Trust in Nottingham.

Journal ArticleDOI
TL;DR: A lower bound of $2-\frac{1}{m}$ on the competitive ratio of any deterministic online algorithm for m machines and unit jobs is proved, and an upper bound of 2 when the algorithm is not restricted computationally is shown.
Abstract: We consider the following problem of scheduling with conflicts (swc): Find a minimum makespan schedule on identical machines where conflicting jobs cannot be scheduled concurrently. We study the problem when conflicts between jobs are modeled by general graphs. Our first main positive result is an exact algorithm for two machines and job sizes in {1,2}. For jobs sizes in {1,2,3}, we can obtain a $\frac{4}{3}$ -approximation, which improves on the $\frac{3}{2}$ -approximation that was previously known for this case. Our main negative result is that for jobs sizes in {1,2,3,4}, the problem is APX-hard. Our second contribution is the initiation of the study of an online model for swc, where we present the first results in this model. Specifically, we prove a lower bound of $2-\frac{1}{m}$ on the competitive ratio of any deterministic online algorithm for m machines and unit jobs, and an upper bound of 2 when the algorithm is not restricted computationally. For three machines we can show that an efficient greedy algorithm achieves this bound. For two machines we present a more complex algorithm that achieves a competitive ratio of $2-\frac{1}{7}$ when the number of jobs is known in advance to the algorithm.

Journal ArticleDOI
TL;DR: The school timetabling problem, although less complicated than its counterpart for the university, still provides a ground for interesting and innovative approaches that promise solutions of high quality, and in this work, a Shift Assignment Problem is solved first and work shifts are assigned to teachers.
Abstract: The school timetabling problem, although less complicated than its counterpart for the university, still provides a ground for interesting and innovative approaches that promise solutions of high quality. In this work, a Shift Assignment Problem is solved first and work shifts are assigned to teachers. In the sequel, the actual Timetabling Problem is solved while the optimal shift assignments that resulted from the previous problem help in defining the values for the cost coefficients in the objective function. Both problems are modelled using Integer Programming and by this combined approach we succeed in modelling all operational and practical rules that the Hellenic secondary educational system imposes. The resulting timetables are conflict free, complete, fully compact and well balanced for the students. They also handle simultaneous, collaborative and parallel teaching as well as blocks of consecutive lectures for certain courses. In addition, they are highly compact for the teachers, satisfy the teachers' preferences at a high degree, and assign core courses towards the beginning of each day.

Journal ArticleDOI
TL;DR: This work applies goal separation to the problem of synthesizing robust schedules, by separating the phase of problem solution from a subsequent phase of solution robustification in which a more flexible set of solutions is obtained and compactly represented through a temporal graph, called a Partial Order Schedule.
Abstract: Goal separation is often a fruitful approach when solving complex problems. It provides a way to focus on relevant aspects in a stepwise fashion and hence bound the problem solving scope along a specific direction at any point. This work applies goal separation to the problem of synthesizing robust schedules. The problem is addressed by separating the phase of problem solution, which may pursue a standard optimization criterion (e.g., minimal makespan), from a subsequent phase of solution robustification in which a more flexible set of solutions is obtained and compactly represented through a temporal graph, called a Partial Order Schedule ( $\mathcal{POS}$ ). The key advantage of a $\mathcal{POS}$ is that it provides the capability to promptly respond to temporal changes (e.g., activity duration changes or activity start-time delays) and to hedge against further changes (e.g., new activities to perform or unexpected variations in resource capacity). On the one hand, the paper focuses on specific heuristic algorithms for synthesis of $\mathcal{POS}$ s, starting from a pre-existing schedule (hence the name Solve-and-Robustify). Different extensions of a technique called chaining, which progressively introduces temporal flexibility into the representation of the solution, are introduced and evaluated. These extensions follow from the fact that in multi-capacitated resource settings more than one $\mathcal{POS}$ can be derived from a specific fixed-times solution via chaining, and carry out a search for the most robust alternative. On the other hand, an additional analysis is performed to investigate the performance gain possible by further broadening the search process to consider multiple initial seed solutions. A detailed experimental analysis using state-of-the-art rcpsp/max benchmarks is carried out to demonstrate the performance advantage of these more sophisticated solve and robustify procedures, corroborating prior results obtained on smaller problems and also indicating how this leverage increases as problem size is increased.

Journal ArticleDOI
TL;DR: A fairly complete classification of the corresponding inverse models under different types of norms that measure the deviation of adjusted parameters from their given estimates is performed.
Abstract: We study a range of counterparts of the single-machine scheduling problem with the maximum lateness criterion that arise in the context of inverse optimization. While in the forward scheduling problem all parameters are given and the objective is to find the optimal job sequence for which the value of the maximum lateness is minimum, in inverse scheduling the exact values of processing times or due dates are unknown, and they should be determined so that a prespecified solution becomes optimal. We perform a fairly complete classification of the corresponding inverse models under different types of norms that measure the deviation of adjusted parameters from their given estimates.

Journal ArticleDOI
TL;DR: This paper addresses an allocation and sequencing problem motivated by an application in unsupervised automated manufacturing and presents the effectiveness of the heuristic and the bound on a large sample of instances.
Abstract: This paper addresses an allocation and sequencing problem motivated by an application in unsupervised automated manufacturing. There are n independent jobs to be processed by one of m machines or units during a finite unsupervised duration or shift. Each job is characterized by a certain success probability p i , and a reward r i which is obtained if the job is successfully carried out. When a job fails during processing, the processing unit is blocked, and the jobs subsequently scheduled on that machine are blocked until the end of the unsupervised period. The problem is to assign and sequence the jobs on the machines so that the expected total reward is maximized. This paper presents the following results for this problem and some extensions: (i) a polyhedral characterization for the single machine case, (ii) the proof that the problem is NP-hard even with 2 machines, (iii) approximation results for a round-robin heuristic, (iv) an effective upper bound. Extensive computational results show the effectiveness of the heuristic and the bound on a large sample of instances.

Journal ArticleDOI
TL;DR: A multi-objective evolutionary algorithm that uses a variable-length chromosome representation and incorporates a micro-genetic algorithm and a hill-climber for local exploitation and a goal-based Pareto ranking scheme for assigning the relative strength of solutions is presented.
Abstract: This paper considers the scheduling of exams for a set of university courses. The solution to this exam timetabling problem involves the optimization of complete timetables such that there are as few occurrences of students having to take exams in consecutive periods as possible but at the same time minimizing the timetable length and satisfying hard constraints such as seating capacity and no overlapping exams. To solve such a multi-objective combinatorial optimization problem, this paper presents a multi-objective evolutionary algorithm that uses a variable-length chromosome representation and incorporates a micro-genetic algorithm and a hill-climber for local exploitation and a goal-based Pareto ranking scheme for assigning the relative strength of solutions. It also imports several features from the research on the graph coloring problem. The proposed algorithm is shown to be a more general exam timetabling problem solver in that it does not require any prior information of the timetable length to be effective. It is also tested against a few influential and recent optimization techniques and is found to be superior on four out of seven publicly available datasets.

Journal ArticleDOI
TL;DR: A pseudo-polynomial algorithm is presented for a restricted case, where late jobs are delivered separately, and it is shown that it becomes polynomial for the special cases when jobs have equal weights and equal delivery costs or equal processing times and equal setup times.
Abstract: We study a supply chain scheduling problem in which n jobs have to be scheduled on a single machine and delivered to m customers in batches. Each job has a due date, a processing time and a lateness penalty (weight). To save batch-delivery costs, several jobs for the same customer can be delivered together in a batch, including late jobs. The completion time of each job in the same batch coincides with the batch completion time. A batch setup time has to be added before processing the first job in each batch. The objective is to find a schedule which minimizes the sum of the weighted number of late jobs and the delivery costs. We present a pseudo-polynomial algorithm for a restricted case, where late jobs are delivered separately, and show that it becomes polynomial for the special cases when jobs have equal weights and equal delivery costs or equal processing times and equal setup times. We convert the algorithm into an FPTAS and prove that the solution produced by it is near-optimal for the original general problem by performing a parametric analysis of its performance ratio.

Journal ArticleDOI
TL;DR: A tabu search heuristic for a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine is introduced and consistently finds better solutions in less computation time than a recent branch-and-cut algorithm.
Abstract: This paper introduces a tabu search heuristic for a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The problem consists in scheduling a set of dependent jobs, where the transition between two jobs comprises an unrestricted setup that can be performed at any time, and a restricted setup that must be performed outside of a given time interval which repeats daily in the same position. The setup time between two jobs is thus a function of the completion time of the first job. The tabu search heuristic relies on shift and swap moves, and a surrogate objective function is used to speed-up the neighborhood evaluation. Computational experiments show that the proposed heuristic consistently finds better solutions in less computation time than a recent branch-and-cut algorithm. Furthermore, on instances where the branch-and-cut algorithm cannot find the optimal solution, the heuristic always identifies a better solution.

Journal ArticleDOI
TL;DR: A modified Branch and Bound algorithm called, the Branch, Bound, and Remember (BB&R) algorithm, which uses the Distributed Best First Search (DBFS) exploration strategy for solving the 1|ri|∑ti scheduling problem, a single machine scheduling problem where the objective is to find a schedule with the minimum total tardiness.
Abstract: This paper presents a modified Branch and Bound (B&B) algorithm called, the Branch, Bound, and Remember (BB&R) algorithm, which uses the Distributed Best First Search (DBFS) exploration strategy for solving the 1|r i |Σem>t i scheduling problem, a single machine scheduling problem where the objective is to find a schedule with the minimum total tardiness. Memory-based dominance strategies are incorporated into the BB&R algorithm. In addition, a modified memory-based dynamic programming algorithm is also introduced to efficiently compute lower bounds for the 1|r i |Σt i scheduling problem. Computational results are reported, which shows that the BB&R algorithm with the DBFS exploration strategy outperforms the best known algorithms reported in the literature.

Journal ArticleDOI
TL;DR: In this paper, in an exemplary way theory and three polynomial solution algorithms for the planar ScheLoc makespan problem are introduced, which includes a specific type of a scheduling and a rather general, planar location problem, respectively.
Abstract: While in classical scheduling theory the locations of machines are assumed to be fixed we will show how to tackle location and scheduling problems simultaneously. Obviously, this integrated approach enhances the modeling power of scheduling for various real-life problems. In this paper, we introduce in an exemplary way theory and three polynomial solution algorithms for the planar ScheLoc makespan problem, which includes a specific type of a scheduling and a rather general, planar location problem, respectively. Finally, a report on numerical tests as well as a generalization of this specific ScheLoc problem is presented.

Journal ArticleDOI
TL;DR: This paper introduces the Traveling Tournament Problem with Predefined Venues, which consists in scheduling a compact single round robin tournament with a predefined venue assignment for each game while the total distance traveled by the teams is minimized.
Abstract: Sports scheduling is a very attractive application area not only because of the interesting mathematical structures of the problems, but also due to their importance in practice and to the big business that sports have become. In this paper, we introduce the Traveling Tournament Problem with Predefined Venues, which consists in scheduling a compact single round robin tournament with a predefined venue assignment for each game (i.e., the venue where each game takes place is known beforehand) while the total distance traveled by the teams is minimized. Three integer programming formulations are proposed and compared. We also propose some simple enumeration strategies to generate feasible solutions to real-size instances in a reasonable amount of time. We show that two original enumeration strategies outperform an improvement heuristic embedded within a commercial solver. Comparative numerical results are presented.

Journal ArticleDOI
TL;DR: This work provides the best possible on-line algorithm for the problem with competitive ratio, where jobs arrive over time and jobs from different families cannot be scheduled in a common batch.
Abstract: We study the on-line scheduling on an unbounded parallel batch machine to minimize makespan of two families of jobs. In this model, jobs arrive over time and jobs from different families cannot be scheduled in a common batch. We provide a best possible on-line algorithm for the problem with competitive ratio $(\sqrt{17}+3)/4\approx1.7808$ .

Journal ArticleDOI
TL;DR: The notion of increasing algorithm and a simple reduction that transforms any increasing algorithm into a truthful one are introduced and it is shown that some of the classical scheduling algorithms are indeed increasing.
Abstract: We consider the problem of designing truthful mechanisms for scheduling n tasks on a set of m parallel related machines in order to minimize the makespan. In what follows, we consider that each task is owned by a selfish agent. This is a variant of the KP-model introduced by Koutsoupias and Papadimitriou (Proc. of STACS 1999, pp. 404---413, 1999) (and of the CKN-model of Christodoulou et al. in Proc. of ICALP 2004, pp. 345---357, 2004) in which the agents cannot choose the machine on which their tasks will be executed. This is done by a centralized authority, the scheduler. However, the agents may manipulate the scheduler by providing false information regarding the length of their tasks. We introduce the notion of increasing algorithm and a simple reduction that transforms any increasing algorithm into a truthful one. Furthermore, we show that some of the classical scheduling algorithms are indeed increasing: the LPT algorithm, the PTAS of Graham (SIAM J. Appl. Math. 17(2):416---429, 1969) in the case of two machines, as well as a simple PTAS for the case of m machines, with m a fixed constant. Our results yield a randomized r(1+?)-approximation algorithm where r is the ratio between the largest and the smallest speed of the related machines. Furthermore, by combining our approach with the classical result of Shmoys et al. (SIAM J. Comput. 24(6):1313---1331, 1995), we obtain a randomized 2r(1+?)-competitive algorithm. It has to be noticed that these results are obtained without payments, unlike most of the existing works in the field of Mechanism Design. Finally, we show that if payments are allowed then our approach gives a (1+?)-algorithm for the off-line case with related machines.

Journal ArticleDOI
TL;DR: A semi-online algorithm which, if the optimal makespan is given in advance, produces an optimal schedule, and matches the performance of the previously known algorithms for the offline case, with a considerably simpler proof.
Abstract: We consider the problem of preemptive scheduling on uniformly related machines. We present a semi-online algorithm which, if the optimal makespan is given in advance, produces an optimal schedule. Using the standard doubling technique, this yields a 4-competitive deterministic and an e?2.71-competitive randomized online algorithm. In addition, it matches the performance of the previously known algorithms for the offline case, with a considerably simpler proof. Finally, we study the performance of greedy heuristics for the same problem.

Journal ArticleDOI
TL;DR: This work considers high-multiplicity parallel machine scheduling problems with identical, uniform, and unrelated machines, and two classic objectives: minimum sum of completion times and minimum makespan, and provides exact, asymptotically exact algorithms for polynomially solvable and hard cases.
Abstract: In many scheduling applications, a large number of jobs are grouped into a comparatively small number of lots made of identical items It is then sufficient to give, for each lot, the number of jobs it involves plus the description of one single job The resulting high-multiplicity input format is much more compact than the standard one As a consequence, in order to be efficient, standard solution methods must be modified We consider high-multiplicity parallel machine scheduling problems with identical, uniform, and unrelated machines, and two classic objectives: minimum sum of completion times and minimum makespan For polynomially solvable cases, we provide exact algorithms, while for hard cases we provide approximate, asymptotically exact algorithms The exact algorithms exploit multiplicities to identify and fix a partial schedule, consisting of most jobs, that is contained in an optimal schedule, and then solve the residual problem optimally The approximate algorithms use the same approach, but in their case neither it is guaranteed that the fixed partial schedule is contained in an optimal one nor the residual problem is optimally solved All proposed algorithms are polynomial and easy to implement for practical purposes

Journal ArticleDOI
TL;DR: In this paper, the authors consider conjugate problems which constitute a new class of mutually related time-dependent scheduling problems and prove basic properties of conjugacy problems and show the relations that hold between such problems.
Abstract: In the paper, we consider conjugate problems which constitute a new class of mutually related time-dependent scheduling problems. Any element from this class is a composite problem, being a pair of two time-dependent scheduling problems connected by a conjugacy formula. We prove basic properties of conjugate problems and show the relations that hold between such problems. We also propose an approach to the construction of greedy heuristics for the conjugate problems. We illustrate applications of the results by examples.

Journal ArticleDOI
TL;DR: This work is based on the original model of CPT, an optimal temporal planner, and it extends the CPT’s formulation to deal with more expressive constraints, and shows that the general formulation can be used for planning and/or scheduling.
Abstract: Planning research is recently concerned with the resolution of more realistic problems as evidenced in the many works and new extensions to the Planning Domain Definition Language (PDDL) to better approximate real problems. Researchers’ works to push planning algorithms and capture more complex domains share an essential ingredient, namely the incorporation of new types of constraints. Adding constraints seems to be the way of approximating real problems: these constraints represent the duration of tasks, temporal and resource constraints, deadlines, soft constraints, etc., i.e. features that have been traditionally associated to the area of scheduling. This desired expressiveness can be achieved by augmenting the planning reasoning capabilities, at the cost of slightly deviating the planning process from its traditional implicit purpose, that is finding the causal structure of the plan. However, the resolution of complex domains with a great variety of different constraints may involve as much planning effort as scheduling effort (and perhaps the latter being more prominent in many problems). For this reason, in this paper we present a general approach to model those problems under a constraint programming formulation which allows us to represent and handle a wide range of constraints. Our work is based on the original model of $\mathsf{CPT}$ , an optimal temporal planner, and it extends the $\mathsf{CPT}$ ’s formulation to deal with more expressive constraints. We will show that our general formulation can be used for planning and/or scheduling, from scheduling a given complete plan to generating the whole plan from scratch. However, our contribution is not a new planner but a constraint programming formulation for representing highly-constrained planning + scheduling problems.

Journal ArticleDOI
TL;DR: In this paper, a cyclic solution approach is proposed to decompose the problem into a batching and a batch-scheduling problem, which is then repeated several times.
Abstract: We deal with the scheduling of processes on a multi-product chemical batch production plant. Such a plant contains a number of multi-purpose processing units and storage facilities of limited capacity. Given primary requirements for the final products, the problem consists in dividing the net requirements for the final and the intermediate products into batches and scheduling the processing of these batches. Due to the computational intractability of the problem, the monolithic MILP models proposed in the literature can generally not be used for solving large-scale problem instances. The cyclic solution approach presented in this paper starts from the decomposition of the problem into a batching and a batch-scheduling problem. The complete production schedule is obtained by computing a cyclic subschedule, which is then repeated several times. In this way, good feasible schedules for large-scale problem instances are found within a short CPU time.