Abstract: This paper considers scheduling problems on two machines to minimise the makespan. It shows that a simple cyclical search can find a flow shop schedule with one job omitted with makespan less than or equal to the maximum of the total processing time of all jobs on either machine. This flow shop schedule is used as the basis for constructing a number of schedules with minimum makespan for the two machine open shop. The search may be applied unchanged to batches of jobs to provide more optimal schedules. PubDate: 2015-06-01

Abstract: In the paper “The complexity of mean flow time scheduling problems with release times”, by Baptiste, Brucker, Chrobak, Dürr, Kravchenko and Sourd, the authors claimed to prove strong
\({\mathbb {NP}}\)
-hardness of the scheduling problem
\(P {\textit{pmtn}},r_j \sum C_j\)
, namely multiprocessor preemptive scheduling where the objective is to minimize the mean flow time. We point out a serious error in their proof and give a new proof of strong
\({\mathbb {NP}}\)
-hardness for this problem. PubDate: 2015-06-01

Abstract: We consider a scheduling problem in which the criterion for assigning due dates is to make them as tight as possible, while the criterion for sequencing jobs is to minimize their tardiness. Because these two criteria conflict, we examine the trade-off between the tightness of the due dates and the tardiness of the jobs. We formulate a version of this trade-off in the case of a stochastic single-machine model with normally distributed processing times. Using lower bounds and dominance properties to curtail the enumeration, we develop a branch-and- bound procedure that is capable of solving large versions of the problem, and we report the results of computational experiments involving several hundred test problems. PubDate: 2015-06-01

Abstract: The resource availability cost problem (RACP) (Möhring, Operations Research, 32:89–120, 1984) is commonly encountered in project scheduling. RACP aims to minimize the resource availability cost of a project by a given project deadline. In this study, RACP is extended from a single mode to a multi-mode called multi-mode RACP (MMRACP), which is more complicated than RACP but more convenient in practice. To solve MMRACP efficiently, forward activity list (FAL), a schedule generation scheme, is proposed. Heuristic algorithms are designed according to the characteristics of FAL to repair infeasible solutions and to improve the fitness of the solution. Modified particle swarm optimization (MPSO), which combines the advantages of particle swarm optimization and scatter search, is proposed to make the search for the best solution efficient. Computational experiments involving 180 instances are performed to validate the performance of the proposed algorithm. The results reveal that MPSO using FAL is a very effective method to solve MMRACP. PubDate: 2015-06-01

Abstract: In this paper, we introduce a new kind of constraint, called a core precedence constraint, in a cyclic resource-constrained project scheduling problem (RCPSP) with precedence delays. We show, by an example, which kind of industrial constraints might be modeled by such core precedences in a periodic production setting. We then establish that these constraints can be quite easily added to an integer linear programming formulation of the cyclic RCPSP. Although core precedences seem to be very similar to classical precedence, they can induce infeasibility even without resource constraints. Moreover, we show that the feasibility checking problem is NP-complete in the strong sense, even assuming unit processing times and no resource constraints. PubDate: 2015-06-01

Abstract: In this paper, we address a deterministic scheduling problem in which two agents compete for the usage of a single machine. Each agent decides on a fixed order to submit its tasks to an external coordination subject, who sequences them according to a known priority rule. We consider the problem from different perspectives. First, we characterize the set of Pareto-optimal schedules in terms of size and computational complexity. We then address the problem from the single-agent point-of-view, that is, we consider the problem of deciding how to submit one agent’s tasks only taking into account its own objective function against the other agent, the opponent. In this regard, we consider two different settings depending on the information available to the agents: In one setting, the considered agent knows in advance all information about the submission sequence of the opponent; and in the second setting (as in minimax strategies in game theory), the agent has no information on the opponent strategy and wants to devise a strategy that minimizes its solution cost in the worst possible case. Finally, we assess the performance of some classical single-agent sequencing rules in the two-agent setting. PubDate: 2015-06-01

Abstract: This paper addresses a scheduling problem with continuous resources and energy constraints. Given a set of non-preemptive activities, each activity requires a continuously divisible resource whose instantaneous usage is limited in maximum and minimum, its processing satisfying a time window and a total energy (time
\(\times \)
resource-usage) requirement. The goal consists of getting a schedule satisfying all the constraints. The problem, which we refer to as the Energy-Constrained Scheduling Problem with Continuous Resources (CECSP), is a generalization of the well-known cumulative scheduling problem for which the “energetic reasoning” or “left-shift/right-shift” necessary feasibility condition yielded a popular polynomially computable satisfiability test. The paper presents a generalization of the energetic reasoning for the CECSP, defining precisely the activity minimum consumptions and exhibiting a polynomial number of relevant time intervals on which it is sufficient to apply the satisfiability tests. A strongly polynomial energetic reasoning satisfiability test can be derived for the considered generalization, which also yields a short proof for the complexity of the original algorithm. Some limits of the approach, as well as an approximation framework for more general resource consumption functions, are also addressed. PubDate: 2015-06-01

Abstract: In this paper, we consider two problems about the preemptive scheduling of a set of jobs with release times on a single machine. In the first problem, each job has a deadline. The objective is to find a feasible schedule which minimizes the total completion time of the jobs. In the second problem (called two-agent scheduling problem), the set of jobs is partitioned into two subsets
\(\mathcal{J}^{(1)}\)
and
\(\mathcal{J}^{(2)}\)
. Each job in
\(\mathcal{J}^{(2)}\)
has a deadline. The objective is to find a feasible schedule which minimizes the total completion time of the jobs in
\(\mathcal{J}^{(1)}\)
. For the first problem, Du and Leung (Journal of Algorithms 14:45–68, 1993) showed that the problem is NP-hard. We show in this paper that there is a flaw in their NP-hardness proof. For the second problem, Leung et al. (Operations Research 58:458–469, 2010) showed that the problem can be solved in polynomial time. Yuan et al. (Private Communication) showed that their polynomial-time algorithm is invalid so the complexity of the second problem is still open. In this paper, by a modification of Du and Leung’s NP-hardness proof, we show that the first problem is NP-hard even when the jobs have only two distinct deadlines. Using the same reduction, we also show that the second problem is NP-hard even when the jobs in
\(\mathcal{J}^{(2)}\)
has a common deadline
\(D>0\)
and a common release time 0. PubDate: 2015-06-01

Abstract: We consider a semi-online multiprocessor scheduling problem with a given a set of identical machines and a sequence of jobs, the sum of whose processing times is known in advance. The jobs are to be assigned online to one of the machines and the objective is to minimize the makespan. The best known algorithm for this problem achieves a competitive ratio 1.6 (Cheng et al. in Theor Comput Sci 337:134–146, 2005). The best known lower bound is approximately 1.585 (Albers and Hellwig in Theor Comput Sci 443:1–9, 2012) if the number of machines tends to infinity. We present an elementary algorithm with competitive ratio equal to this lower bound. Thus, the algorithm is best possible if the number of machines tends to infinity. PubDate: 2015-04-25

Abstract: We study a single-machine scheduling problem that is a generalization of a number of problems for which computational procedures have already been published. Each job has a processing time, a release date, a due date, a deadline, and a weight representing the penalty per unit-time delay beyond the due date. The goal is to schedule all jobs such that the total weighted tardiness penalty is minimized and both the precedence constraints as well as the time windows (implied by the release dates and the deadlines) are respected. We develop a branch-and-bound algorithm that solves the problem to optimality. Computational results show that our approach is effective in solving medium-sized instances, and that it compares favorably with existing methods for special cases of the problem. PubDate: 2015-04-17

Abstract: The project scheduling problem (PSP) is the subject of several studies in computer science, mathematics, and operations research because of the hardness of solving it and its practical importance. This work tackles an extended version of the problem known as the multimode resource-constrained multiproject scheduling problem. A solution to this problem consists of a schedule of jobs from various projects, so that the job allocations do not exceed the stipulated limits of renewable and nonrenewable resources. To accomplish this, a set of execution modes for the jobs must be chosen, as the jobs’ duration and amount of needed resources vary depending on the mode selected. Finally, the schedule must also consider precedence constraints between jobs. This work proposes heuristic methods based on integer programming to solve the PSP considered in the Multidisciplinary International Scheduling Conference: Theory and Applications (MISTA) 2013 Challenge. The developed solver was ranked third in the competition, being able to find feasible and competitive solutions for all instances and improving best known solutions for some problems. PubDate: 2015-04-16

Abstract: We show that the following fundamental question in student sectioning can be efficiently decided in polynomial time: Is it possible to assign
\(m\)
students to
\(k\)
sectioned courses with respect to a given timetable with
\(l\)
timeslots such that the individual capacities of all sections are not exceeded and no student has more than one appointment per timeslot? Our result opens the possibility of efficiently checking the feasibility of candidate timetables with respect to this question as part of timetabling algorithms. Based on a succinct representation of solutions, we also provide an algorithm to compute optimal assignments in
\(O( k^2l^2 \log (\mathrm{sum}_{A}))\)
, where
\(\mathrm{sum}_{A}\)
is the sum of all specified section capacities. On the other hand, we prove that adding any single of the following constraints turns the above question into an NP-complete problem:
Course-selection constraint: Student’s course-selections must be respected.
Timeslot constraint: Students have individual timeslot restrictions.
Multiple-event constraint: Sections may have multiple events in the timetable, and there must be no timeslot clashes between all section-events for each student.
Hence our investigation gives insight into the location of the borderline between efficiently solvable and computationally hard problem variations. PubDate: 2015-04-11

Abstract: Single-machine weighted earliness tardiness scheduling is a prevalent problem in just-in-time production environments. Yet, the case with distinct due dates is strongly NP-hard. Herein, it is approximately solved using ASV, an ant colony-based system with a reduced number of ants and of colonies and with daemon actions that explore the search space around the ants using a variable neighborhood search (VNS). The numerical investigation provides computational proof of the utility of the daemon actions. In addition, it infers that these latter can be applied either to the initial or to subsequent colonies. Furthermore, it highlights the importance of using ant colony optimization as the multiple restart engine of VNS. Finally, it shows that ASV obtains the optimum for most small-sized instances. It has a 0.2 % average deviation from the optimum over all benchmark instances. PubDate: 2015-04-08

Abstract: We consider two-agent scheduling on a single machine with release dates and preemption to minimize the maximum lateness. In this scheduling model, there are two agents
\(A\hbox { and }B\)
each having his own job set
\(\mathcal{J}_A= \{ J^a_1, \ldots , J^a_{n_a}\}\hbox { and }\mathcal{J}_B= \{ J^b_1, \ldots , J^b_{n_b}\}\)
, respectively. Each job
\(J_j\in \mathcal{J}_A\cup \mathcal{J}_B\)
has a release date
\(r_j\)
and the
\(n=n_a+n_b\)
jobs need to be preemptively scheduled on a single machine. Leung et al. (Oper Res 58:458–469, 2010) present a comprehensive study of two-agent scheduling in various machine environments. They show that problem
\(1 r_j,\; \text{ pmtn } L^a_{\max }: f^b_{\max }\le Q\)
can be solved in
\(O(n_a\log n_a+ n_b\log n_b)\)
time. They use the strategy that schedules the jobs of agent
\(B\)
without preemption as late as possible under the restriction
\(f^b_{\max }\le Q\)
. We show that the strategy fails to work even when
\(n_a=n_b=1\)
, invalidating their result. We then study the minimization problem
\(1 r_j,\; \text{ pmtn } L^a_{\max }: f^b_{\max }\le Q\)
and the Pareto optimization problem
\(1 r_j,\; \text{ pmtn } (L^a_{\max }: L^b_{\max })\)
. We show that the two problems can be solved in
\(O(n_an \log n)\hbox { and }O(n_an_bn \log n)\)
time, respectively. PubDate: 2015-04-01

Abstract: In this paper, we present a new scheduling problem and describe a shortest path-based heuristic as well as a dynamic programming-based exact optimization algorithm to solve it. The selective multi-category parallel-servicing problem arises when a set of jobs has to be scheduled on a server (machine) with limited capacity. Each job requests service in a prespecified time window and belongs to a certain category. Jobs may be serviced partially, incurring a penalty; however, only jobs of the same category can be processed simultaneously. One must identify the best subset of jobs to process in each time interval of a given planning horizon, while respecting the server capacity and scheduling requirements. We compare the proposed solution methods with a Mixed Integer Linear Programming (MILP) formulation and show that the dynamic programming approach is faster when the number of categories is large, whereas the MILP can be solved faster when the number of categories is small. PubDate: 2015-04-01

Abstract: In this paper, a scheduling problem is considered which arises in the packaging industry. Plastic and foil wrappers used for packaging candy bars, crisps and other snacks typically require overlay printing with multiple colours. Printing machines used for this purpose usually accommodate a small number of colours which are loaded into a magazine simultaneously. If two consecutively scheduled print jobs require significantly different colour overlays, then substantial down times are incurred during the transition from the former magazine colour configuration to the latter, because ink cartridges corresponding to colours not required for the latter job have to be cleaned after completion of the former job. The durations of these down times are therefore sequence dependent (the washing and refilling time is a function of the number of colours in which two consecutive printing jobs differ). It is consequently desirable to schedule print jobs so that the accumulated down times associated with all magazine colour transitions are as short as possible for each printing machine. We show that an instance of this scheduling problem can be modelled as the well-known tool switching problem, which is tractable for small instances only. The problem can, however, be solved rather effectively in heuristic fashion by decomposing it into two subproblems: a job grouping problem (which can be modelled as a unicost set covering problem) and a group sequencing problem (which is a generalisation of the celebrated travelling salesman problem). We solve the colour print scheduling problem both exactly and heuristically for small, randomly generated test problem instances, studying the trade-off between the time efficiency and solution quality of the two approaches. Finally, we apply both solution approaches to real problem data obtained from a printing company in the South African Western Cape as a special case study. PubDate: 2015-04-01

Abstract: The resource-constrained project scheduling problem (RCPSP) has been widely studied. A fundamental assumption of the basic type of RCPSP is that activity durations are deterministic (i.e., they are known in advance). In reality, however, this is almost never the case. In this article, we illustrate why it is important to incorporate activity duration uncertainty, and develop an exact procedure to optimally solve the stochastic resource-constrained scheduling problem. A computational experiment shows that our approach works best when solving small- to medium-sized problem instances where activity durations have a moderate-to-high level of variability. For this setting, our model outperforms the existing state-of-the-art. In addition, we use our model to assess the optimality gap of existing heuristic approaches, and investigate the impact of making scheduling decisions also during the execution of an activity rather than only at the end of an activity. PubDate: 2015-03-10

Abstract: Makespan minimization on a set of parallel machines is one of the most widely studied problems in scheduling theory. A new result is presented which improves on the classical Coffman–Sethi a posteriori bound on the relative error of the LPT algorithm. It is shown that the ratio of these two bounds (the old one to the new one) can be arbitrarily large. PubDate: 2015-02-11