Showing papers in "Journal of Scheduling in 2013"

A survey on offline scheduling with rejection

Abstract: In classical deterministic scheduling problems, it is assumed that all jobs have to be processed. However, in many practical cases, mostly in highly loaded make-to-order production systems, accepting all jobs may cause a delay in the completion of orders which in turn may lead to high inventory and tardiness costs. Thus, in such systems, the firm may wish to reject the processing of some jobs by either outsourcing them or rejecting them altogether. The field of scheduling with rejection provides schemes for coordinated sales and production decisions by grouping them into a single model. Since scheduling problems with rejection are very interesting both from a practical and a theoretical point of view, they have received a great deal of attention from researchers over the last decade. The purpose of this survey is to offer a unified framework for offline scheduling with rejection by presenting an up-to-date survey of the results in this field. Moreover, we highlight the close connection between scheduling with rejection and other fields of research such as scheduling with controllable processing times and scheduling with due date assignment, and include some new results which we obtained for open problems.

Solving RCPSP/max by lazy clause generation

Abstract: We present a generic exact method for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedence relations (Rcpsp/max). This is a very general scheduling model with applications areas such as project management and production planning. Our method uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply no-good learning and conflict-driven search to the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solution and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. In comparison to other methods, our method is able to find better solutions faster on the Rcpsp/max benchmarks. Indeed, our method closes 573 open problem instances and generates better solutions in most of the remaining instances. Surprisingly, although ours is an exact method, it outperforms the published non-exact methods on these benchmarks in terms of the quality of solutions.

Non-preemptive speed scaling

Abstract: We consider the following offline variant of the speed scaling problem introduced by Yao et al. We are given a set of jobs and we have a variable-speed processor to process them. The higher the processor speed, the higher the energy consumption. Each job is associated with its own release time, deadline, and processing volume. The objective is to find a feasible schedule that minimizes the energy consumption. In contrast to Yao et al., no preemption of jobs is allowed. Unlike the preemptive version that is known to be in P, the non-preemptive version of speed scaling is strongly NP-hard. In this work, we present a constant factor approximation algorithm for it. The main technical idea is to transform the problem into the unrelated machine scheduling problem with $$L_p$$ -norm objective.

Exact algorithms for inventory constrained scheduling on a single machine

Abstract: This paper focuses on single machine scheduling subject to inventory constraints. Jobs add or remove items to or from the inventory, respectively. Jobs that remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine where the objective is to minimize the total weighted completion time. We develop properties of optimal solutions and design a branch and bound algorithm and a dynamic programming algorithm with two extensions. We compare the approaches in our computational study and empirically derive parameter settings leading to instances which are hard to solve.

Mixed integer programming based maintenance scheduling for the Hunter Valley coal chain

Abstract: We consider the scheduling of the annual maintenance for the Hunter Valley Coal Chain. The coal chain is a system comprising load points, railway track and different types of terminal equipment, interacting in a complex way. A variety of maintenance tasks have to be performed on all parts of the infrastructure on a regular basis in order to assure the operation of the system as a whole. The main objective in the planning of these maintenance jobs is to maximize the total annual throughput. Based on a network flow model of the system, we propose a mixed integer programming formulation for this planning task. In order to deal with the resulting large scale model which cannot be solved directly by a general purpose solver, we propose two steps. The number of binary variables is reduced by choosing a representative subset of the variables of the original problem, and a rolling horizon approach enables the approximation of the long term (i.e. annual) problem by a sequence of shorter problems (for instance, monthly).

Flexible weekly tour scheduling for postal service workers using a branch and price

Abstract: This paper addresses the problem of flexible shift scheduling of service employees at mail processing and distribution centers. Our main objective is to determine staffing levels for different worker categories subject to a host of union restrictions and general labor regulations. The problem is modeled as a mixed-integer linear program and solved with branch and price algorithm. Using real data provided by a US Postal Service a variety of computational experiments are performed to quantify the benefits of scheduling flexibility. These include different shift starting times, different shift lengths, a lunch break allowance, and different days-off assignments. In addition, the ratio between regular and flexible workers is varied to investigate its effect on costs. The results show the efficiency of the proposed procedure. Finally, we offer some managerial insights gained from the analysis.

Cyclic staff scheduling: optimization models for some real-life problems

Abstract: In this work, we propose a general integer programming model to address the staff scheduling problem, flexible enough to be easily adapted to a wide-range of real-world problems. The model is applied with slight changes to two case studies: a glass plant and a continuous care unit, and also to a collection of benchmark instances available in the literature. The emphasis of our approach is on a novel formulation of sequence constraints and also on workload balance, which is tackled through cyclic scheduling. Models are solved using the CPLEX solver. Computational results indicate that optimal solutions can be achieved within a reasonable amount of time.

A new hyper-heuristic as a general problem solver: an implementation in HyFlex

Abstract: This study provides a new hyper-heuristic design using a learning-based heuristic selection mechanism together with an adaptive move acceptance criterion. The selection process was supported by an online heuristic subset selection strategy. In addition, a pairwise heuristic hybridization method was designed. The motivation behind building an intelligent selection hyper-heuristic using these adaptive hyper-heuristic sub-mechanisms is to facilitate generality. Therefore, the designed hyper-heuristic was tested on a number of problem domains defined in a high-level framework, i.e., HyFlex. The framework provides a set of problems with a number of instances as well as a group of low-level heuristics. Thus, it can be considered a good environment to measure the generality level of selection hyper-heuristics. The computational results demonstrated the generic performance of the proposed strategy in comparison with other tested hyper-heuristics composed of the sub-mechanisms from the literature. Moreover, the performance and behavior analysis conducted for the hyper-heuristic clearly showed its adaptive characteristics under different search conditions. The principles comprising the here presented algorithm were at the heart of the algorithm that won the first international cross-domain heuristic search competition.

A linear programming-based method for job shop scheduling

Abstract: We present a decomposition heuristic for a large class of job shop scheduling problems. This heuristic utilizes information from the linear programming formulation of the associated optimal timing problem to solve subproblems, can be used for any objective function whose associated optimal timing problem can be expressed as a linear program (LP), and is particularly effective for objectives that include a component that is a function of individual operation completion times. Using the proposed heuristic framework, we address job shop scheduling problems with a variety of objectives where intermediate holding costs need to be explicitly considered. In computational testing, we demonstrate the performance of our proposed solution approach.

Hierarchical scheduling strategies for parallel tasks and advance reservations in grids

Abstract: Recently, the advance reservation functionality gained high importance in grids due to increasing popularity of modern applications that require interactive tasks, co-allocation of multiple resources, and performance guarantees. However, simultaneous scheduling, both advance reservations and batch tasks affects the performance. Advance reservations significantly deteriorate flow time of batch tasks and the overall resource utilization, especially in hierarchical scheduling structures. This is a consequence of unknown batch task processing times and the lack of possibility of altering allocations of advance reservations. To address these issues we present a common model for scheduling both computational batch tasks and tasks with advance reservation requests. We propose simple on-line scheduling policies and generic advices that reduce negative impact of advance reservations on a schedule quality. We also propose novel data structures and algorithms for efficient scheduling of advance reservations. A comprehensive experimental analysis is presented to show the influence of advance reservations on resource utilization, mean flow time, and mean tardiness--the criteria significant for administrators, users submitting batch tasks, and users requesting advance reservations, respectively. All experiments were performed with a well-known real workload using the GSSIM simulator.

Single machine batch scheduling with release times and delivery costs

Abstract: We study single machine batch scheduling with release times. Our goal is to minimize the sum of weighted flow times (or completion times) and delivery costs. Since the problem is strongly $\mathcal{NP}$ -hard even with no delivery cost and identical weights for all jobs, an approximation algorithm is presented for the problem with identical weights. This uses the polynomial time solution we give for the preemptive version of the problem. We also present an evolutionary metaheuristic algorithm for the general case. Computational results show very small gaps between the results of the metaheuristic and the lower bound.

A solution approach based on Benders decomposition for the preventive maintenance scheduling problem of a stochastic large-scale energy system

Abstract: This paper describes a Benders decomposition-based framework for solving the large scale energy management problem that was posed for the ROADEF 2010 challenge. The problem was taken from the power industry and entailed scheduling the outage dates for a set of nuclear power plants, which need to be regularly taken down for refueling and maintenance, in such a way that the expected cost of meeting the power demand in a number of potential scenarios is minimized. We show that the problem structure naturally lends itself to Benders decomposition; however, not all constraints can be included in the mixed integer programming model. We present a two phase approach that first uses Benders decomposition to solve the linear programming relaxation of a relaxed version of the problem. In the second phase, integer solutions are enumerated and a procedure is applied to make them satisfy constraints not included in the relaxed problem. To cope with the size of the formulations arising in our approach we describe efficient preprocessing techniques to reduce the problem size and show how aggregation can be applied to each of the subproblems. Computational results on the test instances show that the procedure competes well on small instances of the problem, but runs into difficulty on larger ones. Unlike heuristic approaches, however, this methodology can be used to provide lower bounds on solution quality.

A multi-start tabu search method for a single-machine scheduling problem with periodic maintenance and sequence-dependent set-up times

Abstract: In this paper we study a problem of sequencing jobs in a machine with programmed preventive maintenance and sequence-dependent set-up times. The problem combines two NP-hard problems, so we propose a heuristic method for solving it, which hybridizes multi-start strategies with Tabu Search. We compare our method with the only published metaheuristic algorithm for this problem on a set of 420 instances. The comparison favors the method developed in this work, showing that is able to find high quality solutions in very short computational times.

Solving the electricity production planning problem by a column generation based heuristic

Abstract: This paper presents a heuristic method based on column generation for the EDF (Electricite De France) long-term electricity production planning problem proposed as subject of the ROADEF/EURO 2010 Challenge. This is to our knowledge the first-ranked method among those methods based on mathematical programming, and was ranked fourth overall. The problem consists in determining a production plan over the whole time horizon for each thermal power plant of the French electricity company, and for nuclear plants, a schedule of plant outages which are necessary for refueling and maintenance operations. The average cost of the overall outage and production planning, computed over a set of demand scenarios, is to be minimized. The method proceeds in two stages. In the first stage, dates for outages are fixed once for all for each nuclear plant. Data are aggregated with a single average scenario and reduced time steps, and a set-partitioning reformulation of this aggregated problem is solved for fixing outage dates with a heuristic based on column generation. The pricing problem associated with each nuclear plant is a shortest path problem in an appropriately constructed graph. In the second stage, the reload level is determined at each date of an outage, considering now all scenarios. Finally, the production quantities between two outages are optimized for each plant and each scenario by solving independent linear programming problems.

The vehicle routing problem with restricted mixing of deliveries and pickups

Abstract: The vehicle routing problem with deliveries and pickups is one of the main problems within reverse logistics. This paper focuses on an important assumption that divides the literature on the topic, namely the restriction that all deliveries must be completed before pickups can be made. A generalised model is presented, together with a mathematical formulation and its resolution. The latter is carried out by adopting a suitable implementation of the reactive tabu search metaheuristic. Results show that significant savings can be achieved by allowing a mixture of delivery and pickup loads on-board and yet not incurring delays and driver inconvenience.

Scheduling to minimize gaps and power consumption

Abstract: This paper considers scheduling tasks while minimizing the power consumption of one or more processors, each of which can go to sleep at a fixed cost $$\alpha $$ . There are two natural versions of this problem, both considered extensively in recent work: minimize the total power consumption (including computation time), or minimize the number of "gaps" in execution. For both versions in a multiprocessor system, we develop a polynomial-time algorithm based on sophisticated dynamic programming. In a generalization of the power-saving problem, where each task can execute in any of a specified set of time intervals, we develop a $$(1+{2 \over 3} \alpha )$$ -approximation, and show that dependence on $$\alpha $$ is necessary. In contrast, the analogous multi-interval gap scheduling problem is set-cover hard (and thus not $$o(\lg n)$$ -approximable), even in the special cases of just two intervals per job or just three unit intervals per job. We also prove several other hardness-of-approximation results. Finally, we give an $$O(\sqrt{n})$$ -approximation for maximizing throughput given a hard upper bound on the number of gaps.

Solving a real-life, large-scale energy management problem

Abstract: This paper introduces a three-phase hybrid heuristic for a large-scale energy management and maintenance scheduling problem. The problem is to schedule maintenance periods and refueling amounts for nuclear power plants with a time horizon of up to five years, and handling a number of scenarios for future demand and prices. The goal is to minimize the expected total production cost. The first phase of the heuristic solves a constraint programming model of a simplified version of the problem, the second performs a local search, and the third handles overproduction in a greedy fashion. This work was initiated in the context of the ROADEF/EURO Challenge 2010. In the concluding phase of the competition, our team ranked second in the junior category and sixth overall. After correcting a small implementation bug in the program that was submitted for final evaluation, our solver ranks first in the overall results from the competition.

Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance

Abstract: We consider a scheduling problem on a single machine to minimize the makespan. The processing conditions are subject to cumulative deterioration, but can be restored by a single maintenance. We link the problem to the Subset-sum problem (if the duration of maintenance is constant) and to the Half-Product Problem (if the duration of maintenance depends on its start time). For both versions of the problem, we adapt the existing fully polynomial-time approximation schemes to our problems by handling the additive constants.

Single machine scheduling with delivery dates and cumulative payoffs

Abstract: We address a single machine scheduling problem with a new optimization criterion and unequal release dates. This new criterion results from a practical situation in the domain of book digitization. Given a set of job-independent delivery dates, the goal is to maximize the cumulative number of jobs processed before each delivery date. We establish the complexity of the general problem. In addition, we discuss some polynomial cases and provide a pseudopolynomial time algorithm for the two-delivery-dates problem based on dynamic programming and some dominance properties. Experimental results are also reported.

A 0---1 integer linear programming approach to schedule outages of nuclear power plants

Abstract: We address the problem of planning outages of nuclear power plants submitted by EDF (Electricite De France) as the challenge EURO/ROADEF 2010. As our team won the first prize of the contest in the senior category, our approach may be of interest: it is conceptually simple, easy to program and computationally relatively fast. We present both our method and some ideas to improve it.

Online capacity maximization in wireless networks

Abstract: In this paper we study a dynamic version of capacity maximization in the physical model of wireless communication. In our model, requests for connections between pairs of points in Euclidean space of constant dimension d arrive iteratively over time. When a new request arrives, an online algorithm needs to decide whether or not to accept the request and to assign one out of k channels and a transmission power to the request. Accepted requests must satisfy constraints on the signal-to-interference-plus-noise (SINR) ratio. The objective is to maximize the number of accepted requests. Using competitive analysis we study algorithms using distance-based power assignments, for which the power of a request relies only on the distance between the points. Such assignments are inherently local and particularly useful in distributed settings. We first focus on the case of a single channel. For request sets with spatial lengths in [1,Δ] and duration in [1,Γ] we derive a lower bound of ?(Γ?Δ d/2) on the competitive ratio of any deterministic online algorithm using a distance-based power assignment. Our main result is a near-optimal deterministic algorithm that is O(Γ?Δ(d/2)+? )-competitive, for any constant ?>0. Our algorithm for a single channel can be generalized to k channels. It can be adjusted to yield a competitive ratio of O(k?Γ 1/k??Δ(d/2k?)+? ) for any factorization (k?,k?) such that k??k?=k. This illustrates the effectiveness of multiple channels when dealing with unknown request sequences. In particular, for ?(log?Γ?log?Δ) channels this yields an O(log?Γ?log?Δ)-competitive algorithm. Additionally, we show how this approach can be turned into a randomized algorithm, which is O(log?Γ?log?Δ)-competitive even for a single channel.

Scheduling of inventory releasing jobs to satisfy time-varying demand: an analysis of complexity

Abstract: This paper studies a new class of single-machine scheduling problems, which are faced by Just-in-Time-suppliers satisfying a given demand. In these models the processing of jobs leads to a release of a predefined number of product units into inventory. Consumption is triggered by predetermined time-varying, and product-specific demand requests. While all demands have to be fulfilled, the objective is to minimize the resulting product inventory. We investigate different subproblems of this general setting with regard to their computational complexity. For more restricted problem versions strongly polynomial time algorithms are presented. In contrast to this, NP-hardness in the strong sense is proven for more general problem versions. Moreover, for the most general version, even finding a feasible solution is shown to be strongly NP-hard.

A constraint programming-based approach to a large-scale energy management problem with varied constraints

Abstract: This paper addresses a large-scale power plant maintenance scheduling and production planning problem, which has been proposed by the ROADEF/EURO Challenge 2010. We develop two lower bounds for the problem: a greedy heuristic and a flow network for which a minimum cost flow problem has to be solved. Furthermore, we present a solution approach that combines a constraint programming formulation of the problem with several heuristics. The problem is decomposed into an outage scheduling and a production planning phase. The first phase is solved by a constraint program, which additionally ensures the feasibility of the remaining problem. In the second phase we utilize a greedy heuristic--developed from our greedy lower bound--to assign production levels and refueling amounts for a given outage schedule. All proposed strategies are shown to be competitive in an experimental evaluation.

An improved FPTAS for maximizing the weighted number of just-in-time jobs in a two-machine flow shop problem

Abstract: Recently, Shabtay and Bensoussan (2012) developed an original exact pseudo-polynomial algorithm and an efficient $$\upvarepsilon $$ -approximation algorithm (FPTAS) for maximizing the weighted number of just-in-time jobs in a two-machine flow shop problem. The complexity of the FPTAS is $$O$$ (( $$n^{4}/\upvarepsilon $$ )log( $$n$$ / $$\upvarepsilon $$ )), where $$n$$ is the number of jobs. In this note we suggest another pseudo-polynomial algorithm that can be converted to a new FPTAS which improves Shabtay---Bensoussan's complexity result and runs in $$O(n^{3}/\upvarepsilon )$$ time.

Semi-online scheduling problems on a small number of machines

Abstract: We consider the semi-online parallel machine scheduling problem of minimizing the makespan given a priori information: the total processing time, the largest processing time, the combination of the previous two or the optimal makespan. We propose a new algorithm that can be applied to the problem with the known total or largest processing time and prove that it has improved competitive ratios for the cases with a small number of machines. Improved lower bounds of the competitive ratio are also provided by presenting adversary lower bound examples.

Stochastic scheduling problems with general position-based learning effects and stochastic breakdowns

Abstract: The focus of this study is to analyze position-based learning effects in single-machine stochastic scheduling problems. The optimal permutation policies for the stochastic scheduling problems with and without machine breakdowns are examined, where the performance measures are the expectation and variance of the makespan, the expected total completion time, the expected total weighted completion time, the expected weighted sum of the discounted completion times, the maximum lateness and the maximum tardiness.

Pareto optimization of rescheduling with release dates to minimize makespan and total sequence disruption

Abstract: We consider the rescheduling on a single machine with release dates to minimize the makespan and total sequence disruption simultaneously. In the literature, a polynomial-time algorithm was presented for minimizing the makespan under a limit on the total sequence disruption. But the algorithm is not strongly polynomial. We present a strongly polynomial-time algorithm for finding all Pareto optimal points of the Pareto optimization problem. Consequently, the rescheduling to minimize the makespan under a limit on the total sequence disruption can be solved in a strongly polynomial time.

Multi-criteria scheduling: an agent-based approach for expert knowledge integration

Abstract: In this work, we present an agent-based approach to multi-criteria combinatorial optimization It allows to flexibly combine elementary heuristics that may be optimal for corresponding single-criterion problems We optimize an instance of the scheduling problem 1|d j |?C j ,L max and show that the modular building block architecture of our optimization model and the distribution of acting entities enables the easy integration of problem specific expert knowledge We present a universal mutation operator for combinatorial problem encodings that allows to construct certain solution strategies, such as advantageous sorting or known optimal sequencing procedures In this way, it becomes possible to derive more complex heuristics from atomic local heuristics that are known to solve fractions of the complete problem We show that we can approximate both single-criterion problems such as P m |d j |?U j as well as more challenging multi-criteria scheduling problems, like P m ||C max,?C j and P m |d j |C max,?C j ,?U j The latter problems are evaluated with extensive simulations comparing the standard multi-criteria evolutionary algorithm NSGA-2 and the new agent-based model

Scheduling of inventory releasing jobs to minimize a regular objective function of delivery times

Abstract: In this note we provide new complexity and algorithmic results for scheduling inventory releasing jobs, a new class of single machine scheduling problems proposed recently by Boysen et al. We focus on tardiness related criteria, while known results are concerned with inventory levels between fixed delivery points. Our interest is motivated by the fact that deciding whether a feasible schedule exists is NP-hard in the strong sense, provided that all delivery deadlines are fixed, and there are no restrictions on the amount of products released by the jobs, nor on the job processing times. We will establish NP-hardness results, or provide polynomial or pseudo-polynomial time algorithms for various special cases, and describe a fully polynomial approximation scheme for one of the variants with the maximum tardiness criterion.

Lower bounds for online makespan minimization on a small number of related machines

Abstract: In online makespan minimization, the jobs characterized by their processing time arrive one-by-one and each has to be assigned to one of the m uniformly related machines. The goal is to minimize the length of the schedule. We prove new combinatorial lower bounds for m=4 and m=5, and computer-assisted lower bounds for m≤11.