Showing papers in "Journal of Scheduling in 2007"

A tabu search heuristic for the quay crane scheduling problem

Abstract: This paper proposes a tabu search heuristic for the Quay Crane Scheduling Problem (QCSP), the problem of scheduling a fixed number of quay cranes in order to load and unload containers into and from a ship. The optimality criterion considered is the minimum completion time. Precedence and non-simultaneity constraints between tasks are taken into account. The former originate from the different kind of operations that each crane has to perform; the latter are needed in order to avoid interferences between the cranes. The QCSP is decomposed into a routing problem and a scheduling problem. The routing problem is solved by a tabu search heuristic, while a local search technique is used to generate the solution of the scheduling problem. This is done by minimizing the longest path length in a disjunctive graph. The effectiveness of our algorithm is assessed by comparing it to a branch-and-cut algorithm and to a Greedy Randomized Adaptive Search Procedure (GRASP).

A classification of predictive-reactive project scheduling procedures

Abstract: The vast majority of the project scheduling research efforts over the past several years have concentrated on the development of workable predictive baseline schedules, assuming complete information and a static and deterministic environment. During execution, however, a project may be subject to numerous schedule disruptions. Proactive-reactive project scheduling procedures try to cope with these disruptions through the combination of a proactive scheduling procedure for generating predictive baseline schedules that are hopefully robust in that they incorporate safety time to absorb anticipated disruptions with a reactive procedure that is invoked when a schedule breakage occurs during project execution. In this paper we discuss the results obtained by a large experimental design set up to evaluate several predictive-reactive resource-constrained project scheduling procedures under the composite objective of maximizing both the schedule stability and the timely project completion probability.

The discrete time/cost trade-off problem: extensions and heuristic procedures

Abstract: Time/cost trade-offs in project networks have been the subject of extensive research since the development of the critical path method (CPM) in the late 50s. Time/cost behaviour in a project activity basically describes the trade-off between the duration of the activity and its amount of non-renewable resources (e.g., money) committed to it. In the discrete version of the problem (the discrete time/cost trade-off problem), it is generally accepted that the trade-off follows a discrete non-increasing pattern, i.e., expediting an activity is possible by allocating more resources (i.e., at a larger cost) to it. However, due to its complexity, the problem has been solved for relatively small instances. In this paper we elaborate on three extensions of the well-known discrete time/cost trade-off problem in order to cope with more realistic settings: time/switch constraints, work continuity constraints, and net present value maximization. We give an extensive literature overview of existing procedures for these problem types and discuss a new meta-heuristic approach in order to provide near-optimal heuristic solutions for the different problems. We present computational results for the problems under study by comparing the results for both exact and heuristic procedures. We demonstrate that the heuristic algorithms produce consistently good results for two versions of the discrete time/cost trade-off problem.

Cyclic preference scheduling of nurses using a Lagrangian-based heuristic

Abstract: This paper addresses the problem of developing cyclic schedules for nurses while taking into account the quality of individual rosters. In this context, quality is gauged by the absence of certain undesirable shift patterns. The problem is formulated as an integer program (IP) and then decomposed using Lagrangian relaxation. Two approaches were explored, the first based on the relaxation of the preference constraints and the second based on the relaxation of the demand constraints. A theoretical examination of the first approach indicated that it was not likely to yield good bounds. The second approach showed more promise and was subsequently used to develop a solution methodology that combined subgradient optimization, the bundle method, heuristics, and variable fixing. After the Lagrangian dual problem was solved, though, there was no obvious way to perform branch and bound when a duality gap existed between the lower bound and the best objective function value provided by an IP-based feasibility heuristic. This led to the introduction of a variable fixing scheme to speed convergence. The full algorithm was tested on data provided by a medium-size U.S. hospital. Computational results showed that in most cases, problem instances with up to 100 nurses and 20 rotational profiles could be solved to near-optimality in less than 20 min.

An insertion heuristic for scheduling Mobility Allowance Shuttle Transit (MAST) services

Abstract: In this paper, we develop an insertion heuristic for scheduling Mobility Allowance Shuttle Transit (MAST) services, an innovative concept that merges the flexibility of Demand Responsive Transit (DRT) systems with the low cost operability of fixed-route systems. A MAST system allows vehicles to deviate from the fixed path so that customers within a service area may be picked up or dropped off at their desired locations. Such a service already exists in Los Angeles County, where MTA Line 646 is a MAST nighttime service, transporting passengers between a business area and a nearby bus terminal. Since the current demand is very low, the service is entirely manageable by the bus operator, but a higher demand would certainly require the development of a scheduling algorithm. The proposed insertion heuristic makes use of control parameters, which properly regulate the consumption of the slack time. A set of simulations performed in the service area covered by the existing MTA Line 646 at different demand levels attests the effectiveness of the algorithm by comparing its performance versus a first-come/first-serve (FCFS) policy and optimal solutions generated by a commercial integer program solver. The results show that our approach can be used as an effective method to automate scheduling of this line and other services similar to it.

When it is worthwhile to work with the stochastic RCPSP

Abstract: The Resource-Constrained Project Scheduling Project (RCPSP), together with some of its extensions, has been widely studied. A fundamental assumption in this basic problem is that the duration of activities is known before their execution. Very little effort has been made in developing heuristics for the RCPSP with stochastic durations, that is, when the duration of activities is given by a distribution of probability. In fact, the deterministic approach is often used even in the presence of non-trivial distributions. In this paper we discuss when it is worth the effort, in heuristic algorithms, to work with stochastic durations instead of deterministic ones. We also describe techniques that seem to be useful for a wide variety of heuristic algorithms for the stochastic problem. We develop two algorithms that include these procedures and that are capable of outperforming other existing heuristics in the literature. Computational experiments are provided on instances based on the standard set j120, generated using ProGen, and on the well-known Patterson set.

Robust optimization models for project scheduling with resource availability cost

Abstract: We address a project scheduling problem with resource availability cost for which the activity durations are uncertain. The problem is formulated within the robust optimization framework, where uncertainty is modeled via a set of scenarios. The proposed solution method is based on the scatter search methodology and employs advanced strategies, such as dynamic updating of the reference set, a frequency-based memory mechanism, and path relinking. A multistart heuristic was also developed and comparative results are reported. The tradeoffs for risk-averse decision makers are discussed.

Hybrid decomposition heuristics for solving large-scale scheduling problems in semiconductor wafer fabrication

Abstract: Most shop-floor scheduling policies used in practice rely on dispatching, making use of only local information at individual workcenters. However, in semiconductor manufacturing environments, we have access to real-time shop-floor status information for the entire facility. In these complex facilities, there would appear to be significant potential for improved schedules by considering global shop information and using optimization-based heuristics. To this end, we propose a rolling horizon (RH) heuristic that decomposes the shop into smaller subproblems that can be solved sequentially over time using a workcenter-based decomposition heuristic. We develop test instances for evaluating our heuristic using a simulation model of an industrial facility. The results demonstrate that the proposed heuristic yields better schedules than the dispatching rules in the vast majority of test instances with reasonable computational effort.

Preemption in single machine earliness/tardiness scheduling

Abstract: We consider a single machine earliness/tardiness scheduling problem with general weights, ready times and due dates. Our solution approach is based on a time-indexed preemptive relaxation of the problem. For the objective function of this relaxation, we characterize cost coefficients that are the best among those with a piecewise linear structure with two segments. From the solution to the relaxation with these best objective function coefficients, we generate feasible solutions for the original non-preemptive problem. We report extensive computational results demonstrating the speed and effectiveness of this approach.

Finding good nurse duty schedules: a case study

Abstract: Constructing duty schedules for nurses at large hospitals is a difficult problem. The objective is usually to ensure that there is always sufficient staff on duty, while taking into account individual preferences with respect to work patterns, requests for leave and financial restrictions, in such a way that all employees are treated fairly. The problem is typically solved via mixed integer programming or heuristic (local) search methods in the operations research literature. In this paper the problem is solved using a tabu search approach as a case study at Stikland Hospital, a large psychiatric hospital in the South African Western Cape, for which a computerized decision support system with respect to nurse scheduling was developed. This decision support system, called NuRoDSS (short for Nurse Rostering Decision Support System) is described in some detail.

A two-stage stochastic programming approach for project planning with uncertain activity durations

Abstract: This paper investigates the problem of setting target finish times (due dates) for project activities with random durations. Using two-stage integer linear stochastic programming, target times are determined in the first stage followed by the development of a detailed project schedule in the second stage. The objective is to balance (1) the cost of project completion as a function of activity target times with (2) the expected penalty incurred by deviating from the specified values. It is shown that the results may be significantly different when deviations are considered, compared to when activities are scheduled as early as possible in the traditional way. For example, the optimal target completion time for a project may be greater than the makespan of the early-start schedules under any scenario. To find solutions, an exact algorithm is developed for the case without a budget constraint and is used as a part of a heuristic when crashing is permitted. All computational procedures are demonstrated on a set of 150 benchmark problems consisting of 90 activities each.

Response time variability

Abstract: Response time variability is a new optimization problem with a broad range of applications and a distinctive number of theoretic flavour. The problem occurs whenever events, jobs, clients or products need to be sequenced so as to minimize the variability of time for which they wait for the next turn in obtaining the resources necessary for their advance. The problem has numerous real-life applications. We study its computational complexity, present efficiency, polynomial time algorithms for some cases, and the NP-hardness proof for a general problem. We propose a position exchange heuristic and apply it to improve the total response time variability of an initial sequence. The latter is the optimum bottleneck sequence, Webster or Jefferson sequence of the apportionment, or a random sequence. We report on computational experiments with the heuristic.

Time slot scheduling of compatible jobs

Abstract: A version of weighted coloring of a graph is introduced which is motivated by some types of scheduling problems: each node v of a graph G corresponds to some operation to be processed (with a processing time w(v)), edges represent nonsimultaneity requirements (incompatibilities) We have to assign each operation to one time slot in such a way that in each time slot, all operations assigned to this slot are compatible; the length of a time slot will be the maximum of the processing times of its operations The number k of time slots to be used has to be determined as well So, we have to find a k-coloring $${\cal S}$$ = $$({S_{1},\ldots ,S_{k}})$$ of G such that w(S 1) + ?s +w(S k ) is minimized where w(S i ) = max {w(v) :v?V} Properties of optimal solutions are discussed, and complexity and approximability results are presented Heuristic methods are given for establishing some of these results The associated decision problems are shown to be NP-complete for bipartite graphs, for line-graphs of bipartite graphs, and for split graphs

The complexity of mean flow time scheduling problems with release times

Abstract: We study the problem of preemptive scheduling of n} jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. In this paper, show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.

Improving simulated annealing with variable neighborhood search to solve the resource-constrained scheduling problem

Abstract: The purpose of this paper is to improve the simulated annealing method with a variable neighborhood search to solve the resource-constrained scheduling problem. We also compare numerically this method with other neighborhood search (local search) techniques: threshold accepting methods and tabu search. Furthermore, we combine these techniques with multistart diversification strategies and with the variable neighborhood search technique. A thorough numerical study is completed to set the parameters of the different methods and to compare the quality of the solutions that they generate. The numerical results indicate that the simulated annealing method improved with a variable neighborhood search technique is indeed the best solution method.

A note on the two machine job shop with the weighted late work criterion

Abstract: The paper presents a dynamic programming approach for the two-machine nonpreemptive job-shop scheduling problem with the total weighted late work criterion and a common due date $$(J2\,|\,n_i \le 2,d_i = d\,|\,Y_w )$$ , which is known to be NP-hard. The late work performance measure estimates the quality of an obtained solution with regard to the duration of late parts of tasks not taking into account the quantity of this delay. Providing a pseudopolynomial time method for the problem mentioned we can classify it as binary NP-hard.

Maximizing the weighted number of just-in-time jobs in flow shop scheduling

Abstract: In this paper we consider the maximization of the weighted number of just-in-time jobs that should be completed exactly on their due dates in n-job, m-machine flow shop problems. We show that a two-machine flow shop problem is NP-complete. When job weights are all identical, we show that the problem can be solved in polynomial time. We also show that a three-machine flow shop problem with identical job weights is NP-hard in the strong sense by reduction of the 3-partition problem.

On-line scheduling of parallel jobs in a list

Abstract: We study an on-line parallel job scheduling problem, where jobs arrive one by one. A parallel job may require a number of machines for its processing at the same time. Upon arrival of a job, its processing time and the number of requested machines become known, and it must be scheduled immediately without any knowledge of future jobs. We present a 7-competitive on-line algorithm, which improves the previous upper bound of 12 by Johannes (J. Sched. 9:433---452, 2006). Furthermore, we investigate a special case in which the largest processing time is known beforehand.

Scheduling for stability in single-machine production systems

Abstract: Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that changes only little when variations in the input parameters arise. This paper presents a model for single-machine scheduling with stability objective and a common deadline. We propose a branch-and-bound algorithm for solving an approximate formulation of the model. The algorithm is exact when exactly one job is disrupted during schedule execution.

Single processor scheduling with job values depending on their completion times

Abstract: The paper deals with a single processor scheduling problem in which the sum of values of all jobs is maximized. The value of a job is characterized by a stepwise nonincreasing function with one or more moments at which the changes of job value occur. Establishing an order of processing of datagrams which are sent by router is a practical example of application of such problems. We prove that the special case of our problem, with a single moment of change of job values, is equivalent to the well-known, NP-hard in the ordinary sense, problem of minimizing weighted number of late jobs. Next, we show that, based on this equivalence, the existing algorithms for solving the latter problem can be adopted to solve special cases of our problem. Additionally, we construct a pseudopolynomial time algorithm based on the dynamic programming method, for the case with arbitrary number of common moments of job value changes. At the end of the paper, we generalize this algorithm to the corresponding case with parallel processors. Thus, we show that these two problems are also NP-hard in the ordinary sense. Moreover, we construct exact polynomial time algorithms for two further special cases of our problem. Finally, in order to solve the general version of the problem, we construct and experimentally test a number of heuristic algorithms.

Resource allocation in stochastic, finite-capacity, multi-project systems through the cross entropy methodology

Abstract: This paper addresses the problem of resource allocation in a finite-capacity, stochastic (random) and dynamic multi-project system. The system is modeled as a queuing network that is controlled by limiting the number of concurrent projects. We propose a Cross Entropy (CE) based approach to determine near-optimal resource allocations to the entities that execute the projects. The performance of the suggested approach is demonstrated through numerical experiments and compared to that of a heuristic, rough-cut based method.

Single machine batch scheduling to minimize total completion time and resource consumption costs

Abstract: In this paper we study the single-machine batch scheduling problem under batch availability, where both setup and job processing times are controllable by allocating a continuously divisible nonrenewable resource. Under batch availability a set of jobs is processed contiguously and completed together, when the processing of the last job in the batch is finished. We present polynomial time algorithms to find the job sequence, the partition of the job sequence into batches and the resource allocation, which minimize the total completion time or the total production cost (inventory plus resource costs).

A bicriteria approach to minimize maximal lateness and resource consumption for scheduling a single machine

Abstract: We extend the classical single-machine maximal lateness scheduling problem to the case where the job processing times are controllable by allocating a continuous and nonrenewable resource to the processing operations. Our aim is to construct an efficient trade-off curve between maximal lateness and total resource consumption using a bicriteria approach. We present a polynomial time algorithm that constructs this trade-off curve assuming a specified general type of convex decreasing resource consumption function. We illustrate the algorithm with a numerical example.

Batching and scheduling in a multi-machine flow shop

Abstract: We study the problem of batching and scheduling n jobs in a flow shop comprising m, m?2, machines. Each job has to be processed on machines 1,?,m in this order. Batches are formed on each machine. A machine dependent setup time precedes the processing of each batch. Jobs of the same batch are processed on each machine sequentially so that the processing time of a batch is equal to the sum of the processing times of the jobs contained in it. Jobs of the same batch formed on machine l become available for a downstream operation on machine l+1 at the same time when the processing of the last job of the batch on machine l has been finished. The objective is to minimize maximum job completion time. We establish several properties of an optimal schedule and develop polynomial time algorithms for important special cases. They are improvements over the existing methods with regard to their generality and time efficiency.

A robust approach for the single machine scheduling problem

Abstract: This paper describes a robust approach for the single machine scheduling problem 1|r i |L max?. The method is said to be robust since it characterizes a large set of optimal solutions allowing to switch from one solution to another, without any performance loss, in order to face potential disruptions which occur during the schedule execution. It is based on a dominance theorem that characterizes a set of dominant sequences, using the interval structure defined by the relative order of the release and the due dates of jobs. The performance of a set of dominant sequences can be determined in polynomial time by computing the most favorable and the most unfavorable sequences associated with each job, with regard to the lateness criterion. A branch and bound procedure is proposed which modifies the interval structure of the problem in order to tighten the dominant set of sequences so that only the optimal sequences are conserved.

Single-machine scheduling to stochastically minimize maximum lateness

Abstract: We study the problem of scheduling a set of jobs on a single machine, to minimize the maximum lateness ML or the maximum weighted lateness MWL under stochastic order. The processing time P i , the due date D i , and the weight W i of each job i may all be random variables. We obtain the optimal sequences in the following situations: (i) For ML, the {P i } can be likelihood-ratio ordered, the {D i } can be hazard-rate ordered, and the orders are agreeable; (ii) For MWL, {D i } are exponentially distributed, {P i } and {W i } can be likelihood-ratio ordered and the orders are agreeable with the rates of {D i }; and (iii) For ML, P i and D i are exponentially distributed with rates μ i and ? i , respectively, and the sequence {? i (? i +μ i )} has the same order as {? i (? i +μ i +A 0)} for some sufficiently large A 0. Some related results are also discussed.

Rostering in a rail passenger carrier

Abstract: In this paper we present an applied study, commissioned by the regional rail passenger carrier EuskoTren, into how the annual workload of drivers can be allocated in an egalitarian fashion. The allocation must meet the constraints arising from working conditions and the preferences of employees, as reflected in collective bargaining agreements. The workload varies over the five periods, into which the year is divided, and according to the day of the week. Moreover, not all morning, evening and night shifts are of equal duration. Reduced services on public holidays are also considered. The solution to the problem proposed is obtained in four linked steps, at each of which a binary programming problem is solved using commercial software. Step one is to build five lists of weekly multi-shift patterns, two of them rotating, that contain all the shifts in the week. Step two consists of the partially rotating annual assignment of patterns to drivers, step three involves the extraction of shifts by reduction of services on public holidays, and step four incorporates the durations in hours into the shifts already assigned. The final solution obtained is quite satisfactory: all drivers are assigned a similar number of morning, evening and night shifts and Sundays off, and they work practically the same number of days and hours per year. The results obtained, the adaptability of the system to new requirements and the computation time used are fully satisfactory to the firm, which has decided to implement the model.

List scheduling for jobs with arbitrary release times and similar lengths

Abstract: This paper considers the problem of on-line scheduling a list of independent jobs in which each job has an arbitrary release time and length in [1,r] with r?1 on m parallel identical machines. For the list scheduling algorithm, we give an upper bound of the competitive ratio for any m?1 and show that the upper bound is tight when m=1. When m=2, we present a tight bound for r?4. For r<4, we give a lower bound and show that 2 provides an upper bound.

Semi on-line scheduling on three processors with known sum of the tasks

Abstract: We consider a semi on-line version of the multiprocessor scheduling problem on three processors, where the total size of the tasks is known in advance. We prove a lower bound $1+\frac{\sqrt{129}-9}{6}>1.3929$ on the competitive ratio of any algorithm and propose a simple algorithm with competitive ratio equal to 1.5. The performance is improved to $1+\frac{8}{19}<1.4211$ by a preprocessing strategy. The latter algorithm is only 2% away from the lower bound.

Single-machine scheduling with trade-off between number of tardy jobs and compression cost

Abstract: We consider a single-machine scheduling problem, in which the job processing times are controllable or compressible. The performance criteria are the compression cost and the number of tardy jobs. For the problem, where no tardy jobs are allowed and the objective is to minimize the total compression cost, we present a strongly polynomial time algorithm. For the problem to construct the trade-off curve between the number of tardy jobs and the maximum compression cost, we present a polynomial time algorithm. Furthermore, we extend the problem to the case of discrete controllable processing times, where the processing time of a job can only take one of several given discrete values. We show that even some special cases of the discrete controllable version with the objective of minimizing the total compression cost are NP-hard, but the general case is solvable in pseudo-polynomial time. Moreover, we present a strongly polynomial time algorithm to construct the trade-off curve between the number of tardy jobs and the maximum compression cost for the discrete controllable version.