One-machine Scheduling Problem Research Articles

Models and algorithms for a yard crane scheduling problem in container ports

This paper addresses the scheduling of a yard crane in an automated container block, considering its relationships with the other terminal subsystems. Containers coming into the block to be stored have release times, indicating the moment at which they arrive from ships or trucks. Containers being retrieved have due times, indicating when they will be required by other subsystems. The problem can be seen as a pickup routing problem and also as a one-machine scheduling problem. As a starting point, integer linear models were developed for both approaches. Then, to obtain good solutions for large instances, several heuristic algorithms, coupled with a local search, were proposed. An extensive computational study, based on a newly generated benchmark, shows the limits of the exact methods and the quality of the solutions obtained by the heuristics.

An Improved Branch-and-Bound Algorithm for the One-Machine Scheduling Problem with Delayed Precedence Constraints

In this paper, we discuss the one-machine scheduling problem with release and delivery times with the minimum makespan objective. Both heuristics and branch-and-bound algorithms have been formulated for the problem. One such branch-and-bound algorithm solves the problem and a variation that requires a delay between the completion of one job and the start of another (delayed precedence constraints). This paper analyzes key components of this branch-and-bound algorithm and proposes an improved heuristic to be used in conjunction with a different search strategy. Computational experiments demonstrate that the modifications lead to substantial improvements in running time and number of iterations on the one-machine problem instances both with and without delayed precedence constraints.

Supply chain optimisation with both production and transportation integration: multiple vehicles for a single perishable product

This paper deals with an extension of the integrated production and transportation scheduling problem (PTSP) by considering multiple vehicles (PTSPm) for optimisation of supply chains. The problem reflects a real concern for industry since production and transportation subproblems are commonly addressed independently or sequentially, which leads to sub-optimal solutions. The problem includes specific capacity constraints, the short lifespan of products and the special case of the single vehicle that has already been studied in the literature. A greedy randomised adaptive search procedure (GRASP) with an evolutionary local search (ELS) is proposed to solve the instances with a single vehicle as a special case. The method has been proven to be more effective than those published and provides shorter computational times with new best solutions for the single vehicle case. A new set of instances with multiple vehicles is introduced to favour equitable future research. Our study extends previous research using an indirect resolution approach and provides an algorithm to solve a wide range of one-machine scheduling problems with the proper coordination of single or multiple vehicles.

One-machine scheduling problems with deteriorating jobs and position-dependent learning effects under group technology considerations

In this paper, we introduce a group scheduling model with general deteriorating jobs and learning effects in which deteriorating jobs and learning effects are both considered simultaneously. This means that the actual processing time of a job depends not only on the processing time of the jobs already processed, but also on its scheduled position. In our model, the group setup times are general linear functions of their starting times and the jobs in the same group have general position-dependent learning effects and time-dependent deterioration. The objective of scheduling problems is to minimise the makespan and the sum of completion times, respectively. We show that the problems remain solvable in polynomial time under the proposed model.

Scheduling with compressible and stochastic release dates

In this work we study a one-machine scheduling problem which is featured by: (a) the release date of each job is compressible and stochastic, (b) each job has to be delivered before its due date (deadline) and (c) the manufacturer can expedite the production through overtime at an extra cost. The objective function of the scheduling problem is to minimize the total cost which includes the compressing cost and the overtime production cost. We propose a heuristic algorithm in which the stochastic problem is converted to the deterministic problem by a release-time “converting policy”. We coin a concept of a job's late-release-impact factor (LRIF) and we propose a LRIF based converting policy. We compare the LRIF based converting policy with the ones used in practice, and the numerical test shows that the LRIF based converting policy can obtain the schedule with the lowest actual total cost.

Single-machine scheduling with no idle time and release dates to minimize a regular criterion

We address the one-machine scheduling problem with release dates, in which the machine is subject to the non-idling constraint, i.e. no intermediate idle time is permitted between the jobs processed by the machine. The objective is to minimize a regular objective function. We describe a constraint programming approach for solving this type of problem exactly. Some necessary and/or sufficient conditions for obtaining non-idling semi-active, active and optimal schedules are described. We propose some propagation rules based on these properties. As an application, we apply the proposed method to the total (weighted) completion time problem, and we provide some experimental results to illustrate its effectiveness.

Dominance-based heuristics for one-machine total cost scheduling problems

We study the one-machine scheduling problem with release dates and we look at several objective functions including total (weighted) tardiness and total (weighted) completion time. We describe dominance rules for these criteria, as well as techniques for using these dominance rules to build heuristic solutions. We use them to improve certain well-known greedy heuristic algorithms from the literature. Finally, we introduce a Tabu Search method with a neighborhood based on our dominance rules. Experiments show the effectiveness of our techniques in obtaining very good solutions for all studied criteria.

A faster branch-and-bound algorithm for the earliness-tardiness scheduling problem

This paper addresses the one-machine scheduling problem with earliness-tardiness penalties. We propose a new branch-and-bound algorithm that can solve instances with up to 50 jobs and that can solve problems with even more general non-convex cost functions. The algorithm is based on the combination of a Lagrangean relaxation of resource constraints and new dominance rules.

A branch and bound algorithm for the one-machine scheduling problem with minimum and maximum time lags

We consider the one-machine scheduling problem with minimum and maximum time lags while minimizing the makespan. This problem typically arises in a manufacturing environment where the next job has to be carried out within a specific time range after the completion of the immediately preceding job. We describe a branch and bound algorithm, based on the input and output of a clique and the relevant propositions, for finding the optimal waiting times. The computational experiments give promising results, showing whether a given instance is feasible or infeasible. With the proposed branch and bound algorithm we can either find an optimal schedule or establish the infeasibility within an acceptable run time.

Scheduling with periodic availability constraints and irregular cost functions

This paper addresses a one-machine scheduling problem in which the efficiency of the machine is not constant, that is the duration of a task is longer in badly efficient time periods. Each task has an irregular completion cost. Under the assumption that the efficiency constraints are time-periodic, we show that the special case where the sequence is fixed can be solved in polynomial time. The general case is NP-complete so that we propose a two-phase heuristic to find good solutions. Our approach is tested on problems with earliness-tardiness costs.

Efficient neighborhood search for the one-machine earliness–tardiness scheduling problem

This paper addresses the one-machine scheduling problem where the objective is to minimize a sum of costs such as earliness–tardiness costs. Since the sequencing problem is NP-hard, local search is very useful for finding good solutions. Unlike scheduling problems with regular cost functions, the scheduling (or timing) problem is not trivial when the sequence is fixed. Therefore, the local search approaches must deal with both job interchanges in the sequence and the timing of the sequenced jobs. We present a new approach that efficiently searches in a large neighborhood and always returns a solution for which the timing is optimal.

Single-machine scheduling with time window-dependent processing times

In the one-machine scheduling problems analysed in this paper, the processing time of a job depends on the time at which the job is started. More precisely, the horizon is divided into time windows and with each one a coefficient is associated that is used to determine the actual processing time of a job starting in it. Two models are introduced, and one of them has direct connections with models considered in previous papers on scheduling problems with time-dependent processing times. Various computational complexity results are presented for the makespan criterion, which show that the problem is NP-hard, even with two time windows. Solving procedures are also proposed for some special cases.

Dynasearch for the earliness–tardiness scheduling problem with release dates and setup constraints

A large dynasearch neighborhood is introduced for the one-machine scheduling problem with sequence-dependent setup times and costs and earliness–tardiness penalties. Finding the best schedule in this neighborhood is NP-complete in the ordinary sense but can be done in pseudo-polynomial time. We also present experimental results.

Minimizing the earliness–tardiness costs on a single machine

In this paper the one-machine scheduling problem with linear earliness and tardiness costs is considered. The cost functions are job dependent and asymmetric. The problem consists of two sub-problems. The first one is to find a sequence of jobs and the second one is to find the job completion times that are optimal for the given sequence. We consider the second sub-problem and propose an algorithm solving the problem in O ( n log n ) time.

Earliness–tardiness scheduling with setup considerations

The one-machine scheduling problem with sequence-dependent setup times and costs and earliness–tardiness penalties is addressed. A time-indexed formulation of the problem is presented as well as different relaxations that give lower bounds of the problem. Then, a branch-and-bound procedure based on one of these lower bounds is presented. The efficiency of this algorithm also relies on new dominance rules and on a heuristic to derive good feasible schedules. Computational tests are finally presented.

Investigating the use of genetic programming for a classic one-machine scheduling problem

Genetic programming has rarely been applied to manufacturing optimisation problems. In this paper the potential use of genetic programming for the solution of the one-machine total tardiness problem is investigated. Genetic programming is utilised for the evolution of scheduling policies in the form of dispatching rules. These rules are trained to cope with different levels of tardiness and tightness of due dates.

A Polynomial Algorithm for Special Case of the One-Machine Scheduling Problem with Time-Lags

The standard one-machine scheduling problem consists in scheduling a set of jobs in one machine which can handle only one job at a time, minimizing the maximum lateness. Each job is available for processing at its release date, requires a known processing time and after finishing the processing, it is delivery after a certain time. There also can exists precedence constraints between pairs of jobs, requiring that the first jobs must be completed before the second job can start. An extension of this problem consists in assigning a time interval between the processing of the jobs associated with the precedence constrains, known by finish-start time-lags. In presence of this constraints, the problem is NP-hard even if preemption is allowed. In this work, we consider a special case of the one-machine preemption scheduling problem with time-lags, where the time-lags have a chain form, and propose a polynomial algorithm to solve it. The algorithm consist in a polynomial number of calls of the preemption version of the Longest Tail Heuristic. One of the applicability of the method is to obtain lower bounds for NP-hard one-machine and job-shop scheduling problems. We present some computational results of this application, followed by some conclusions.

Minimizing the number of late jobs under the group technology assumption

We consider the one-machine scheduling problem to minimize the number of late jobs under the group technology assumption, where jobs are classified into groups and all jobs from the same group must be processed contiguously. This problem is shown to be strongly NP-hard, even for the case of unit processing time and zero set-up time. A polynomial time algorithm is developed for the restricted version in which the jobs in each group have the same due date. However, the problem is proved to be ordinarily NP-hard if the jobs in a group have the same processing time as well as the same due date.

An improved heuristic for one-machine scheduling with delays constraints

An improved heuristic is proposed for one-machine scheduling problem with delay constraints, thus an open problem raised by Wikumet al. is solved. The heuristic solves the corresponding unit-execution-time problem optimally.

One-machine scheduling to minimize mean tardiness with minimum number tardy

In this paper the one-machine scheduling problem with the objective of minimizing the mean tardiness subject to maintaining a prescribed number of tardy jobs is analysed. An algorithm for solving this problem is presented. It is proved that the schedule generated by the proposed algorithm is indeed optimal.