Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan

This paper studies the single-machine scheduling problem with deteriorating jobs and learning considerations. The objective is to minimize the makespan. We first show that the schedule produced by the largest growth rate rule is unbounded for our model, although it is an optimal solution for the scheduling problem with deteriorating jobs and no learning. We then consider three special cases of the problem, each corresponding to a specific practical scheduling scenario. Based on the derived optimal properties, we develop an optimal algorithm for each of these cases. Finally, we consider a relaxed model of the second special case, and present a heuristic and analyze its worst-case performance bound.     

Bin packing and multiprocessor scheduling problems with side constraint on job types

This paper deals with the bin packing problem and the multiprocessor scheduling problem both with an additional constraint specifying the maximum number of jobs in each type to the processed on a processor. Since these problems are NP-complete, various approximation algorithms are proposed by generalizing those algorithms known for the ordinary bin packing and multiprocessor scheduling problems. The worst-case performance of the proposed algorithms are analyzed, and some computational results are reported to indicate their average case behavior.     

The bounded single-machine parallel-batching scheduling problem with family jobs and release dates to minimize makespan

We consider the problem of scheduling family jobs with release dates on a bounded batching machine to minimize the makespan. A polynomial-time approximation scheme for the identical job size model and an approximation algorithm with a worst-case ratio of for the non-identical job size model will be derived.     

Power-aware scheduling of preemptable jobs on identical parallel processors to minimize makespan

This paper deals with power-aware scheduling of preemptable jobs on identical parallel processors to minimize schedule length when jobs are described by continuous, strictly concave functions relating their processing speed at time t to the amount of power allotted at the moment. Power is a continuous, doubly constrained resource, i.e. both: its availability at time t and consumption over scheduling horizon are constrained. Precedence constraints among jobs are represented by a task-on-arc graph. A methodology based on properties of optimal schedules is presented for solving the problem optimally for a given ordering of nodes in the graph. Heuristics for finding an ordering which leads to possibly short schedules are proposed and examined experimentally.     

Batch scheduling of simple linear deteriorating jobs on a single machine to minimize makespan

We consider a scheduling problem in which n jobs are to be processed on a single machine. The jobs are processed in batches and the processing time of each job is a simple linear function of its waiting time, i.e., the time between the start of the processing of the batch to which the job belongs and the start of the processing of the job. The objective is to minimize the makespan, i.e., the completion time of the last job. We first show that the problem is strongly NP-hard. Then we show that, if the number of batches is B  , the problem remains strongly NP-hard when B?U$B?U$ for a variable U?2$U?2$ or B?U$B?U$ for any constant U?2$U?2$. For the case of B?U$B?U$, we present a dynamic programming algorithm that runs in pseudo-polynomial time and a fully polynomial time approximation scheme (FPTAS) for any constant U?2$U?2$. Furthermore, we provide an optimal linear time algorithm for the special case where the jobs are subject to a linear precedence constraint, which subsumes the case where all the job growth rates are equal.     

Two-machine flow shop scheduling with deteriorating jobs: minimizing the weighted sum of makespan and total completion time

This paper considers a two-machine flow shop scheduling problem with deteriorating jobs in which the processing times of jobs are dependent on their starting times in the sequence. The objective is to minimize the weighted sum of makespan and total completion time. To analyse the problem, we propose a mixed integer programming model, and discuss several polynomially solvable special cases. We also present a branch-and-bound algorithm with several dominance rules, an upper bound and a lower bound. Finally, we present results of computational experiments conducted to evaluate the performance of the proposed model and the exact algorithm.     

An improved heuristic for two-machine flow shop scheduling with an availability constraint and nonresumable jobs

In this paper, we deal with the two-machine flow shop scheduling problem having an unavailability interval on the first machine, and nonresumable jobs. We first present an enhancement procedure that, once applied to any arbitrary solution, produces a schedule that is at most equal 2 times the optimal makespan. We then develop an improved heuristic, with a relative worst-case error of 3/2.     

Minimizing energy consumption and makespan in a two-machine flowshop scheduling problem

Energy consumption has become a key concern for manufacturing sector because of negative environmental impact of operations. We develop constructive heuristics and multi-objective genetic algorithms (MOGA) for a two-machine sequence-dependent permutation flowshop problem to address the trade-off between energy consumption as a measure of sustainability and makespan as a measure of service level. We leverage the variable speed of operations to develop energy-efficient schedules that minimize total energy consumption and makespan. As minimization of energy consumption and minimization of makespan are conflicting objectives, the solutions to this problem constitute a Pareto frontier. We compare the performance of constructive heuristics and MOGAs with CPLEX and random search in a wide range of problem instances. The results show that MOGAs hybridized with constructive heuristics outperform regular MOGA and heuristics alone in terms of quality and cardinality of Pareto frontier. We provide production planners with new and scalable solution techniques that will enable them to make informed decisions considering energy consumption together with service objectives in shop floor scheduling.     

A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs

In this paper, we consider the problem of permutation flowshop scheduling with the objectives of minimizing the makespan and total flowtime of jobs, and present a Multi-Objective Simulated-annealing Algorithm (MOSA). Two initial sequences are obtained by using simple and fast existing heuristics, supplemented by the implementation of three improvement schemes. Each of the two resultant sequences corresponds to a possible non-dominated solution containing the minimum value of one objective function. These sequences, taken one at a time, are given as the starting sequences to the MOSA. The MOSA seeks to obtain non-dominated solutions through the implementation of a simple probability function that attempts to generate solutions on the Pareto-optimal front. The probability function selects probabilistically a particular objective function, considering which the algorithm uncovers non-dominated solutions. Moreover, the probability function is varied in such a way that the entire objective-function space is covered uniformly so as to obtain as many non-dominated and well-dispersed solutions as possible. The parameters in the proposed MOSA are determined after conducting a pilot study. Two variants of the proposed algorithm, called MOSA-I and MOSA-II, with different parameter settings with respect to the temperature and epoch length, are considered in the performance evaluation of algorithms. In order to evaluate MOSA-I and MOSA-II, we have made use of 90 benchmark problems provided by Taillard [Eur. J. Operation. Res. 64 (1993) 278]. After an extensive literature survey, the following flowshop multi-objective scheduling algorithms have been identified as benchmark procedures: (a) MOGLS (Multi-Objective Genetic Local Search) by Ishibuchi and Murata [IEEE Trans. Syst., Man, Cybernet. C: Appl. Rev. 28 (1998) 392]; (b) Elitist Non-dominated sorting Genetic Algorithm (ENGA) by Bagchi [Multi-Objective Scheduling by Genetic Algorithms, Kluwer Academic Publishers, 1999]; (c) GPW (Gradual Priority Weighting) approach by Chang, Hsieh and Lin [Int. J. Prod. Econ. 79 (2002) 171]; and (d) a posteriori approach based heuristic by Framinan, Leisten and Ruiz-Usano [Eur. J. Operation. Res. 141 (2002) 559]. The non-dominated sets obtained from each of the existing benchmark algorithms and the proposed MOSA-I and MOSA-II are compared, and subsequently combined to obtain a net non-dominated front. It is found that most of the solutions in the net non-dominated front are yielded by MOSA-I and MOSA-II. In addition, it is noteworthy that both MOSA-I and MOSA-II require less computational effort than the MOGLS, ENGA and GPW.     

On no-wait and no-idle flow shops with makespan criterion

The paper deals with the NP-hard problems of minimizing the makespan in m-machine no-wait and no-idle permutation flow shops. We identify networks whose longest path lengths represent the makespans. These networks reveal the duality between the two problems, and show graphical explanations of the fact that under no-wait and no-idle conditions the makespan can be a decreasing function of some job processing times. Moreover, they also lead to a natural reduction of the no-wait flow shop problem to the traveling salesman problem, some lower bounds on the shortest makespan, and new efficiently solvable special cases.     

A dynamic programming algorithm for scheduling jobs in a two-machine open shop with an availability constraint

This paper studies a two-machine open shop scheduling problem with an availability constraint, ie we assume that a machine is not always available and that the processing of the interrupted job can be resumed when the machine becomes available again. We consider the makespan minimization as criterion. This problem is NP-hard. We develop a pseudo-polynomial time dynamic programming algorithm to solve the problem optimally when the machine is not available at time s>0. Then, we propose a mixed integer linear programming formulation, that allows to solve instances with up to 500 jobs optimally in less than 5?min with CPLEX solver. Finally, we show that any heuristic algorithm has a worst-case error bound of 1.     

Nearly on-line scheduling of multiprocessor systems with memories

We show that no multiprocessor system that contains at least one processor with memory size smaller than at least two other processors can be scheduled nearly on-line to minimize the finish time. An efficient nearly on-line algorithm to minimize C_max is developed for multiprocessor systems that do not satisfy the preceding requirement.     

Considerations of single-machine scheduling with deteriorating jobs

This paper considers some scheduling problems with deteriorating jobs. The objectives are to minimize the makespan, the total completion time, the total absolute deviation of completion time, the earliness, tardiness, and due date penalty, the sum of earliness penalties subject to no tardy jobs, respectively. We also explore two resource constrained scheduling problems: how to minimize the resource consumption with makespan constraints and how to minimize the makespan with the total resource consumption constraints. Several polynomial time algorithms are proposed to optimally solve the problems with the above objective functions.     

Crane scheduling with non-crossing constraint

In this paper, we examine crane scheduling for ports. This important component of port operations management is studied when the non-crossing spatial constraint, which is common to crane operations, is considered. We assume that ships can be divided into holds and that cranes can move from hold to hold but jobs are not pre-emptive, so that only one crane can work on one hold or job to complete it. Our objective is to minimize the latest completion time for all jobs. We formulate this problem as an integer programming problem. We provide the proof that this problem is NP-complete and design a branch-and-bound algorithm to obtain optimal solutions. A simulated annealing meta-heuristic with effective neighbourhood search is designed to find good solutions in larger size instances. The elaborate experimental results show that the branch-and-bound algorithm runs much faster than CPLEX and the simulated annealing approach can obtain near optimal solutions for instances of various sizes.     

Multi-machine scheduling with deteriorating jobs and scheduled maintenance

In this paper, we investigate a multi-machine scheduling problem in which job processing times are increasing functions of their starting times and machines are not always available. Job processing times are assumed to follow simple linear deteriorations. Moreover, each machine is assumed to have a maintenance period which is known in advance. Both the resumable and non-resumable cases are discussed with the objective of minimizing the makespan. A lower bound and a heuristic algorithm are derived for each case. Numerical results are also provided to evaluate the efficiency of the proposed procedures.     

Due-date assignment and parallel-machine scheduling with deteriorating jobs

In this paper we study the problem of scheduling n deteriorating jobs on m identical parallel machines. Each job's processing time is a nondecreasing function of its start time. The problem is to determine an optimal combination of the due-date and schedule so as to minimize the sum of the due-date, earliness and tardiness penalties. We show that this problem is NP-hard, and we present a heuristic algorithm to find near-optimal solutions for the problem. When the due-date penalty is 0, we present a polynomial time algorithm to solve it.     

Two-dedicated-machine scheduling problem with precedence relations to minimize makespan

Two-dedicated-parallel-machine scheduling problem with precedence constraints to minimize makespan is considered. This problem originally appeared as a sub-problem in assembly line balancing but it has also its own applications. Complexity and approximation results for this scheduling problem and its special cases with chains of jobs or equal-processing-times are presented.