Search

This paper addresses the problem of open shop scheduling on two machines with resources constraints. In the context of our study, in order to be executed, a job requires first, for its preparation for a given period of time, a number of resources which cannot exceed a given resource capacity. Then, it goes onto its execution while the resources allocated to it become available again. We seek a schedule that minimizes the makespan. We first prove the $\mathcal{N}\mathcal{P}$ -hardness of several versions of this problem. Then, we present a well solvable case, lower bounds, and heuristic algorithms along with an experimental study. [ABSTRACT FROM AUTHOR]

This paper studies two single-machine scheduling problems with the effect of deterioration and learning. In this model, the processing times of jobs are defined as functions of their starting times and positions in a sequence. For the following two objective functions: the weighted sum of completion times and the maximum lateness, this paper proposes two heuristics according to the corresponding single machine problems without learning effect. This paper also gives the worst-case error bound for the heuristics and provides computational results to evaluate the performance of the heuristics. [ABSTRACT FROM AUTHOR]

In this paper, a more general version of the flow shop scheduling problem with the objective of minimizing the total flow time is investigated. In order to get closer to the actual conditions of the problem, some realistic assumptions including non-permutation scheduling, learning effect, multiple availability constraints, and release times are considered. It is assumed that the real processing time of each job on a machine depends on the position of that job in the sequence, and after processing a specified number of jobs at each machine, an unavailability period is occurring because of maintenance activities. Moreover, it is supposed that each job may not be ready for processing at time zero and may have a release time. According to these assumptions, a new mixed integer linear programming (MILP) model is proposed to formulate the problem. Due to the high complexity of the problem, a heuristic method and a simulated annealing algorithm are presented to find the nearly optimal solutions for medium- and large-sized problems. To obtain better and more robust solutions, the Taguchi method is used in order to calibrate the simulated annealing algorithm parameters. Finally, the computational results are provided for evaluating the performance and effectiveness of the proposed solution methods. [ABSTRACT FROM AUTHOR]

This paper deals with a single-machine scheduling problem with setup time and learning effects. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are job-independent and past-sequence-dependent, and the learning effects are job-independent and position-dependent. The objective is to minimize the sum of earliness penalties subject to no tardy jobs. Wang, Wang, Gao, and Huang [Int J Adv Manuf Technol 48: 739-746, ] showed that an optimal sequence for this problem could be obtained by arranging jobs in non-increasing order of processing times. In this paper, we first demonstrate that this result is incorrect, and then introduce new exact solution strategies that polynomially solve problems whose earliness penalties are strictly increasing functions of job earliness. Polynomial time solutions are also presented for some special cases. [ABSTRACT FROM AUTHOR]

Machine learning exists in many realistic scheduling situations. This study focuses on permutation flow shop scheduling problems, where the actual processing time of a job is defined by a general non-increasing function of its scheduled position, i.e., general position-dependent learning effects. The objective functions are to minimize the total completion time, the makespan, the total weighted completion time, and the total weighted discounted completion time, respectively. To solve these problems, we present approximation algorithms based on the optimal permutations for the corresponding single machine scheduling problems and analyze their worst-case error bound. [ABSTRACT FROM AUTHOR]

Proofs of strong NP-hardness of single machine and two-machine flowshop scheduling problems with learning or aging effect given in Rudek (Computers & Industrial Engineering 61:20-31, ; Annals of Operations Research 196(1):491-516, ; International Journal of Advanced Manufacturing Technology 59:299-309, ; Applied Mathematics and Computations 218:6498-6510, ; Applied Mathematical Modelling 37:1523-1536, ) contain a common mistake that make them incomplete. We reveal the mistake and provide necessary corrections for the problems in Rudek (Computers & Industrial Engineering 61:20-31, ; Annals of Operations Research 196(1):491-516, ; Applied Mathematical Modelling 37:1523-1536, ). NP-hardness of problems in Rudek (International Journal of Advanced Manufacturing Technology 59:299-309, ; Applied Mathematics and Computations 218:6498-6510, ) remains unknown because of another mistake which we are unable to correct. [ABSTRACT FROM AUTHOR]