Single machine scheduling with general positional deterioration and rate-modifying maintenance

We present polynomial-time algorithms for single machine problems with generalized positional deterioration effects and machine maintenance. The decisions should be taken regarding possible sequences of jobs and on the number of maintenance activities to be included into a schedule in order to minimize the overall makespan. We deal with general non-decreasing functions to represent deterioration rates of job processing times. Another novel extension of existing models is our assumption that a maintenance activity does not necessarily fully restore the machine to its original perfect state. In the resulting schedules, the jobs are split into groups, a particular group to be sequenced after a particular maintenance period, and the actual processing time of a job is affected by the group that job is placed into and its position within the group

Parallel-Machine Scheduling Problems with Past-Sequence-Dependent Delivery Times and Aging Maintenance

We consider parallel-machine scheduling problems with past-sequence-dependent (psd) delivery times and aging maintenance. The delivery time is proportional to the waiting time in the system. Each machine has an aging maintenance activity. We develop polynomial algorithms to three versions of the problem to minimize the total absolute deviation of job completion times, the total load, and the total completion time

Scheduling Jobs and a Variable Maintenance on a Single Machine with Common Due-Date Assignment

We investigate a common due-date assignment scheduling problem with a variable maintenance on a single machine. The goal is to minimize the total earliness, tardiness, and due-date cost. We derive some properties on an optimal solution for our problem. For a special case with identical jobs we propose an optimal polynomial time algorithm followed by a numerical example

A single-machine scheduling problem with multiple unavailability constraints: A mathematical model and an enhanced variable neighborhood search approach

AbstractThis research focuses on a scheduling problem with multiple unavailability periods and distinct due dates. The objective is to minimize the sum of maximum earliness and tardiness of jobs. In order to optimize the problem exactly a mathematical model is proposed. However due to computational difficulties for large instances of the considered problem a modified variable neighborhood search (VNS) is developed. In basic VNS, the searching process to achieve to global optimum or near global optimum solution is totally random, and it is known as one of the weaknesses of this algorithm. To tackle this weakness, a VNS algorithm is combined with a knowledge module. In the proposed VNS, knowledge module extracts the knowledge of good solution and save them in memory and feed it back to the algorithm during the search process. Computational results show that the proposed algorithm is efficient and effective

Combining time and position dependent effects on a single machine subject to rate-modifying activities

We introduce a general model for single machine scheduling problems, in which the actual processing times of jobs are subject to a combination of positional and time-dependent effects, that are job-independent but additionally depend on certain activities that modify the processing rate of the machine, such as, maintenance. We focus on minimizing two classical objectives: the makespan and the sum of the completion times. The traditional classification accepted in this area of scheduling is based on the distinction between the learning and deterioration effects on one hand, and between the positional effects and the start-time dependent effects on the other hand. Our results show that in the framework of the introduced model such a classification is not necessary, as long as the effects are job-independent. The model introduced in this paper covers most of the previously known models. The solution algorithms are developed within the same general framework and their running times are no worse than those available earlier for problems with less general effects

Integrating Preventive Maintenance Scheduling as Probability Machine Failure and Batch Production Scheduling

This paper discusses integrated model of batch production scheduling and machine maintenance scheduling. Batch production scheduling uses minimize total actual flow time criteria and machine maintenance scheduling uses the probability of machine failure based on Weibull distribution. The model assumed no nonconforming parts in a planning horizon. The model shows an increase in the number of the batch (length of production run) up to a certain limit will minimize the total actual flow time. Meanwhile, an increase in the length of production run will implicate an increase in the number of PM. An example was given to show how the model and algorithm work

Comparison of new metaheuristics, for the solution of an integrated jobs-maintenance scheduling problem

This paper presents and compares new metaheuristics to solve an integrated jobs-maintenance scheduling problem, on a single machine subjected to aging and failures. The problem, introduced by Zammori et al. (2014), was originally solved using the Modified Harmony Search (MHS) metaheuristic. However, an extensive numerical analysis brought to light some structural limits of the MHS, as the analysis revealed that the MHS is outperformed by the simpler Simulated Annealing by Ishibuchi et al. (1995). Aiming to solve the problem in a more effective way, we integrated the MHS with local minima escaping procedures and we also developed a new Cuckoo Search metaheuristic, based on an innovative Levy Flight. A thorough comparison confirmed the superiority of the newly developed Cuckoo Search, which is capable to find better solutions in a smaller amount of time. This an important result, both for academics and practitioners, since the integrated job-maintenance scheduling problem has a high operational relevance, but it is known to be extremely hard to be solved, especially in a reasonable amount of time. Also, the developed Cuckoo Search has been designed in an extremely flexible way and it can be easily readapted and applied to a wide range of combinatorial problems. (C) 2018 Elsevier Ltd. All rights reserved

A note on optimization in deteriorating systems using scheduling problems with the aging effect and resource allocation models

AbstractThis paper concerns scheduling problems with the aging effect and additional resource allocation. A measurable result of the aging phenomenon is that the time required to perform a job increases whereas the additional resource allocation allows one to decrease it. As an example of a deteriorating system that can be described and optimized by the application of the models and algorithms considered, we choose the pickling process, where cleaning of metal items decreases the efficiency of the pickling (cleaning) bath (i.e., one containing an active substance), whereas heating it up can improve the efficiency. In particular, we focus on the optimization problems for such systems and model them as single-machine scheduling problems with job processing times dependent on the fatigue of a machine and on the allocation of additional resources. The objectives considered are the minimization of time criteria (the maximum completion time and the maximum lateness) under a given resource consumption as well as the minimization of the resource consumption under given time criteria. The computational complexity of the problems is determined and solution properties are proved. On the basis of these, we construct optimal polynomial time algorithms for some cases of the problems considered