Single-machine scheduling with periodic maintenance to minimize makespan

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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

Single machine scheduling with job-dependent machine deterioration

We consider the single machine scheduling problem with job-dependent machine deterioration. In the problem, we are given a single machine with an initial non-negative maintenance level, and a set of jobs each with a non-preemptive processing time and a machine deterioration. Such a machine deterioration quantifies the decrement in the machine maintenance level after processing the job. To avoid machine breakdown, one should guarantee a non-negative maintenance level at any time point; and whenever necessary, a maintenance activity must be allocated for restoring the machine maintenance level. The goal of the problem is to schedule the jobs and the maintenance activities such that the total completion time of jobs is minimized. There are two variants of maintenance activities: in the partial maintenance case each activity can be allocated to increase the machine maintenance level to any level not exceeding the maximum; in the full maintenance case every activity must be allocated to increase the machine maintenance level to the maximum. In a recent work, the problem in the full maintenance case has been proven NP-hard; several special cases of the problem in the partial maintenance case were shown solvable in polynomial time, but the complexity of the general problem is left open. In this paper we first prove that the problem in the partial maintenance case is NP-hard, thus settling the open problem; we then design a $2$-approximation algorithm.Comment: 15 page

Exact solution of the single-machine scheduling problem with periodic maintenances and sequence-dependent setup times

The single-machine scheduling problem with periodic maintenances and sequence-dependent setup times aims at scheduling jobs on a single machine in which periodic maintenances and setups are required. The objective is the minimization of the makespan. We propose an exact algorithm based on the iterative solution of three alternative arc-time-indexed models. Extensive computational experiments are carried out on 420 benchmark instances with up to 50 jobs, and on 405 newly proposed instances involving up to 150 jobs. We compare the results found by all formulations with those obtained by the best available mathematical formulation. All instances from the existing dataset are solved to optimality for the first time

Single machine scheduling with periodic machine availability

In this paper we address the problem of scheduling jobs on a single machine with cyclical machine availability periods. In this problem, the scheduling horizon is composed of periods where the machine is available followed by other periods where no operation can be performed. In the literature, the problem is denoted as scheduling with periodic maintenance, as it is usually assumed that these unavailability periods are employed to perform maintenance activities. Another situation is the one inspiring our research, i.e. the need of completing manufacturing operations within a shift. More specifically, we focus the single machine scheduling problem with makespan objective subject to periodic machine availability. There are several contributions proposing approximate procedures due to the NP-hardness shown for the problem. However, we are not aware of a computational evaluation among these procedures. Furthermore, the problem is similar to the classical bin packing problem, so it is of interest to explore the relation between both problems. In this paper, we address these two issues, and propose new approximate solution procedures for the problem.Ministerio de Ciencia e Innovación DPI2016-80750-

A Mathematical Model for HVLV Systems Scheduling and Optimization With Periodic Preventive Maintenance Using (max, +) Algebra

International audienceThe High-Variety, Low-Volume (HVLV) scheduling problem is one of the most arduous combinatorial optimization problems. This paper considers an interesting formulation of the HVLV scheduling problem using (max, +) algebra while periodic Preventive Maintenance (PM) is considered. Maintenance is time based since activities are periodically fixed: maintenance is required after a periodic time interval (all periods are equals on each machine). In this paper, the maintenance tasks of machines are controllable.The jobs and the maintenance operations are scheduled simultaneously. Also, the maintenance operations are scheduled between each other, so that a regular criterion is optimized. To generate feasible schedules, constrained decision variables are incorporated into the (max, +) model. The validity of the proposed approach is illustrated by simulation examples

Non-identical parallel machines batch processing problem with release dates, due dates and variable maintenance activity to minimize total tardiness

[EN] Combination of job scheduling and maintenance activity has been widely investigated in the literature. We consider a non-identical parallel machines batch processing (BP) problem with release dates, due dates and variable maintenance activity to minimize total tardiness. An original mixed integer linear programming (MILP) model is formulated to provide an optimal solution. As the problem under investigation is known to be strongly NP-hard, two meta-heuristic approaches based on Simulated Annealing (SA) and Variable Neighborhood Search (VNS) are developed. A constructive heuristic method (H) is proposed to generate initial feasible solutions for the SA and VNS. In order to evaluate the results of the proposed solution approaches, a set of instances were randomly generated. Moreover, we compare the performance of our proposed approaches against four meta heuristic algorithms adopted from the literature. The obtained results indicate that the proposed solution methods have a competitive behaviour and they outperform the other meta-heuristics in most instances. Although in all cases, H + SA is the most performing algorithm compared to the others.Beldar, P.; Moghtader, M.; Giret Boggino, AS.; Ansaripoord, AH. (2022). Non-identical parallel machines batch processing problem with release dates, due dates and variable maintenance activity to minimize total tardiness. Computers & Industrial Engineering. 168:1-28. https://doi.org/10.1016/j.cie.2022.10813512816

Preventive Maintenance Supply Chain Management Optimal Scheduling on VMACL Machines by Implementing Simulation Annealing Algorithms

PT. Braja Mukti Cakra uses various types of engines to produce parts for truck cars. Vertical Lathe Automatic Chucking Machine (VMACL) is a machine that has the highest frequency of damage when compared to other machines. To reduce damage costs, preventive maintenance is well scheduled. This scheduling problem solving is done using the Annealing Simulation Algorithm. The results of the analysis give direction that the scheduling that must be done are: The maintenance action schedule for the Lifter component is at month 1,6,7,22,24,34, for the Insert component at 4,15,18,27,33 months, and for the Door component at the 2nd month, 12,13,16,17,30,36. Replacement actions for the Lifter component were carried out in the 4,5th month, 1,17,20,29, for the Insert component in the 9,19,22,23,35 months, and for the Door component in the 1,20,27 months. . Scheduling for 36 months using the Simulated Annealing Algorithm will cost IDR. 84,119,244.60 and produce greater reliability than the previous reliability of 58.44%

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