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

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

Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance

We consider a scheduling problem on a single machine to minimize the makespan. The processing conditions are subject to cumulative deterioration, but can be restored by a single maintenance. We link the problem to the Subset-sum problem (if the duration of maintenance is constant) and to the Half-Product Problem (if the duration of maintenance depends on its start time). For both versions of the problem, we adapt the existing fully polynomial-time approximation schemes to our problems by handling the additive constants

Common due date early

Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 91-96.This study considers a scheduling problem with position-dependent deteriorating jobs and a maintenance activity in a single machine. Even in the absence of maintenance activity and deterioration problem is NP-hard. A solution comprises the following: (i) positions of jobs, (ii) the position of the maintenance activity, (iii) starting time of the first job in the schedule. After the maintenance activity, machine will revert to its initial condition and deterioration will start anew. The objective is to minimize the total weighted earliness and tardiness costs. Jobs scheduled before (after) the due-date are penalized according to their earliness (tardiness) value. Polynomial (O(n log n)) time solutions are provided for some special cases. No polynomial solution exists for instances with tight due-dates. We propose a mixed integer programming model and efficient algorithms for the cases where mathematical formulation is not efficient in terms of computational time requirements. Computational results show that the proposed algorithms perform well in terms of both solution quality and computation time.Şirvan, FatmaM.S

Minimizing the Makespan for Scheduling Problems with General Deterioration Effects

This paper investigates the scheduling problems with general deterioration models. By the deterioration models, the actual processing time functions of jobs depend not only on the scheduled position in the job sequence but also on the total weighted normal processing times of the jobs already processed. In this paper, the objective is to minimize the makespan. For the single-machine scheduling problems with general deterioration effects, we show that the considered problems are polynomially solvable. For the flow shop scheduling problems with general deterioration effects, we also show that the problems can be optimally solved in polynomial time under the proposed conditions

Theoretical and Computational Research in Various Scheduling Models

Nine manuscripts were published in this Special Issue on “Theoretical and Computational Research in Various Scheduling Models, 2021” of the MDPI Mathematics journal, covering a wide range of topics connected to the theory and applications of various scheduling models and their extensions/generalizations. These topics include a road network maintenance project, cost reduction of the subcontracted resources, a variant of the relocation problem, a network of activities with generally distributed durations through a Markov chain, idea on how to improve the return loading rate problem by integrating the sub-tour reversal approach with the method of the theory of constraints, an extended solution method for optimizing the bi-objective no-idle permutation flowshop scheduling problem, the burn-in (B/I) procedure, the Pareto-scheduling problem with two competing agents, and three preemptive Pareto-scheduling problems with two competing agents, among others. We hope that the book will be of interest to those working in the area of various scheduling problems and provide a bridge to facilitate the interaction between researchers and practitioners in scheduling questions. Although discrete mathematics is a common method to solve scheduling problems, the further development of this method is limited due to the lack of general principles, which poses a major challenge in this research field

Preventive Maintenance & Replacement Scheduling Model for Repairable and Maintainable Systems

Maintenance plan is required when there is a need to decide on production rate and preventive maintenance (PM) scheduling for complex production systems in industry. The more complex the system is, the more components that may fail and cause the entire piece of equipment to be taken out of service, that in turn could affect production rate. Usually, most of equipment has its PM schedule set during plant design phase and generally follow recommendation from equipment manufacturer. After years of operation (operation and maintenance phase), the PM schedule might not be optimised due to various reasons – lack of full information on failure rate, repair rate, maintenance cost, etc. Thus, the objectives of this project are to develop an appropriate model for preventive maintenance and replacement scheduling using Mixed Integer Non – Linear Programming (MINLP), and also to analyze the results and effectiveness of the optimized model through trade – offs curves, that are one of the project deliverables. The project is initiated by identifying problem and objectives, study on literature review regarding various types of preventive maintenance and replacement scheduling model, and then come out with a model concept. It was found out that various parametric change effects were observed in component age graphs and scheduling tables in two developed models. In Model 1, three different trends were seen for each three cases such as cost increment was observed as required reliability increased where no changes happened in required reliability when shutdown cost varied and required reliability increased when time period was decreased respectively. In Model 2, it can be also seen that as time period decreased required reliability increased where higher amount of given budget can also increase required reliability of components. After all, these studies should be useful for maintenance planners and engineers tasked with the problem of developing maintenance plans for complex systems of components

A Survey of Fault-Tolerance Techniques for Embedded Systems from the Perspective of Power, Energy, and Thermal Issues

The relentless technology scaling has provided a significant increase in processor performance, but on the other hand, it has led to adverse impacts on system reliability. In particular, technology scaling increases the processor susceptibility to radiation-induced transient faults. Moreover, technology scaling with the discontinuation of Dennard scaling increases the power densities, thereby temperatures, on the chip. High temperature, in turn, accelerates transistor aging mechanisms, which may ultimately lead to permanent faults on the chip. To assure a reliable system operation, despite these potential reliability concerns, fault-tolerance techniques have emerged. Specifically, fault-tolerance techniques employ some kind of redundancies to satisfy specific reliability requirements. However, the integration of fault-tolerance techniques into real-time embedded systems complicates preserving timing constraints. As a remedy, many task mapping/scheduling policies have been proposed to consider the integration of fault-tolerance techniques and enforce both timing and reliability guarantees for real-time embedded systems. More advanced techniques aim additionally at minimizing power and energy while at the same time satisfying timing and reliability constraints. Recently, some scheduling techniques have started to tackle a new challenge, which is the temperature increase induced by employing fault-tolerance techniques. These emerging techniques aim at satisfying temperature constraints besides timing and reliability constraints. This paper provides an in-depth survey of the emerging research efforts that exploit fault-tolerance techniques while considering timing, power/energy, and temperature from the real-time embedded systems’ design perspective. In particular, the task mapping/scheduling policies for fault-tolerance real-time embedded systems are reviewed and classified according to their considered goals and constraints. Moreover, the employed fault-tolerance techniques, application models, and hardware models are considered as additional dimensions of the presented classification. Lastly, this survey gives deep insights into the main achievements and shortcomings of the existing approaches and highlights the most promising ones

Simulation and optimization techniques applied in semiconductor assembly and test operations

The importance of back-end operations in semiconductor manufacturing has been growing steadily in the face of higher customer expectations and stronger competition in the industry. In order to achieve low cycle times, high throughput, and high utilization while improving due-date performance, more effective tools are needed to support machine setup and lot dispatching decisions. In previous work, the problem of maximizing the weighted throughput of lots undergoing assembly and test (AT), while ensuring that critical lots are given priority, was investigated and a greedy randomized adaptive search procedure (GRASP) developed to find solutions. Optimization techniques have long been used for scheduling manufacturing operations on a daily basis. Solutions provide a prescription for machine setups and job processing over a finite the planning horizon. In contrast, simulation provides more detail but in a normative sense. It tells you how the system will evolve in real time for a given demand, a given set of resources and rules for using them. A simulation model can also accommodate changeovers, initial setups and multi-pass requirements easily. The first part of the research is to show how the results of an optimization model can be integrated with the decisions made within a simulation model. The problem addressed is defined in terms of four hierarchical objectives: minimize the weighted sum of key device shortages, maximize weighted throughput, minimize the number of machines used, and minimize makespan for a given set of lots in queue, and a set of resources that includes machines and tooling. The facility can be viewed as a reentrant flow shop. The basic simulation was written in AutoSched AP (ASAP) and then enhanced with the help of customization features available in the software. Several new dispatch rules were developed. Rule_First_setup is able to initialize the simulation with the setups obtained with the GRASP. Rule_All_setups enables a machine to select the setup provided by the optimization solution whenever a decision is about to be made on which setup to choose subsequent to the initial setup. Rule_Hotlot was also proposed to prioritize the processing of the hot lots that contain key devices. The objective of the second part of the research is to design and implement heuristics within the simulation model to schedule back-end operations in a semiconductor AT facility. Rule_Setupnum lets the machines determine which key device to process according to a machine setup frequency table constructed from the GRASP solution. GRASP_asap embeds a more robust selection features of GRASP in the ASAP model through customization. This allows ASAP to explore a larger portion of the feasible region at each decision point by randomizing machine setups using adaptive probability distributions that are a function of solution quality. Rule_Greedy, which is a simplification of GRASP_asap, always picks the setup for a particular machine that gives the greatest marginal improvement in the objective function among all candidates. The purpose of the third part of the research is to statistically validate the relative effectiveness of our top six dispatch rules by comparing their performance on 30 real and randomly generated data sets. Using both GRASP and our ASAP discrete event simulation model, we have (1) identified the general order of dispatch rule performance, (2) investigated the impact of having setups installed on machines at time zero on rule performance, (3) determined the conditions under which restricting the maximum number of changeover affects the rule performance, and (4) studied the factors that might simultaneously affect rule performance with the help of a common random numbers experimental design. In the analysis, the first two objectives, weighted key device shortages and weighted throughput, are used to measure outcomes.Operations Research and Industrial Engineerin