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

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

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

Single machine scheduling with time-dependent linear deterioration and rate-modifying maintenance

We study single machine scheduling problems with linear time-dependent deterioration effects and maintenance activities. Maintenance periods (MPs) are included into the schedule, so that the machine, that gets worse during the processing, can be restored to a better state. We deal with a job-independent version of the deterioration effects, that is, all jobs share a common deterioration rate. However, we introduce a novel extension to such models and allow the deterioration rates to change after every MP. We study several versions of this generalized problem and design a range of polynomial-time solution algorithms that enable the decision-maker to determine possible sequences of jobs and MPs in the schedule, so that the makespan objective can be minimized. We show that all problems reduce to a linear assignment problem with a product matrix and can be solved by methods very similar to those used for solving problems with positional effects

Single machine scheduling with a generalized job-dependent cumulative effect

We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which the processing time of a job depends on the sum of certain parameters associated with previously scheduled jobs. In previous papers, these parameters are assumed to be equal to the normal processing times of jobs, which seriously limits the practical application of this model. We further generalize this model by allowing every job to respond differently to these cumulative effects. For the introduced model, we solve the problem of minimizing the makespan, with and without precedence constraints. For the problem without precedence constraints, we also consider a situation in which a maintenance activity is included in the schedule, which can improve the processing conditions of the machine, not necessarily to its original state. The resulting problem is reformulated as a variant of a Boolean programming problem with a quadratic objective, known as a half-product, which allows us to develop a fully polynomial-time approximation scheme with the best possible running time

Due-Window Assignment and Scheduling with Multiple Rate-Modifying Activities under the Effects of Deterioration and Learning

This paper discusses due-window assignment and scheduling with multiple rate-modifying activities. Multiple types of rate-modifying activities are allowed to perform on a single machine. The learning effect and job deterioration are also integrated concurrently into the problem which makes the problem more realistic. The objective is to find jointly the optimal location to perform multiple rate-modifying activities, the optimal job sequence, and the optimal location and size of the due window to minimize the total earliness, tardiness, and due-window-related costs. We propose polynomial time algorithms for all the cases of the problem under study

Single-Machine Scheduling with Aging Effects and Optional Maintenance Activity Considerations

This paper explores a single-machine scheduling with aging effects and the problem regarding optional maintenance activity assignment. The jobs’ processing time is assumed to follow a power position-dependent aging model. The optional maintenance activity refers to the situation in which the maintenance activity can be scheduled immediately after processing of any job has been completed except for the last job and the duration of maintenance activity can be of any value from zero to a fixed time interval. A recovery function is proposed to reflect the efficiency of the machine or worker which is improved. The objective of this study is to decide whether and when to implement the maintenance activity into the job sequence, how long the duration of maintenance activity is, and how to schedule so as to minimize the makespan. Once the duration of maintenance activity is known, we introduce an efficient solution for this problem. In addition, when the maintenance activity is completely performed, we showed that the optimal policy is to schedule the maintenance activity in the middle of the task sequence and optimally solved it by lower order algorithm. Finally, we extend the problem to the case of multiple maintenance activities which are completely performed. Hence, the problem is regarded as polynomial time solvable

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

Proceedings from the ECFIN Workshop "The budgetary implications of structural reforms" - Brussels, 2 December 2005

Most of the reforms discussed within the framework of the Lisbon strategy will benefit public finances in the long term. However, in the short-term, there could a trade-off between some structural reforms and budgetary discipline. This possible tension between reforms and fiscal discipline was identified by academic economists as a possible drawback of the Stability and Growth Pact since its inception.budgetary discipline, Stability and Growth Pact, Lisbon strategy, fiscal discipline, Deroose, Flores, Turrini

The Integration of Maintenance Decisions and Flow Shop Scheduling

In the conventional production and service scheduling problems, it is assumed that the machines can continuously process the jobs and the information is complete and certain. However, in practice the machines must stop for preventive or corrective maintenance, and the information available to the planners can be both incomplete and uncertain. In this dissertation, the integration of maintenance decisions and production scheduling is studied in a permutation flow shop setting. Several variations of the problem are modeled as (stochastic) mixed-integer programs. In these models, some technical nuances are considered that increase the practicality of the models: having various types of maintenance, combining maintenance activities, and the impact of maintenance on the processing times of the production jobs. The solution methodologies involve studying the solution space of the problems, genetic algorithms, stochastic optimization, multi-objective optimization, and extensive computational experiments. The application of the problems and managerial implications are demonstrated through a case study in the earthmoving operations in construction projects