Linear Deterioration Research Articles

Single machine scheduling with decreasing linear deterioration under precedence constraints

This paper deals with single-machine scheduling problems with decreasing linear deterioration, i.e., jobs whose processing times are a decreasing function of their starting times. In addition, the jobs are related by parallel chains and a series–parallel graph precedence constraints, respectively. It is shown that for the problems of minimization of the makespan, polynomial algorithms exist.

Optimal run lengths in deteriorating production processes in random fuzzy environments

This paper presents a random fuzzy economic manufacturing quantity (EMQ) model in a deteriorating process. It is assumed that the setup cost and the average holding cost are characterized as fuzzy variables and the elapsed time until shift is a random fuzzy variable. As a function of these parameters, the average total cost is also a random fuzzy variable, and the unimodality of its expected value is studied. To obtain the optimal run length and the minimum average cost, simultaneous perturbation stochastic approximation (SPSA) algorithm based on random fuzzy simulation is provided. Random fuzzy EMQ models with fuzzy deterioration, fuzzy linear deterioration and fuzzy exponential deterioration are presented, respectively. These models can be solved by the proposed algorithm. Numerical examples are presented in the end.

An Optimal Inventory Policy for Items having Linear Demand and Variable Deterioration Rate with Trade Credit

Problem statement: Demand considered in most of the classical inventory models is constant, while in most of the practical cases the demand changes with time. In this study model has been framed to study the items whose demand changes with time and deterioration rate increases with time. The effect of permissible delay is also incorporated in this study. The objective of this research is to develop an inventory model for perishable items whose perish-ability rate as well as demand increases with time Approach: Firstly, problem is framed in the form of linear differential equation model and this model had been solved using general solution techniques of linear differential equations. The solution obtained gives the inventory level at any particular time of the cycle period. With the help of this inventory level, total as well as average inventory cost has been obtained. Results: This study developed a model to determine an optimal order quantity by using calculus technique of maxima and minima. Thus it helps retailer to decide its optimal ordering quantity under the constraints of variable deterioration rate and linear pattern of demand. Conclusion: Numerical solution of the suggested model had also been proposed, the above model can be converted into constant demand model, or for items having no deterioration. This study can further be extended for items having some other demand pattern, also time value of money and inflation can be incorporated in this model to make it more realistic and present business environment suited.

Parallel machine scheduling problem to minimize the earliness/tardiness costs with learning effect and deteriorating jobs

The focus of this work is to analyze parallel machine earliness/tardiness (ET) scheduling problem with simultaneous effects of learning and linear deterioration, sequence-dependent setups, and a common due-date for all jobs. By the effects of learning and linear deterioration, we mean that the processing time of a job is defined by an increasing function of its starting time and a decreasing function of the position in the sequence. We develop a mixed integer programming formulation for the problem and show that the optimal sequence is V-shaped: all jobs scheduled before the shortest jobs and all jobs scheduled after the shortest job are in a non-increasing and non-decreasing order of processing times, respectively. The developed model allows sequence-dependent setups and sequence-dependent early/tardy penalties. The illustrative example with 11 jobs for 2 machines and 3 machines shows that the model can easily provide the optimal solution, which is V-shaped, for problem.

Scheduling deteriorating jobs to minimize the makespan on a single machine

Machine scheduling problems with deteriorating jobs have received increasing attention in recent years, mostly focusing on the linear deterioration models. However, if certain maintenance procedures fail to be completed prior to a prespecified deadline, jobs will require extra time for successful accomplishment in some situations. Therefore, this paper addresses a single-machine problem where the objective is to minimize the makespan under the piecewise linear deterioration model. A branch-and-bound algorithm and two heuristic algorithms are provided to search for the optimal solution and near-optimal solutions, respectively. Computational results are also presented to evaluate the performance of the proposed algorithms.

Mechanistic–Empirical Modeling in Network-Level Pavement Management

Researchers and practitioners have long recognized the advantages of mechanistic modeling. As agencies implement the Guide for Mechanistic–Empirical Design of New and Rehabilitated Pavement Structures [referred to as the Mechanistic–Empirical Pavement Design Guide (MEPDG)] in the local project-level pavement management system (PMS), its potential as a planning tool in network-level analyses remains unrecognized. A unique, large-scale application of MEPDG is presented. The Nebraska Department of Roads uses a decision tree that systematically screens and identifies candidates for entry into a multiyear optimization program. The process uses linear deterioration rates that have been shown to provide an R2 value as low as 14%. In a retroactive 5-year analysis, 86 sections were prescreened by using the existing models. Predictions indicated that 85 of the 86 sections would have been candidates for maintenance in the first 5 years, whereas field data suggested that only 23 should have been targeted. Calibrated MEPDG distress models calculated with local performance indices replaced the existing linear models. When the analysis was repeated with the mechanistic–empirical models, 35 of the 86 sections qualified for entry into the 5-year analysis, a 70% improvement in the accuracy of the forecasted cost. This research fulfills a timely need for the transitioning of network-level PMS toward mechanistic practices. Consideration of fundamental material properties, climatic conditions, and the structural response to traffic loading provides improved accuracy in planning. Furthermore, production variability and prediction uncertainties can be quantified and used as an additional probabilistic decision-making parameter. Detailed results of the implementation of MEPDG in the local network-level PMS are presented.

Monitoring of fetuses with intrauterine growth restriction: longitudinal changes in ductus venosus and aortic isthmus flow

To explore in growth-restricted fetuses the sequence of changes in aortic isthmus and ductus venosus blood flow in relation to other arterial Doppler parameters commonly used to evaluate fetal wellbeing. Umbilical and middle cerebral arteries, ductus venosus and aortic isthmus were explored serially by means of pulsed Doppler in a cohort of singleton small-for-gestational age fetuses requiring delivery before 34 weeks. Longitudinal changes in the last 30 days before delivery were modeled by multilevel analysis. Individual regression lines for each variable were calculated for each fetus and from these the regression lines for the whole group were derived, in order to estimate the mean time point at which each Doppler parameter became abnormal (outside the 5th-95th centile range). A survival analysis was performed during the monitoring period, in which the endpoint was an abnormal Doppler pulsatility index. A total of 162 observations were performed on 46 fetuses (median, 3; range, 2-10). The median gestational age at inclusion was 28.9 (range, 23.6-33.4) weeks and delivery occurred at a median gestational age of 30.5 (range, 25.9-33.9) weeks. Six (13%) cases of perinatal mortality occurred. Umbilical and middle cerebral artery Doppler showed an almost linear deterioration throughout monitoring, becoming abnormal on average 24 days and 20 days before delivery, respectively. Aortic isthmus Doppler became abnormal on average 13 days before delivery, while ductus venosus Doppler did so within the last week before delivery. In preterm growth-restricted fetuses, aortic isthmus blood flow becomes abnormal on average 1 week earlier than does that in the ductus venosus. This could provide a sound basis to better define management protocols aimed to improve intact fetal survival.

Are encapsulated anterior glass-ionomer restoratives better than their hand-mixed equivalents?

Objectives The performance of encapsulated anterior GI restoratives were compared with their hand-mixed equivalents for the range of powder to liquid mixing ratios routinely encountered clinically. The clinically induced variability of powder to liquid mixing variations of an anhydrous GI restorative formulation was also compared with conventional GI restorative formulations that contained a polyalkenoic acidic liquid. Methods Mean compressive fracture strengths, mean elastic moduli and mean total volumetric wear were determined for the encapsulated anterior GI restoratives mechanically mixed in a Capmix™ or Rotomix™ machine and the hand-mixed GI restoratives prepared with powder contents reduced from that recommended by the manufacturer (100%) in 10% increments to 50% for a constant weight of liquid. Multiple comparisons of the group means were made using a one-way analysis of variance (ANOVA) and Tukey's multiple range tests employed at P < 0.05. Results For the encapsulated GI restoratives, the mean compressive fracture strength, mean elastic modulus and in-vitro wear resistance were significantly increased compared with their hand-mixed equivalents prepared with powder contents below that recommended by the manufacturers. The conventional GI restoratives resulted in a linear deterioration ( R 2 > 0.95) of the mean compressive fracture strength and mean elastic modulus with powder content compared with the bi-modal deterioration for the anhydrous GI restorative. Conclusions Encapsulated anterior GI restoratives outperform their hand-mixed equivalents for the range of powder to liquid mixing ratios routinely encountered clinically such that they are advocated for use in clinical practice. Anhydrous GI restorative formulations are more susceptible to clinically induced variability on mixing compared with conventional GI restorative formulations that contained a polyalkenoic acidic liquid.

Single machine group scheduling with general linear deterioration to minimize the makespan

In this paper, we consider a single machine scheduling problem with deteriorating jobs and group technology assumption. By deteriorating jobs and group technology assumption, we mean that the group setup times and job processing times are both increasing functions of their starting times, i.e., group setup times and job processing times are both described by function, which is a general linear function of time. The objective of the scheduling problem is to minimize the makespan. We show that the problem remains solvable in polynomial time when general linear deterioration and group technology are considered simultaneously.

The meaning of quality of life: Narrations by patients with incurable cancer in palliative home care

The objective of this qualitative study was to elucidate the meaning of quality of life as narrated by patients with incurable cancer approaching death in palliative home care in Sweden. To gain a deeper understanding of what quality of life means for dying patients, data were collected from narrative interviews with eight patients in their homes in 2004-2006. Qualitative content analysis was used to interpret the meaning regarding quality of life. Three main themes were found: being in intense suffering, having breathing space in suffering, and being at home. Living with incurable cancer at the end of life was experienced as living in physical distress as the body became incapacitated by unexpected physical complications. This incapacity had consequences on patients' psychological, social, and existential well-being. As the complication phase abated, the patients experienced that they regained hopefulness and had time to reflect on existential issues. Patients were provided affirmative care at home from family caregivers and the palliative home care team. This study shows that it is feasible to perform individual interviews with patients approaching death and elucidate the meaning of patients' quality of life in palliative home care. Patients oscillate between being in intense suffering and having breathing space in this suffering, which somewhat opposes the traditional picture of a continuous linear deterioration. Being cared for at home by family caregivers and health care professionals provided a sense of independency and security. Being at home safeguards patients' entire life situation and increases quality of life.

Parallel-machine scheduling with simple linear deterioration to minimize total completion time

We consider the parallel-machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the total completion time. We give a fully polynomial-time approximation scheme (FPTAS) for the case with m identical machines, where m is fixed. This study solves an open problem that has been posed in the literature for ten years.

Minimizing the makespan with an availability constraint on a single machine under simple linear deterioration

This article considers a single machine scheduling problem with an availability constraint under simple linear deterioration. The non-preemptive case is taken into account as well. The objective is to minimize the makespan in the system. The addressed problem is first described as a 0–1 integer programming model, and is then solved optimally. Subsequently, we prove that the addressed problem belongs to NP-hard. Thus, some heuristic algorithms based on the bin packing concepts are provided for solving the addressed problem. Computational results show that the proposed algorithm H3 performs well. In addition, a good strategy that sets the maintenance to start epoch when half the jobs have been already processed is suggested as well.

A heuristic MBLS algorithm for the two semi-online parallel machine scheduling problems with deterioration jobs

The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processing time are considered. In the first problem, it is assumed that the deterioration rates of jobs are known in an interval, that is, bj ∊ [0, α], where 0 < α ⩽ 1 and bj denotes the linear deterioration rate. In the second problem, it is assumed that the largest deterioration rate of jobs is known in advance, that is, \(b_{\max } = \mathop {\max }\limits_{1 \leqslant j \leqslant n} \{ b_j \} \). For each of the two problems, a heuristic MBLS algorithm is worked out and its worst-case ratio is analyzed. At the same time, the worst-case ratio of the list (LS) algorithm is investigated and it is proved that all the ratios are tight.

Short-Duration, High-Intensity Exercise and Performance of a Sports-Specific Skill: A Preliminary Study

The purpose of this study was to examine the effect of one bout and three intermittent bouts of short-duration, high-intensity running on the performance of a sports-specific psychomotor skill. Participants (N=13) were male soccer players (M age 20.5 yr., SD=2.0) who had been playing semi-professionally for M=2.1 years, SD=1.11 and trained twice a week. They undertook a soccer-passing test in three conditions: following rest, following a 100-m sprint and following 3 x 100-m sprints, with 30-sec. rest intervals between sprints. Passing accuracy showed a significant linear deterioration, while number of passes showed a significant quadratic effect. Low to moderate linear regression correlations were found between posttest heart rate and absolute and variable errors on the test. It was concluded that short-duration, high-intensity exercise has a negative effect on accuracy in a sports-specific task that requires both perceptual judgment and motor control.

An approximation algorithm for parallel machine scheduling with simple linear deterioration

In this paper, a parallel machine scheduling problem was considered, where the processing time of a job is a simple linear function of its starting time. The objective is to minimize makespan. A fully polynomial time approximation scheme for the problem of scheduling n deteriorating jobs on two identical machines was worked out. Furthermore, the result was generalized to the case of a fixed number of machines.

Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach

In this study, we introduce a mixed nonlinear integer programming formulation for parallel machine earliness/tardiness (ET) scheduling with simultaneous effects of learning and linear deterioration, sequence-dependent setups, and a common due-date for all jobs. By the effects of learning and linear deterioration, we propose that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. The developed model allows sequence-dependent setups and sequence-dependent early/tardy penalties. The model can easily provide the optimal solution to problems involving about eleven jobs and two machines.

A note on single-machine makespan scheduling with deteriorating jobs and scheduled maintenance

A single-machine scheduling problem with simple linear deteriorating jobs is considered in this paper. The objective is to minimize the makespan when the machine is not always available. We study the scheduling problem under a deterministic environment; specifically, the availability periods are known in advance and jobs are non-resumable. It is shown that the problem is NP-hard even with a single maintenance period. Thus, the 0–1 integer programming technique is utilized to solve the simple linear deterioration model.

Single machine group scheduling under decreasing linear deterioration

This paper considers single machine scheduling problems with group technology (GT) and deteriorating jobs. A sequence independent setup is required to process a job from a different group and jobs in each group are processed together. We consider the case of jobs whose processing times are a decreasing function of their starting time. The objectives of scheduling problems are to minimize the makespan and the total completion time, respectively. We also provide polynomial time algorithms to solve these problems.

Progression detection in glaucoma can be made more efficient by using a variable interval between successive visual field tests

This study aimed to gain insight into the optimal spacing in time for visual field tests for progression detection in glaucoma. Three perimetric strategies for progression detection were compared by means of simulation experiments in a theoretical cohort. In strategies 1 and 2, visual field testing was performed with fixed-spaced inter-test intervals, using intervals of 3 and 6 months respectively. In strategy 3, the inter-test interval was kept at 1 year as long as the fields appeared unchanged. Then, as soon as progression was suspected, confirmation or falsification were performed promptly. Follow-up fields were compared against a baseline assuming linear deterioration, using various progression criteria. Outcome measures were: (1) specificity, (2) time delay until the diagnosis of definite progression, and (3) number of required tests. Strategies 2 and 3 had a higher specificity than strategy 1. Strategies 1 and 3 detected progression earlier than strategy 2. The number of required visual field tests was lowest for strategy 3. Perimetry in glaucoma can be optimised by postponing the next test under apparently stable field conditions and bringing the next test forward once progression is suspected.

Single machine scheduling with simple linear deterioration to minimize total absolute deviation of completion times

We consider a single machine scheduling problem with simple linear deterioration. Job processing times are assumed to be a simple linear function of a job-dependent growth rate and the job's starting time. We seek an optimal schedule, so as to minimize the total absolute deviation of completion times ( TADC). We prove several interesting properties of an optimal schedule, and introduce two efficient heuristics which are tested against a lower bound. Scope and purpose In most scheduling problems jobs are assumed to have time-independent processing times. In many real life applications, jobs deteriorate at a certain rate while waiting to be processed. We study the effect of job deterioration when addressing a scheduling problem with the non-regular objective function of minimizing the total deviation of completion times. This objective can be regarded as a measure of “fairness” towards customers of the production system.