Rejection Cost Research Articles

A bi-objective model for the single-machine scheduling problem with rejection cost and total tardiness minimization

We study the problem of scheduling jobs on a single machine with a rejection possibility, concurrently minimizing the total tardiness of the scheduled jobs and the total cost of the rejected ones. The model we consider is fully bi-objective, i.e. its aim is to enumerate the Pareto front. We tackle the problem both with and without the presence of hard deadlines. For the case without deadlines, we provide a pseudo-polynomial time algorithm, based on the dynamic program of Steiner and Zhang (2011), thereby proving that the problem is weakly NP-hard. For the case with deadlines, we propose a branch-and-bound algorithm and prove its efficiency by comparing it to an ε-constrained approach on benchmark instances based on those proposed in the literature on similar problems.

The Dating Game

I examine a game-theoretic model of heterosexual courtship. Players decide whether to make romantic advances towards members of the opposite sex, and receive payoffs that depends on the utility from a romantic match, and the costs of rejection and 'unwanted advances /harassment'. The game has three interesting Nash equilibria: the 'MI' equilibrium where males always play the 'initiator' role and females never do, the 'FI' equilibrium where females always play the initiator role and males never do, and a completely mixed equilibrium where both males and females play initiator probabilistically. The former two equilibria are evolutionary stable; the latter is not. I argue that the MI equilibrium is most likely to describe reality. On the other hand, I show that the FI equilibrium is a Pareto improvement upon the other equilibria if females are more 'selective' than males. I present evidence that this is indeed the case. The natural 'policy recommendation' then is a movement from a cultural norm where males predominantly initiate romantic advances, to one where females do. In particular, this would reduce the incidence of unwanted advances/sexual harassment.

Progressively Censored Reliability Sampling Plans Based on Mean Product Lifetime

Reliability sampling plans are often used to determine the compliance of the product with relevant quality standards and customers’ expectations and needs. This paper presents a proposed design of reliability sampling plans when the underlying lifetime model is Weibull based on progressively Type-II censored data in the presence of binomial removals. We employ Bayesian decision theory using the Bayes estimator of the mean product lifetime. When both parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. The Bayes estimators of the mean lifetime are evaluated using the Metropolis-within-Gibbs algorithm, under the assumption of mean squared error loss as well as the linear-exponential (LINEX) loss commonly used in the literature on asymmetric loss. The corresponding probability density functions are estimated using kernel density estimation. A cost function which includes the sampling cost, the cost of the testing time, as well as acceptance and rejection costs is proposed to determine the Bayes risk and the corresponding optimal sampling plan. We illustrate, through simulation studies as well as a real life data set, the application of the proposed method. Sensitivity of the proposed plans is performed.

Cost-effectiveness of hepatitis C-positive donor kidney transplantation for hepatitis C-negative recipients with concomitant direct-acting antiviral therapy.

Pilot studies suggest that transplanting hepatitis C virus (HCV)-positive donor (D+) kidneys into HCV-negative renal transplant (RT) recipients (R-), then treating HCV with direct-acting antivirals (DAA) is clinically feasible. To determine whether this is a cost-effective approach, a decision tree model was developed to analyze costs and effectiveness over a 5-year time frame between 2 choices: RT using a D+/R- strategy compared to continuing dialysis and waiting for a HCV-negative donor (D-/R-). The strategy of accepting a HCV+ organ then treating HCV was slightly more effective and substantially less expensive and resulted in an expected 4.8years of life (YOL) with a cost of ≈$138000 compared to an expected 4.7 YOL with a cost of ≈$329000 for the D-/R- strategy. The D+/R- strategy remained dominant after sensitivity analyses including the difference in RT death probabilities or acute rejection probabilities between using D+ vs D- kidney; time that D-/R- patients waited for RT; dialysis death probabilities while waitlisted for RT in the D-/R- strategy; DAA therapy expected cure rate; costs of transplant, immunosuppressives, DAA therapy, dialysis, or acute rejection. The D+/R- strategy followed by treatment with DAA is less costly and slightly more effective compared to the D-/R- strategy.

On the parameterized tractability of single machine scheduling with rejection

In this paper we study a single machine scheduling problem with rejection. In such a scheduling problem, the scheduler can reject to process a job in the shop at a certain cost. Our objective is to minimize the total completion time of the jobs to be processed in the shop, given that the total rejection cost will not exceed a certain predefined threshold. The problem is known to be NP-hard, and to better investigate its hardness our objective is to study whether the problem becomes tractable when some specific natural parameters are of a limited size. The analysis is done by using the theory of parameterized complexity and includes the following parameters: the cardinality of the set of accepted jobs, the number of different processing times, the number of different rejection costs, the maximal processing time, and the maximal rejection cost. We show that the problem is W[1]-hard for the first parameter, while it is fixed-parameterized tractable for all other parameters.

Optimizing buffer size for the retrial queue: two state space collapse results in heavy traffic

We study a single server queueing model with admission control and retrials. In the heavy traffic limit, the main queue and retrial queue lengths jointly converge to a degenerate two-dimensional diffusion process. When this model is considered with holding and rejection costs, formal limits lead to a free boundary curve that determines a threshold on the main queue length as a function of the retrial queue length, above which arrivals must be rejected. However, it is known to be a notoriously difficult problem to characterize this curve. We aim instead at optimizing the threshold on the main queue length independently of the retrial queue length. Our main result shows that in the small and large retrial rate limits, this problem is governed by the Harrison–Taksar free boundary problem, which is a Bellman equation in which the free boundary consists of a single point. We derive the asymptotically optimal buffer size in these two extreme cases, as the scaling parameter and the retrial rate approach their limits.

Parallel-machine rescheduling with job unavailability and rejection

We study the scheduling problem where a set of jobs has already been scheduled for processing on identical parallel machines to minimize the total completion time under the assumption that all the jobs are available at time zero. However, before processing begins, some jobs are delayed and become unavailable at time zero, so all the jobs need to be rescheduled with a view to not causing excessive schedule disruption with respect to the original schedule. To reduce the negative impact of job unavailability and achieve an acceptable service level, one option in rescheduling the jobs is to reject a subset of the jobs at a cost (the rejection cost). Three criteria are involved: the total completion time of the accepted jobs in the adjusted schedule, the degree of disruption measured by the maximum completion time disruption to any accepted job between the original and adjusted schedules, and the total rejection cost. The overall objective is to minimize the former criterion, while keeping the objective values of the latter two criteria to no greater than the given limits. We present two exact methods to solve the problem: (i) A dynamic programming based approach, establishing that the problem is NP-hard in the ordinary sense when the number of machines is fixed. (ii) An enhanced branch-and-price method that includes several features such as execution of the differential evolution algorithm for finding good initial feasible solutions and solving the pricing sub-problem, inclusion of reduced cost fixing during the inner iterations of the algorithm, and use of a heuristic procedure for constructing a good integer feasible solution. We perform extensive computational experiments to assess the efficiency of the proposed algorithms. The computational results demonstrate that the incorporated enhancements greatly improve the performance of the algorithm.

Heterogenic transplantation of bone marrow-derived rhesus macaque mesenchymal stem cells ameliorates liver fibrosis induced by carbon tetrachloride in mouse.

Liver fibrosis is a disease that causes high morbidity and has become a major health problem. Liver fibrosis can lead to the end stage of liver diseases (livercirrhosisand hepatocellularcarcinoma). Currently, liver transplantation is the only effective treatment for end-stage liver disease. However, the shortage of organ donors, high cost of medical surgery, immunological rejection and transplantation complications severely hamper liver transplantation therapy. Mesenchymal stem cells (MSCs) have been regarded as promising cells for clinical applications in stem cell therapy in the treatment of liver diseases due to their unique multipotent differentiation capacity, immunoregulation and paracrine effects. Although liver fibrosis improvements by MSC transplantation in preclinical experiments as well as clinical trials have been reported, the in vivo fate of MSCs after transportation and their therapeutic mechanisms remain unclear. In this present study, we isolated MSCs from the bone marrow of rhesus macaques. The cells exhibited typical MSC markers and could differentiate into chondrocytes, osteocytes, and adipocytes, which were not affected by labeling with enhanced green fluorescent protein (EGFP). The harvested MSCs respond to interferon-γ stimulation and have the ability to inhibit lymphocyte proliferation in vitro. EGFP-labeled MSCs (1 × 106 cells) were transplanted into mice with carbon tetrachloride-induced liver fibrosis via tail vein injection. The ability of the heterogenic MSC infusion to ameliorate liver fibrosis in mice was evaluated by a blood plasma chemistry index, pathological examination and liver fibrosis-associated gene expression. Additionally, a small number of MSCs that homed and engrafted in the mouse liver tissues were evaluated by immunofluorescence analysis. Our results showed that the transplantation of heterogenic MSCs derived from monkey bone marrow can be used to treat liver fibrosis in the mouse model and that the paracrine effects of MSCs may play an important role in the improvement of liver fibrosis.

Admission control strategies for tandem Markovian loss systems

Motivated by communication networks, we study an admission control problem for a Markovian loss system comprised of two finite capacity service stations in tandem. Customers arrive to station 1 according to a Poisson process, and a gatekeeper, who has complete knowledge of the number of customers at both stations, decides whether to accept or reject each arriving customer. If a customer is rejected, a rejection cost is incurred. If an admitted customer finds that station 2 is full at the time of his service completion at station 1, he leaves the system and a loss cost is incurred. The goal is to find easy-to-implement policies that minimize long-run average cost per unit time. We formulate two intuitive, extremal policies and provide analytical results on their performances. We also present necessary and/or sufficient conditions under which each of these policies is optimal. Next, we show that for some states of the system it is always optimal to admit new arrivals. We also fully characterize the optimal policy when the capacity of each station is two and discuss some characteristics of optimal policies in general. Finally, we design heuristic admission control policies using these insights. Numerical experiments indicate that these heuristic policies yield near-optimal long-run average cost performance.

Models and algorithms for energy-efficient scheduling with immediate start of jobs

We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(nlog n) time in the single-machine case and in O(n^{2}m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution.

An approach to optimizing abstaining area for small sample data classification

Given a classification task, an approach to improve accuracy relies on the use of abstaining classifiers. These classifiers are trained to reject observations for which predicted values are not reliable enough: these rejected observations belong to an abstaining area in the feature space. Two equivalent methods exist to theoretically compute the optimal abstaining area for a given classification problem. The first one is based on the posterior probability computed by the model and the other is based on the derivative of the ROC function of the model. Although the second method has proved to give the best results, in small-sample settings such as the one found in omics data, the estimation of posterior probabilities and derivative of ROC curve are both lacking of precision leading to far from optimal abstaining areas. As a consequence none of the two methods bring the expected improvements in accuracy. We propose five alternative algorithms to compute the abstaining area adapted to small-sample problems. The idea of these algorithms is to compute an accurate and robust estimation of the ROC curve and its derivatives. These estimation are mainly based on the assumption that the distribution of the output of the classifier for each class is normal or mixture of normal distributions. These distributions are estimated by a kernel density estimator or Bayesian semiparametric estimator. Another method works on the approximation of the convex hull of the ROC curve. Once the derivative of the ROC curve are estimated, the optimal abstaining area can be directly computed. The performance of our algorithms are directly related to their capacity to compute an accurate estimation of the ROC curve. A sensitivity analysis of our methods to the dataset size and rejection cost has been done on a set of experiments. We show that our methods improve the performances of the abstaining classifiers on several real datasets and for different learning algorithms.

Multi-objective ACO algorithms to minimise the makespan and the total rejection cost on BPMs with arbitrary job weights

ABSTRACTIn this paper, we investigate the batch-scheduling problem with rejection on parallel machines with non-identical job sizes and arbitrary job-rejected weights. If a job is rejected, the corresponding penalty has to be paid. Our objective is to minimise the makespan of the processed jobs and the total rejection cost of the rejected jobs. Based on the selected multi-objective optimisation approaches, two problems, P1 and P2, are considered. In P1, the two objectives are linearly combined into one single objective. In P2, the two objectives are simultaneously minimised and the Pareto non-dominated solution set is to be found. Based on the ant colony optimisation (ACO), two algorithms, called LACO and PACO, are proposed to address the two problems, respectively. Two different objective-oriented pheromone matrices and heuristic information are designed. Additionally, a local optimisation algorithm is adopted to improve the solution quality. Finally, simulated experiments are conducted, and the comparative results verify the effectiveness and efficiency of the proposed algorithms, especially on large-scale instances.

Integrated production and maintenance planning for parallel machine system considering cost of rejection

Production scheduling and maintenance planning have interdependencies but been often considered and optimized independently in practice and in the literature. Furthermore, product quality has direct relationship with maintenance planning. This paper proposes an integrated approach for production scheduling and maintenance planning for parallel machine system considering the effect of cost of rejection. The approach aims to determine optimal production schedule and maintenance plan such that overall operations cost is minimized. A simulation-based optimization approach is used to solve the problem. A numerical investigation is performed to illustrate the approach. The integrated approach shows between 0.6 and 35.8% improvement in term of overall operations cost over independent approach for various scenarios. The results indicate that simultaneous consideration of production scheduling and maintenance planning results into better system performance.

Reject option to reduce false prediction rates for EEG-motor imagery based BCI.

The Filter Bank Common Spatial Pattern (FBCSP) algorithm had been shown to be effective in performing multi-class Electroencephalogram (EEG) decoding of motor imagery using the one-versus-the-rest approach on the BCI Competition IV Dataset IIa. In this paper, we propose a method to reduce false detection rates of decoding through a rejection option based on the difference in the posterior probability computed by the Naïve Bayesian classifier. We applied the proposed approach on the BCI Competition IV Dataset IIa, and the results showed a decrease in the false detection rates from 34.6 % to 6.9%, while average decoded trials decreased from 93.2% to 34.2% using a rejection threshold between 0.1 and 0.9. We subsequently formulated a method to optimize the rejection threshold based on the maximum F0.5 score. The optimal rejection threshold yielded an average decrease in false detection rate to 19.1% with an average of 67.5% of trials decoded. The results showed the feasibility of decreasing false detection rates at a cost of rejection. Nevertheless, the results suggest that the use of reject option (RO) may be used as a training feedback system to train subjects' overt and covert EEG control strategies for better (dexterity and safety) continuous control of external device.

Capacity planning framework for mobile network operator cloud using analytical performance model

SummaryA mobile network operator cloud (MNOC), solely or with the help of public clouds, provides the computational resources in the form of virtual machines on physical machines (PMs) to handle heavy tasks, which are offloaded by the subscribers. Definitely, cost is a constant source of worry for an MNOC. In fact, although a large number of used PMs of the MNOC and public clouds decreases the penalty cost of request rejection, other associated costs, such as infrastructure, power consumption, cooling, and virtual machine instances of public clouds, are imposed on the MNOC. Therefore, to minimize the overall cost, finding the optimal number of required PMs in all participant clouds, including the MNOC and public clouds, is recognized as an important issue. To deal with this issue, in the present paper, using analytical performance model of a MNOC, a capacity planning framework is proposed. Specifically, this framework solves a cost optimization problem using a simulated annealing algorithm. Numerical results demonstrate the ability of the proposed framework to identify the optimal solution within an acceptable duration of the time.

Determining optimal sizes of bounded batches with rejection via quadratic min-cost flow

In this article, we consider a single machine scheduling problem, in which identical jobs are split into batches of bounded sizes. For each batch, it is allowed to produce less jobs than a given upper bound, that is, some jobs in a batch can be rejected, in which case a penalty is paid for each rejected job. The objective function is the sum of several components, including the sum of the completion times, total delivery cost, and total rejection cost. We reduce this problem to a min-cost flow problem with a convex quadratic function and adapt Tamir's algorithm for its solution.© 2017 Wiley Periodicals, Inc. Naval Research Logistics, 2017

Single machine scheduling problems with generalised due-dates and job-rejection

We study single machine scheduling problems. Generalised due dates are assumed, i.e. job due dates are specified according to the positions of the jobs in the sequence, rather than their identity. Thus, assuming that due dates are numbered in a non-decreasing order, the jth due date refers to the job assigned to the jth position. In addition, we allow the option of job rejection, i.e. not all jobs must be processed. In this case, the scheduler is penalised for each rejected job, and the total rejection cost becomes part of the objective function. Two objective functions are considered: maximum tardiness plus rejection cost, and total tardiness plus rejection cost. Both problems are proved to be NP-hard. Pseudo-polynomial dynamic programmes and efficient heuristics are introduced and tested numerically.

Scheduling parallel machines with inclusive processing set restrictions and job rejection

In this article, we study a parallel machine scheduling problem with inclusive processing set restrictions and the option of job rejection. In the problem, each job is compatible to a subset of machines, and machines are linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process (but not conversely). To achieve a tight production due date, some of the jobs might be rejected at certain penalty. We first study the problem of minimizing the makespan of all accepted jobs plus the total penalty cost of all rejected jobs, where we develop a ( 5 3 + e ) -approximation algorithm with a time complexity of O ( n 2 / e 2 ) . We then study two bicriteria variants of the problem. For the variant problem of minimizing the makespan subject to a given bound on the total rejection cost, we develop a ( 5 3 + e ) -approximation algorithm with a time complexity of O ( n m e 2 · log P ) . For the variant problem of maximizing the total rejection cost of the accepted jobs subject to a given bound on the makespan, we present a 0.5-approximation algorithm with a time complexity of O ( n log n ) .© 2017 Wiley Periodicals, Inc. Naval Research Logistics, 2017

A cost-sensitive rotation forest algorithm for gene expression data classification

Existing works show that the rotation forest algorithm has competitive performance in terms of classification accuracy for gene expression data. However, most existing works only focus on the classification accuracy and neglect the classification costs. In this study, we propose a cost-sensitive rotation forest algorithm for gene expression data classification. Three classification costs, namely misclassification cost, test cost and rejection cost, are embedded into the rotation forest algorithm. This extension of the rotation forest algorithm is named as cost-sensitive rotation forest algorithm. Experimental results show that the cost-sensitive rotation forest algorithms effectively reduce the classification cost and make the classification result more reliable.

Improved Algorithms for Single-Machine Serial-Batch Scheduling With Rejection to Minimize Total Completion Time and Total Rejection Cost

Recently, Shabtay considered a scheduling problem on a single serial-batching machine with rejection to minimize the dual criteria of total completion time and total rejection cost, where the number of jobs to be included in each batch is not restricted. He studied four variants of the problem: the first is to minimize the sum of the two criteria; the second and third are to minimize one criterion, subject to the other criterion not exceeding a given value; and the last is to find the Pareto-optimal solutions for the bicriterion problem. Shabtay provided an ${O}$ ( $\textit{n}^{\mathbf {5}}$ ) algorithm for the first variant and an ${O}$ ( ${n} ^{\mathbf {6}}$/$\boldsymbol {\varepsilon }^{\mathbf {2}}$ ) fully polynomial-time approximation scheme (FPTAS) for the fourth variant. In this paper, we provide an alternative ${O}$ ( ${n} ^{\mathbf {4}}$ ) algorithm to solve the first variant and an ${O}$ ( ${n} ^{\mathbf {5}}$/$\boldsymbol {\varepsilon }$ ) FPTAS for the fourth variant, which are more efficient than those developed by Shabtay from a theoretical perspective. However, when the size of each batch is bounded by a given number ${b}~\boldsymbol {>}1$ , the corresponding time complexities of our algorithms for the first and fourth variants reduce to ${O}$ ( bn $^{\mathbf {3}}$ ) and ${O}$ ( bn $^{\mathbf {4}}$/$\boldsymbol {\varepsilon }$ ), respectively.