A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

Two-Dimensional Loading in Vehicle Routing Problem With Release and Due Dates

In this paper, we study a two-dimensional vehicle loading and routing problem, in which customer orders with deadlines become available for dispatch as per their release dates. The objective is to minimize the sum of transportation, inventory, and tardiness costs, while respecting various loading and routing constraints. This scenario allows us to study various tradeoffs that tend to arise due to temporal order aggregation across release dates. We thereby propose an integrated mathematical formulation to simultaneously model both the routing and loading requirements of the problem at hand. Specifically, as the problem is NP-hard, we propose a scatter search based heuristic approach to solve large-size instances. Further, its performance is enhanced using problem-specific procedures and strategic oscillation approaches. Additionally, the numerical experiments illustrate the influence of cost structures on both the optimal loading configurations along with the optimal routes. Importantly, our experiments also suggest that the proposed scatter search method can produce good quality solutions in less time.

Applying to residency: survey of neurosurgical residency applicants on virtual recruitment during COVID-19

OBJECTIVE The COVID-19 pandemic caused a significant disruption to residency recruitment, including a sudden, comprehensive transition to virtual interviews. The authors sought to characterize applicant experiences and perceptions concerning the change in the application, interview, and match process for neurological surgery residency during the 2020–2021 recruitment cycle. METHODS A national survey of neurosurgical residency applicants from the 2020–2021 application cycle was performed. This survey was developed in cooperation with the Society of Neurological Surgeons (SNS) and the American Association of Neurological Surgeons Young Neurosurgeons Committee (YNC) and sent to all applicants (n = 280) who included academic video submissions to the SNS repository as part of their application package. These 280 applicants accounted for 69.6% of the total 402 neurosurgical applicants this year. RESULTS Nearly half of the applicants responded to the survey (44.3%, 124 of 280). Applicants favored additional reform of the interview scheduling process, including a centralized scheduling method, a set of standardized release dates for interview invitations, and interview caps for applicants. Less than 8% of students desired a virtual-only platform in the future, though the majority of applicants supported incorporating virtual interviews as part of the process to contain applicant costs and combining them with traditional in-person interview opportunities. Program culture and fit, as well as clinical and research opportunities in subspecialty areas, were the most important factors applicants used to rank programs. However, subjective program "fit" was deemed challenging to assess during virtual-only interviews. CONCLUSIONS Neurosurgery resident applicants identified standardized interview invitation release dates, centralized interview scheduling methods, caps on the number of interviews available to each candidate, and regulated opportunities for both virtual and in-person recruitment as measures that could significantly improve the applicant experience during and effectiveness of future neurosurgery residency application cycles. Applicants prioritized program culture and "fit" during recruitment, and a majority were open to incorporating virtual elements into future cycles to reduce costs while retaining in-person opportunities to gauge programs and their locations.

SORTING APPROACHES IN THE HEURISTIC BASED ON REMAINING AVAILABLE AND PROCESSING PERIODS TO MINIMIZE TOTAL WEIGHTED TARDINESS IN PROGRESSIVE IDLING-FREE 1-MACHINE PREEMPTIVE SCHEDULING

Background. In preemptive job scheduling, total weighted tardiness minimization is commonly reduced to solving a combinatorial problem, which becomes practically intractable as the number of jobs and the numbers of their processing periods increase. To cope with this challenge, heuristics are used. A heuristic, in which the decisive ratio is the weighted reciprocal of the maximum of a pair of the remaining processing period and remaining available period, is closely the best one. However, the heuristic may produce schedules of a few jobs whose total weighted tardiness is enormously huge compared to the real minimum. Therefore, this heuristic needs further improvements, one of which already exists for jobs without priority weights with a sorting approach where remaining processing periods are minimized. Three other sorting approaches still can outperform it, but such exceptions are quite rare. Objective. The goal is to determine the influence of the four sorting approaches and try to select the best one in the case where jobs have their priority weights. The heuristic will be applied to tight-tardy progressive idling-free 1-machine preemptive scheduling, where the release dates are given in ascending order starting from 1 to the number of jobs, and the due dates are tightly set after the release dates. Methods. To achieve the said goal, a computational study is carried out with applying each of the four heuristic approaches to minimize total weighted tardiness. For this, two series of 4151500 scheduling problems are generated. In the solution of a scheduling problem, a sorting approach can “win” solely or “win” in a group of approaches, producing the heuristically minimal total weighted tardiness. In each series, the distributions of sole-and-group “wins” are ascertained. Results. The sole “wins” and non-whole-group “wins” are rare: the four sorting approaches produce schedules with the same total weighted tardiness in over 98.39 % of scheduling problems. Although the influence of these approaches is different, it is therefore not really significant. Each of the sorting approaches has heavy disadvantages leading sometimes to gigantic inaccuracies, although they occur rarely. When the inaccuracy occurs to be more than 30 %, this implies that 3 to 9 jobs are scheduled. Conclusions. Unlike the case when jobs do not have their priority weights, it is impossible to select the best sorting approach for the case with job priority weights. Instead, a hyper-heuristic comprising the sorting approaches (i. e., the whole group, where each sorting is applied) may be constructed. If a parallelization can be used to process two or even four sorting routines simultaneously, the computation time will not be significantly affected.