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.

Influence of audibility and distortion on the recognition of reverberant speech for children and adults with hearing aid amplification

Background: Adults and children with sensorineural hearing loss (SNHL) have trouble understanding speech in rooms with reverberation when using hearing aid amplification. While the use of amplitude compression signal processing in hearing aids may contribute to this difficulty, there is conflicting evidence on the effects of amplitude compression settings on speech recognition. Less clear is the effect of a fast release time for adults and children with SNHL when using compression ratios derived from a prescriptive procedure. Purpose: To determine whether release time impacts speech recognition in reverberation for children and adults with SNHL and to determine if these effects of release time and reverberation can be predicted using indices of audibility or temporal and spectral distortion. Research Design: A quasi-experimental cohort study. Participants used a hearing aid simulator set to the Desired Sensation Level algorithm m[i/o] for three different amplitude compression release times. Reverberation was simulated using three different reverberation times. Participants: Participants were 20 children and 16 adults with SNHL. Data Collection and Analyses: Participants were seated in a sound-attenuating booth and then nonsense syllable recognition was measured. Predictions of speech recognition were made using indices of audibility, temporal distortion, and spectral distortion and the effects of release time and reverberation were analyzed using linear mixed models. Results: While nonsense syllable recognition decreased in reverberation; release time did not significantly affect nonsense syllable recognition. Participants with lower audibility were more susceptible to the negative effect of reverberation on nonsense syllable recognition. Conclusions: We have extended previous work on the effects of reverberation on aided speech recognition to children with SNHL. Variations in release time did not impact the understanding of speech. An index of audibility best predicted nonsense syllable recognition in reverberation and, clinically, these results suggest that patients with less audibility are more susceptible to nonsense syllable recognition in reverberation.

A Scheduling and Rescheduling Decision Support System for Apparel Manufacturing

The manufacturing environment for apparel is subject to a variety of constraints, stochasticity, and unforeseen events. In order to create an accurate scheduling-system for this environment, these complexities must be considered. This article presents the development and the application of a scheduling and rescheduling decision support system for an apparel manufacturer. Furthermore, the results of applying the proposed system are presented and discussed. The scheduling and rescheduling decision support system presented in this article takes advantage of a variable neighborhood search and Monte Carlo simulation in order to minimize tardiness in the presence of different release times, sequence-based setup times, blocking, and resource constraints. The results show that the quality of the schedules generated by the proposed scheduling and rescheduling decision support system is superior to the current firm’s scheduling practice, which is based on an earliest due date heuristic. Moreover, the percentage of the realized schedule and overall equipment effectiveness were improved.

Scheduling Multiprocessor Tasks with Equal Processing Times as a Mixed Graph Coloring Problem

This article extends the scheduling problem with dedicated processors, unit-time tasks, and minimizing maximal lateness for integer due dates to the scheduling problem, where along with precedence constraints given on the set of the multiprocessor tasks, a subset of tasks must be processed simultaneously. Contrary to a classical shop-scheduling problem, several processors must fulfill a multiprocessor task. Furthermore, two types of the precedence constraints may be given on the task set . We prove that the extended scheduling problem with integer release times of the jobs to minimize schedule length may be solved as an optimal mixed graph coloring problem that consists of the assignment of a minimal number of colors (positive integers) to the vertices of the mixed graph such that, if two vertices and are joined by the edge , their colors have to be different. Further, if two vertices and are joined by the arc , the color of vertex has to be no greater than the color of vertex . We prove two theorems, which imply that most analytical results proved so far for optimal colorings of the mixed graphs , have analogous results, which are valid for the extended scheduling problems to minimize the schedule length or maximal lateness, and vice versa.

Mathematical Modeling of Water-Soluble Astaxanthin Release from Binary Polysaccharide/Gelatin Blend Matrices

Water-soluble AstaSana astaxanthin (AST) was loaded into 75/25 blend films made of polysaccharides (carboxymethyl cellulose (CMC), gum Arabic (GAR), starch sodium octenyl succinate (OSA), water-soluble soy polysaccharides (WSSP)) and gelatin (GEL) at levels of 0.25, 0.5, and 1%, respectively. Due to the presence of starch granules in the AST formulation, the supplemented films exhibited increased surface roughness as compared to the AST-free films. Apart from the CMC/GEL carrier, the migration of AST to water (25 °C, 32 h) was incomplete. Excluding the CMC-based carrier, the gradual rise in the AST concentration decreased the release rate. The Hopfenberg with time lag model provided the best fit for all release series data. Based on the quarter-release times (t25%), the 0.25% AST-supplemented OSA/GEL film (t25% = 13.34 h) ensured a 1.9, 2.2, and 148.2 slower release compared to the GAR-, WSSP- and CMC-based carriers, respectively. According to the Korsmeyer–Peppas model, the CMC-based films offered a quasi-Fickian release of AST (n < 0.5) with the burst effect (t100% = 0.5–1 h). In general, the release of AST from the other films was multi-mechanistic (n > 0.5), i.e., controlled at least by Fickian diffusion and the polymer relaxation (erosion) mechanism. The 1% AST-added WSSP/GEL system provided the most linear release profile.

Scheduling with gaps: new models and algorithms

We consider scheduling problems for unit jobs with release times, where the number or size of the gaps in the schedule is taken into consideration, either in the objective function or as a constraint. Except for several papers on minimum-energy scheduling, there is no work in the scheduling literature that uses performance metrics depending on the gap structure of a schedule. One of our objectives is to initiate the study of such scheduling problems. We focus on the model with unit-length jobs. First we examine scheduling problems with deadlines, where we consider two variants of minimum-gap scheduling: maximizing throughput with a budget for the number of gaps and minimizing the number of gaps with a throughput requirement. We then turn to other objective functions. For example, in some scenarios gaps in a schedule may be actually desirable, leading to the problem of maximizing the number of gaps. A related problem involves minimizing the maximum gap size. The second part of the paper examines the model without deadlines, where we focus on the tradeoff between the number of gaps and the total or maximum flow time. For all these problems we provide polynomial time algorithms, with running times ranging from $$O(n\log n)$$ O ( n log n ) for some problems to $$O(n^7)$$ O ( n 7 ) for other. The solutions involve a spectrum of algorithmic techniques, including different dynamic programming formulations, speed-up techniques based on searching Monge arrays, searching $$X+Y$$ X + Y matrices, or implicit binary search. Throughout the paper, we also draw a connection between gap scheduling problems and their continuous analogues, namely hitting set problems for intervals of real numbers. As it turns out, for some problems the continuous variants provide insights leading to efficient algorithms for the corresponding discrete versions, while for other problems completely new techniques are needed to solve the discrete version.

Corrigendum: Greed Works—Online Algorithms for Unrelated Machine Stochastic Scheduling

This corrigendum fixes an incorrect claim in the paper Gupta et al. [Gupta V, Moseley B, Uetz M, Xie Q (2020) Greed works—online algorithms for unrelated machine stochastic scheduling. Math. Oper. Res. 45(2):497–516.], which led us to claim a performance guarantee of 6 for a greedy algorithm for deterministic online scheduling with release times on unrelated machines. The result is based on an upper bound on the increase of the objective function value when adding an additional job [Formula: see text] to a machine [Formula: see text] (Gupta et al., lemma 6). It was pointed out by Sven Jäger from Technische Universität Berlin that this upper bound may fail to hold. We here present a modified greedy algorithm and analysis, which leads to a performance guarantee of 7.216 instead. Correspondingly, also the claimed performance guarantee of [Formula: see text] in theorem 4 of Gupta et al. for the stochastic online problem has to be corrected. We obtain a performance bound [Formula: see text].

Experimental Study on Fire Characteristics of Lithium-ion Battery using Cone Calorimeter

The lithium-ion battery is the most popular type of secondary battery because of its high energy density. It has been widely used in mobile power and energy storage systems. However, several accidents can occur in systems using lithium-ion batteries, and most of the reported losses have resulted from battery fires and explosions. In this study, a cone calorimeter experiment was performed to investigate the fire characteristics of lithium-ion batteries and assess their heat release rate (HRR), which is the most representative property for fire events. Fires involving cylindrical standard batteries consist of two combustion stages. The first burning stage is due to the package material and intercalated lithium of the battery, and the second stage is attributed to the thermal runaway reactions of the electrolyte. The second combustion stage has a greater peak HRR than the first stage and is accompanied by a violent explosion. In a comparison of the HRRs with the oxygen consumption rate, the HRRs measured on the basis of the mass loss rate show higher maximum values and extremely narrow heat release times.