Optimal Allocations in the Construction of k-Out-of-n Reliability Systems

2021 ◽

pp. 1748006X2110308

Author(s):

Hong Sun ◽

Yiying Zhang ◽

Peng Zhao

Keyword(s):

Optimal Allocation ◽

Stochastic Ordering ◽

Industrial Engineering ◽

Simulation Studies ◽

Engineering Applications ◽

Random Weights ◽

Optimal Allocations ◽

Total Capacity ◽

Arrangement Increasing ◽

Reliability Systems

In industrial engineering applications, randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems can model many reliability systems whose components may contribute unequally and randomly to the systems’ performance. This paper investigates optimal allocations of hot standbys for [Formula: see text]-out-of-[Formula: see text]: G systems with random weights. First, optimal allocation policies are presented by maximizing the total capacity according to the usual stochastic ordering and the expectation ordering when the system is constituted by independent and heterogeneous components accompanied with independent random weights. Second, we investigate hot standbys allocation for randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems with right [left] tail weakly stochastic arrangement increasing random weights in the sense of the usual stochastic ordering [increasing concave ordering]. Simulation studies are provided to illustrate our theoretical findings as well. These established results can provide useful guidance for system designers on how to introduce hot standbys in randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems in order to enhance their total capacities.

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OPTIMAL ANALYSIS OF FARM AGRICULTURAL MACHINERY EQUIPMENT BASED ON MATHEMATICAL MODELLING

INMATEH Agricultural Engineering ◽

10.35633/inmateh-62-35 ◽

2020 ◽

pp. 333-340

Keyword(s):

Mathematical Modelling ◽

Production Efficiency ◽

Programming Model ◽

Constraint Equation ◽

Economic Benefits ◽

Agricultural Machinery ◽

Optimization Analysis ◽

Agricultural Modernization ◽

Actual Equipment ◽

Optimal Allocations

With the development of science and technology, the degree of agricultural mechanization is getting higher and higher. Agricultural machinery is an important support for the development of agricultural modernization. Optimizing the allocation of agricultural machinery is conducive to improving agricultural production efficiency and economic benefits. In this paper, mathematical modelling method is mainly used in the analysis and optimization of agricultural machinery configuration. By determining the objective function and constraint equation, combined with the actual situation of Xinjiang Production and Construction Corps, the linear programming model and workload model of agricultural machinery and equipment optimization are established. Finally, the actual number of agricultural machinery and equipment and the number of optimal allocations of Xinjiang Production and Construction Corps farm were compared. The effectiveness of the optimization model is verified by comparing the optimized agricultural machinery equipment with the actual equipment. The results show that the optimized equipment model has good optimization effect. On the basis of reducing the number of agricultural machinery and equipment, the matching rate of agricultural machinery is improved, and the operation cost of agricultural machinery is effectively reduced. It is hoped that this study can provide certain reference and reference for the optimization analysis of agricultural machinery and equipment based on mathematical modelling.

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Asymptotic Inference for Optimal Rerandomization Designs

Open Statistics ◽

10.1515/stat-2020-0102 ◽

2021 ◽

Vol 1 (1) ◽

pp. 49-58

Author(s):

Mårten Schultzberg ◽

Per Johansson

Keyword(s):

Experimental Design ◽

Normal Distribution ◽

Mahalanobis Distance ◽

Design Strategy ◽

Sampling Distribution ◽

Optimal Designs ◽

Asymptotic Inference ◽

Optimal Allocations ◽

Asymptotic Sampling

AbstractRecently a computational-based experimental design strategy called rerandomization has been proposed as an alternative or complement to traditional blocked designs. The idea of rerandomization is to remove, from consideration, those allocations with large imbalances in observed covariates according to a balance criterion, and then randomize within the set of acceptable allocations. Based on the Mahalanobis distance criterion for balancing the covariates, we show that asymptotic inference to the population, from which the units in the sample are randomly drawn, is possible using only the set of best, or ‘optimal’, allocations. Finally, we show that for the optimal and near optimal designs, the quite complex asymptotic sampling distribution derived by Li et al. (2018), is well approximated by a normal distribution.

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Optimal Scheduling for Laboratory Automation of Life Science Experiments with Time Constraints

SLAS TECHNOLOGY Translating Life Sciences Innovation ◽

10.1177/24726303211021790 ◽

2021 ◽

pp. 247263032110217

Author(s):

Takeshi D. Itoh ◽

Takaaki Horinouchi ◽

Hiroki Uchida ◽

Koichi Takahashi ◽

Haruka Ozaki

Keyword(s):

Scheduling Algorithms ◽

Mixed Integer ◽

Time Constraints ◽

Live Cells ◽

Laboratory Automation ◽

Simulation Based Design ◽

Simulation Based ◽

Optimal Allocations ◽

Scheduling Method ◽

Time Required

In automated laboratories consisting of multiple different types of instruments, scheduling algorithms are useful for determining the optimal allocations of instruments to minimize the time required to complete experimental procedures. However, previous studies on scheduling algorithms for laboratory automation have not emphasized the time constraints by mutual boundaries (TCMBs) among operations, which is important in procedures involving live cells or unstable biomolecules. Here, we define the “scheduling for laboratory automation in biology” (S-LAB) problem as a scheduling problem for automated laboratories in which operations with TCMBs are performed by multiple different instruments. We formulate an S-LAB problem as a mixed-integer programming (MIP) problem and propose a scheduling method using the branch-and-bound algorithm. Simulations show that our method can find the optimal schedules of S-LAB problems that minimize overall execution time while satisfying the TCMBs. Furthermore, we propose the use of our scheduling method for the simulation-based design of job definitions and laboratory configurations.

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The human factor in operation and maintenance of complex high-reliability systems

10.2514/6.1989-5064 ◽

1989 ◽

Cited By ~ 3

Author(s):

THOMAS RYAN

Keyword(s):

Human Factor ◽

High Reliability ◽

Operation And Maintenance ◽

Reliability Systems

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On Optimal Allocations of Target-Date Funds

The Journal of Retirement ◽

10.3905/jor.2021.1.094 ◽

2021 ◽

pp. jor.2021.1.094

Author(s):

Radu Gabudean ◽

Francisco Gomes ◽

Alexander Michaelides ◽

Yuxin Zhang

Keyword(s):

Target Date ◽

Optimal Allocations ◽

Target Date Funds

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A concept of inner prederivative for set-valued mappings and its applications

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2017024 ◽

2018 ◽

Vol 24 (3) ◽

pp. 1059-1074

Author(s):

Michel H. Geoffroy ◽

Yvesner Marcelin

Keyword(s):

Optimality Conditions ◽

Necessary Optimality Conditions ◽

Welfare Economics ◽

Inverse Mapping ◽

First Order ◽

Inverse Mapping Theorem ◽

Homogeneous Set ◽

Optimal Allocations ◽

Variational Perturbations ◽

Set Valued Mappings

We introduce a class of positively homogeneous set-valued mappings, called inner prederivatives, serving as first order approximants to set-valued mappings. We prove an inverse mapping theorem involving such prederivatives and study their stability with respect to variational perturbations. Then, taking advantage of their properties we establish necessary optimality conditions for the existence of several kind of minimizers in set-valued optimization. As an application of these last results, we consider the problem of finding optimal allocations in welfare economics. Finally, to emphasize the interest of our approach, we compare the notion of inner prederivative to the related concepts of set-valued differentiation commonly used in the literature.

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