Power Of 2 Research Articles

Coordinated replenishment policies for a single-supplier multi-retailer cold chain for fresh produce

Purpose The single-supplier multi-retailer cold chain is a widely adopted type of supply chain in the real-world food industry. This paper aims to consider the problem of effectively designing and managing a single-supplier multi-retailer cold chain for fresh produce with deterministic demand to minimize the total cost, which includes cooling, loss of value and carbon emission costs. Design/methodology/approach The global stability index (GSI) method and the non-Arrhenius model are integrated to describe the behavior of food quality degradation. The power-of-two (PoT) policy is adopted in determining the coordinated replenishment policies for the suppliers and retailers, and an appropriate wholesale price structure that can achieve the coordination of the chain is presented. Findings The properties of the cold chain are uncovered, and an appropriate wholesale price scheme that achieves chain coordination with the optimal PoT decision is provided. In the numerical examples, different scenarios are investigated, and it is found that the cold chain parameters influence the optimal decisions in certain ways. Originality/value The PoT policy – an efficient policy to determine the replenishment strategy – has not been adopted in finding the solution of a single-supplier multi-retailer cold chain in the literature. Also, no study has compared the uncoordinated and coordinated cold chain. Moreover, in the existing literature, the wholesale price is usually a constant rather than having a coordinated scheme. This research aims to fill these research gaps.

Q-A2NN: Quantized All-Adder Neural Networks for Onboard Remote Sensing Scene Classification

Performing remote sensing scene classification (RSSC) directly on satellites can alleviate data downlink burdens and reduce latency. Compared to convolutional neural networks (CNNs), the all-adder neural network (A2NN) is a novel basic neural network that is more suitable for onboard RSSC, enabling lower computational overhead by eliminating multiplication operations in convolutional layers. However, the extensive floating-point data and operations in A2NNs still lead to significant storage overhead and power consumption during hardware deployment. In this article, a shared scaling factor-based de-biasing quantization (SSDQ) method tailored for the quantization of A2NNs is proposed to address this issue, including a powers-of-two (POT)-based shared scaling factor quantization scheme and a multi-dimensional de-biasing (MDD) quantization strategy. Specifically, the POT-based shared scaling factor quantization scheme converts the adder filters in A2NNs to quantized adder filters with hardware-friendly integer input activations, weights, and operations. Thus, quantized A2NNs (Q-A2NNs) composed of quantized adder filters have lower computational and memory overheads than A2NNs, increasing their utility in hardware deployment. Although low-bit-width Q-A2NNs exhibit significantly reduced RSSC accuracy compared to A2NNs, this issue can be alleviated by employing the proposed MDD quantization strategy, which combines a weight-debiasing (WD) strategy, which reduces performance degradation due to deviations in the quantized weights, with a feature-debiasing (FD) strategy, which enhances the classification performance of Q-A2NNs through minimizing deviations among the output features of each layer. Extensive experiments and analyses demonstrate that the proposed SSDQ method can efficiently quantize A2NNs to obtain Q-A2NNs with low computational and memory overheads while maintaining comparable performance to A2NNs, thus having high potential for onboard RSSC.

Development of Math Modules Based on Active Learning Type the Power of Two in the Junior High School Curriculum

Modules in learning emphasize more on the activeness and activity of students. This study aims to develop a mathematics module based on an Active Learning (AL) strategy with the Active Learning (AL) type, namely The Power of Two (PT). This study uses an RD research design with the ADDIE model, which consists of 5 stages: analysis, design, development, implementation, and evaluation. This study involved three validators in assessing the validity of the module and 12 small group students to test student responses to the module, which was used to determine the practicality of the module. Based on the research results, it is known that the module developed has very valid criteria, with a percentage of 91.48% by two expert lecturers and a mathematics teacher. The results of student response tests used to assess the practicality of the developed module have very practical criteria, with a percentage of 90.22% by students. This shows that the mathematics module developed based on an Active Learning (AL) strategy with The Power of Two (PT) type is very valid and very practical.

On the Analysis and Evaluation of Proximity-based Load-balancing Policies

Distributed load balancing is the act of allocating jobs among a set of servers as evenly as possible. The static interpretation of distributed load balancing leads to formulating the load-balancing problem as a classical balls-and-bins problem with jobs (balls) never leaving the system and accumulating at the servers (bins). While most of the previous work in the static setting focus on studying the maximum number of jobs allocated to a server or maximum load , little importance has been given to the implementation cost , or the cost of moving a job/data to/from its allocated server, for such policies. This article designs and evaluates server proximity aware static load-balancing policies with a goal to reduce the implementation cost . We consider a class of proximity aware Power of Two (POT) choice-based assignment policies for allocating jobs to servers, where both jobs and servers are located on a two-dimensional Euclidean plane. In this framework, we investigate the tradeoff between the implementation cost and load-balancing performance of different allocation policies. To this end, we first design and evaluate a Spatial Power of two (sPOT) policy in which each job is allocated to the least loaded server among its two geographically nearest servers. We provide expressions for the lower bound on the asymptotic expected maximum load on the servers and prove that sPOT does not achieve classical POT load-balancing benefits. However, experimental results suggest the efficacy of sPOT with respect to expected implementation cost. We also propose two non-uniform server sampling-based POT policies that achieve the best of both implementation cost and load-balancing performance. We then extend our analysis to the case where servers are interconnected as an n -vertex graph G(S, E) . We assume each job arrives at one of the servers, u, chosen uniformly at random from the vertex set S. We then assign each job to the server with minimum load among servers u and v where v is chosen according to one of the following two policies: (i) Unif-POT( k ): Sample a server v uniformly at random from k -hop neighborhood of u; (ii) InvSq-POT( k ): Sample a server v from k -hop neighborhood of u with probability proportional to the inverse square of the distance between u and v . An extensive simulation over a wide range of topologies validates the efficacy of both the policies. Our simulation results show that both policies consistently produce a load distribution that is much similar to that of a classical POT. Depending on topology, we observe the total variation distance to be of the order of 0.002–0.08 for both the policies while achieving a 8%–99% decrease in implementation cost as compared to the classical POT.

Hybrid bi-objective economic lot scheduling problem with feasible production plan equipped with an efficient adjunct search technique

In this research, the economic lot scheduling problem (ELSP), as an NP-hard problem in terms of a bi-objective approach considering deteriorating items and shortage, is studied. The goal is to simultaneously minimise ‘setup and inventory holding costs, comprising deterioration’, and ‘total amount of units facing shortage throughout every period. Two policies besides a heuristic method are employed simultaneously, named extended basic period and Power-of-Two (PoT), to make sure of having feasible replenishment cycles. For handling the considered problem, three multi-objective techniques are employed: non-dominated sorting genetic algorithm II (NSGAII), non-dominated ranking genetic algorithm (NRGA), and a multi-objective procedure hybridized of NSGAII and particle swarm optimization (PSO), called PSNSGAII. Also, three metrics are used to assess the quality of the algorithms’ outputs, including spacing, mean ideal distance, and spread. Experimental results, including extensive conducted parametric and non-parametric statistical analyses, prove that the proposed hybrid PSNSGAII algorithm can well meet discussed criteria compared to other employed algorithms in both ‘quality of solutions’ and ‘diversity’ in almost all small, medium and large test instances. Finally, some useful managerial and practical insights are presented.

On the Analysis of Spatially Constrained Power of Two Choice Policies

We consider a class of power of two choice based assignment policies for allocating users to servers, where both users and servers are located on a two-dimensional Euclidean plane. In this framework, we investigate the inherent tradeoff between the communication cost, and load balancing performance of different allocation policies. To this end, we first design and evaluate a Spatial Power of two (sPOT) policy in which each user is allocated to the least loaded server among its two geographically nearest servers sequentially. When servers are placed on a two-dimensional square grid, sPOT maps to the classical Power of two (POT) policy on the Delaunay graph associated with the Voronoi tessellation of the set of servers. We show that the associated Delaunay graph is 4-regular and provide expressions for asymptotic maximum load using results from the literature. For uniform placement of servers, we map sPOT to a classical balls and bins allocation policy with bins corresponding to the Voronoi regions associated with the second order Voronoi diagram of the set of servers. We provide expressions for the lower bound on the asymptotic expected maximum load on the servers and prove that sPOT does not achieve POT load balancing benefits. However, experimental results suggest the efficacy of sPOT with respect to expected communication cost. Finally, we propose two non-uniform server sampling based POT policies that achieve the best of both the performance metrics. Experimental results validate the effectiveness of our proposed policies.

On pairs of equations involving unlike powers of primes and powers of 2

On pairs of equations involving unlike powers of primes and powers of 2

Eight cubes of primes and 204 powers of 2

It was proved that, for [Formula: see text] every sufficiently large even integer can be represented in the form of eight cubes of primes and [Formula: see text] powers of 2. In this paper, we sharpen the value of [Formula: see text] to 204.

The joint replenishment problem with trade credits

It is a widespread financial practice in procurement management for a supplier aiming to attract customers to offer trade credits when customers make inquiries about the sold products. In this paper, we examine the joint replenishment problem considering trade credits (JRP-TC) under the power-of-two (PoT) policy. We formulate a mathematical model and conduct an analysis that reveals insights into the properties of the optimal objective function. From there, we propose an effective search algorithm that obtains the global optimal solution for the JRP-TC under the PoT policy. Our complexity analysis shows that the JRP-TC and the conventional joint replenishment problem under the PoT policy are pseudo-polynomial time solvable.

On unequal powers of primes and powers of 2

In this note, we will show that every sufficiently large even integer can be represented as a sum of two squares of primes, two cubes of primes, two fourths of primes and 24 powers of 2. This is an improvement of Z. Liu’s result.

Inventory management for one warehouse multi-retailer systems with carbon emission costs

In this paper, we study inventory management for the one warehouse multi-retailer (OWMR) system with considering carbon emissions, in which we determine the reorder intervals for the warehouse and the retailers while minimizing the inventory ordering and holding cost and the carbon emission cost. We consider the carbon emissions from the holding and replenishing inventory activities in the OWMR system, and calculate the carbon emissions based on the frequency of the inventory replenishment at the warehouse and the retailers. We focus on stationary and integer-ratio policies, and formulate the problem as an optimization model with a convex objective function and a set of integer-ratio constraints. We relax the integer-ratio constraints, and introduce an algorithm to solve the corresponding relaxed problem to optimality in O(nlogn) times, where n represents the number of retailers. Based on the optimal solution of the relaxed problem, we build an integer-ratio policy, i.e., power-of-two (POT) policy, with 94% optimality for the primal problem. The computational results show that with considering the carbon emission cost, the reorder intervals of the warehouse and the retailers both increase, and that the integrated model proposed in this paper has more superiorities in terms of reducing the system-wide cost and the carbon emissions.

On the Kräuter–Seifter Theorem on Permanent Divisibility

The paper investigates the divisibility of the permanent function of (1,−1)-matrices by different powers of 2. It is shown that the Krauter–Seifter bound is the best possible one for generic (1,−1)-matrices.

On pairs of equations in unlike powers of primes and powers of 2

Abstract In this paper, we obtained that when k = 455, every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of 2.

Determination of trace element silver in animal serum, tissues and organs by microwave digestion-ICP-MS

Nowadays, the silver is widely used in the biological field and its biological safety catches great attention. It is important to know the distribution of silver ions within the biological organism and the toxic threshold concentration in the tissue. Therefore, a highly sensitive method for measurement of trace amount of silver ion in the medical biological samples is needed. With its high sensitivity for detection of metal ions, inductively coupled plasma mass spectrometry (ICP-MS) method is well suited for quantification of trace amount of silver ion in such samples, but method development is still in its infancy. Consequently, a simple and convenient method for determination of trace amount of silver in the animal serum, tissues or organs was developed, in which the samples were subjected to the microwave digestion, followed by the ICP-MS analysis. To begin with, the samples of serum, muscle, bone marrow, bone, heart, liver, spleen, and kidney were sequently processed in 5 mL of HNO3 and 2 mL of H2O2 solution. Then the samples were completely digested by microwave with the power of 2 000 watts. The temperature was raised gradually by 3-step program. Moreover, the data achieved were reproducible and the method was time saving and especially for large amounts of sample processing. Then the digested solutions were diluted to constant volume. Finally, the concentration of 107Ag in the samples was analyzed by the method of ICP-MS under the optimized conditions. Element yttrium (Y) was used as the internal standard to compensate for matrix suppression effect and improve the accuracy of measurement. For one thing, the analytical results showed that the detection limit of the trace element 107Ag was 0.98 μg · kg(-1), and furthermore, the correlation coefficient of standard curve was 0.999 9. For another thing, the recovery rate of the silver element ranged from 98% to 107%, which was calculated according to measured quantity before adding standard, adding standard and measured quantity after adding standard. At the same time, the relative standard deviation (RSD) of the method was in the range of 2.0%-4.3%. The concentrations of element silver in animal serum, tissues and organs were determined by the aboved method. The obtained results showed that silver ions were mainly accumulated in the liver after they were intaken into the body. The results suggested that the microwave digestion-ICP-MS method could accurately determine the trace element Ag in the body. The method developed has good feasibility and is suitable for the determination of trace element Ag in various types of medical and biological samples, especially for large quantities of biological samples. The process has the advantages of easysample processing and it is simple and convenient. In addition, the accurate results could be obtained in a short time with high sensitivity. Last but not least, the method provides the guidance for the determination of trace elements in other biological samples.

An artificial bee colony algorithm for the economic lot scheduling problem

In this study, we present an artificial bee colony (ABC) algorithm for the economic lot scheduling problem modelled through the extended basic period (EBP) approach. We allow both power-of-two (PoT) and non-power-of-two multipliers in the solution representation. We develop mutation strategies to generate neighbouring food sources for the ABC algorithm and these strategies are also used to develop two different variable neighbourhood search algorithms to further enhance the solution quality. Our algorithm maintains both feasible and infeasible solutions in the population through the use of some sophisticated constraint handling methods. Experimental results show that the proposed algorithm succeeds to find the all the best-known EBP solutions for the high utilisation 10-item benchmark problems and improves the best known solutions for two of the six low utilisation 10-item benchmark problems. In addition, we develop a new problem instance with 50 items and run it at different utilisation levels ranging from 50 to 99% to see the effectiveness of the proposed algorithm on large instances. We show that the proposed ABC algorithm with mixed solution representation outperforms the ABC that is restricted only to PoT multipliers at almost all utilisation levels of the large instance.

A Novel Hybrid Monotonic Local Search Algorithm for FIR Filter Coefficients Optimization

This work presents a formulation of the FIR filter problem with sum of power-of-two (POT) coefficients as a mixed integer linear problem and solves it heuristically. The optimization problem is formulated to minimize the number of nonzero bits in each coefficient without violating the filter specifications within the pass and stop bands. A novel fast and efficient local search optimization algorithm for the filter coefficients is proposed. The algorithm called POTx does not use a tree structure in contrast to conventional MILP algorithms and offers fast computation because of a presorted search space, a monotonic dedicated search space, and the use of abort conditions. The proposed approach achieves comparable reductions to nonheuristic approaches because of a hybrid allocation scheme and multiple optimization iterations. The usefulness of the proposed algorithm for low power design of FIR filters is shown through the evaluation of several benchmark filters.

The economic lot scheduling problem with deteriorating items and shortage: an imperialist competitive algorithm

This paper addresses an economic lot scheduling problem (ELSP) for manufacturing environments regarding slack costs and deteriorating items using the extended basic period approach under Power-of-Two (PoT) policy. The purpose of this research is to determine an optimal batch size for a product and minimizing total related costs to such a problem. The cost function consists of three components, namely, setup cost, holding cost includes deteriorating factor, and slack cost. The ELSP is concerned with the scheduling decision of n items and lot sizing. Avoiding schedule interference is the main problem in ELSP. The used PoT policy ensures that the replenishment cycle of each item to be integer and this task reduces potential schedule interferences. Since the ELSP is shown as an NP-hard problem, an imperialist competitive algorithm is employed to provide good solutions within reasonable computational times. Computational results show that the proposed approach can efficiently solve such complicated problems.

Analysis of optical energy delivery through multi-core optical fibers

Many researchers worldwide have been making a lot of effort to find sustainable clean energy source to replace the current fossil fuels. However, solar energy is considered as the ultimate energy solution to supply the world total power consumption. Light can be used for lighting, heating, wired and wireless communications, etc. Moreover, even light-driven motors which can directly convert optical energy into kinetic energy are studied recently. In this paper, we analyze optical energy delivery through multi-core optical fibers. Our estimation shows that an optical power of 2 kW can be transmitted through a multi-core fiber and an optical power of >10 MW can be transmitted through a bundle of optical fibers with a diameter of several centimeters. It seems competitive compared with the electric power delivery through a copper cable.

Solving the Economic Lot and Inspection Scheduling Problem using the Extended Basic Period approach under Power-of-Two policy

The focus of this study is to solve the Economic Lot and Inspection Scheduling Problem (ELISP) using the Extended Basic Period (EBP) approach under Power-of-Two (PoT) policy. The objective of the ELISP is to determine an optimal cycle time and an optimal production and inspection schedule so as to minimize the total cost per unit time. Under PoT policy, we formulate a mathematical model by taking into account the constraints for both production and inspection capacities. Also, we propose a Hybrid Genetic Algorithm (HGA) which is equipped with a search algorithm that not only seeks to improve solution quality, but also assures a feasible solution for each chromosome obtained from the evolutionary processes. Our numerical experiments show that the proposed HGA effectively solves the ELISP using the EBP approach, and its solutions outperform the solutions from the ELISP using the Common Cycle approach.

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