Optimal Rebuilding Research Articles

Optimal Reutilization Strategy for a Shipbuilder under the Carbon Quota Policy

Reducing carbon emissions is crucial for humanity. Recently, the International Maritime Organization has set carbon emission quotas to limit the extensive carbon emissions from the marine industry. This paper examines how shipbuilders can adopt the rebuilding of decommissioned ships to reduce carbon emissions and also make more profits. Incorporating the carbon emission quota policy, we formulate the dynamic rebuilding model of decommissioned ships and derive the optimal rebuilding and pricing control strategies for the shipbuilder. We investigate the evolutionary dynamics as well as the impact of carbon quotas and carbon emission savings on shipbuilder’s strategies. The study’s findings suggest that shipbuilders have the potential to improve their profitability while also contributing to energy conservation and emission reduction. This can be achieved through the implementation of technological innovations aimed at reducing carbon emissions from their production activities. The government has a crucial role to play in regulating and managing shipbuilders. In cases where the cost per unit of carbon quota is deemed excessively high, it may be necessary to establish appropriate regulations that prevent shipbuilders from directly benefiting from the trade of carbon quotas. This approach can also help ensure the positive development of the carbon trading market.

A Generic Transformation for Optimal Node Repair in MDS Array Codes Over F2

For high-rate linear systematic maximum distance separable (MDS) codes, most early constructions could initially optimally repair all the systematic nodes but not all the parity nodes. Fortunately, this issue was first solved by Li et al. in (IEEE Trans. Inform. Theory, 64(9), 6257-6267, 2018), where a transformation that can convert any nonbinary MDS array code into another one with desired properties was proposed. However, the transformation does not work for binary MDS array codes. In this paper, we address this issue by proposing another generic transformation that can convert any $[n, k]$ binary MDS array code into a new one, which endows any $r=n-k\ge2$ chosen nodes with optimal repair bandwidth and optimal rebuilding access properties, and at the same time, preserves the normalized repair bandwidth/rebuilding access for the remaining $k$ nodes under some conditions. As two immediate applications, we show that 1) by applying the transformation multiple times, any binary MDS array code can be converted into one with optimal rebuilding access for all nodes, 2) any binary MDS array code with optimal repair bandwidth or optimal rebuilding access for the systematic nodes can be converted into one with the corresponding optimality property for all nodes.

ПРИМЕНЕНИЕ ГЕНЕТИЧЕСКОГО АЛГОРИТМА В ЗАДАЧЕ КОММИВОЯЖЕРА

The relevance of the work is due to the wide application of methods for solving the traveling voyager problem in various applied fields. The article deals with issues related to the need for optimal rebuilding of compiled routes when adding new destinations. A modified genetic algorithm for solving the traveling salesman problem is considered and an analysis is made of the effectiveness of this algorithm in constructing optimal routes.

Redevelopment Strategies and Building Ages

An improved real option pricing model that incorporates the depreciation effect for two-stage redevelopment projects will be demonstrated to estimate the redevelopment project values in a wide range of scenarios. Based on a stochastic differential equation, numerical analyses will focus on new factors that influence the expected exercise time, that is, depreciation rate, the annual increase in average building age, building age of the targeted property, and the average building ages in the same region. The depreciation rate is the most influential factor in this model. More importantly, this study will summarize three exercise strategies that cover all combination of the parameters. In some cases, with a low capital return rate, or high depreciation rate, or both, the traditional simultaneous exercise strategy based on the optimal demolition price-to-cost ratio is not feasible. Instead, either a sequential exercise or simultaneous exercise that is based on the optimal rebuilding price-to-cost ratio is the best choice. Detailed procedures on how to adopt the best strategy will be demonstrated. The acquisition price of the old property proved to be sensitive to the depreciation rate and the capital return rate within a certain range. To apply this model properly, the feasible time interval for the traditional simultaneous exercise strategy and the depreciation rate should be estimated accurately.

A Generic Transformation to Enable Optimal Repair in MDS Codes for Distributed Storage Systems

We propose a generic transformation that can convert any nonbinary (n = k + r, k) maximum distance separable (MDS) code into another (n, k) MDS code over the same field such that: 1) some arbitrarily chosen r nodes have the optimal repair bandwidth and the optimal rebuilding access; 2) for the remaining k nodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved; and 3) the sub-packetization level is increased only by a factor of r. Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinary (n, k) scalar MDS code can be converted into an (n, k) MDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal.

Optimal Rebuilding of Multiple Erasures in MDS Codes

MDS array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with $r$ redundancy nodes can correct any $r$ node erasures by accessing all the remaining information in the surviving nodes. However, in practice, $e$ erasures is a more likely failure event, for $1\le e<r$. Hence, a natural question is how much information do we need to access in order to rebuild $e$ storage nodes? We define the rebuilding ratio as the fraction of remaining information accessed during the rebuilding of $e$ erasures. In our previous work we constructed MDS codes, called zigzag codes, that achieve the optimal rebuilding ratio of $1/r$ for the rebuilding of any systematic node when $e=1$, however, all the information needs to be accessed for the rebuilding of the parity node erasure. The (normalized) repair bandwidth is defined as the fraction of information transmitted from the remaining nodes during the rebuilding process. For codes that are not necessarily MDS, Dimakis et al. proposed the regenerating codes framework where any $r$ erasures can be corrected by accessing some of the remaining information, and any $e=1$ erasure can be rebuilt from some subsets of surviving nodes with optimal repair bandwidth. In this work, we study 3 questions on rebuilding of codes: (i) We show a fundamental trade-off between the storage size of the node and the repair bandwidth similar to the regenerating codes framework, and show that zigzag codes achieve the optimal rebuilding ratio of $e/r$ for MDS codes, for any $1\le e\le r$. (ii) We construct systematic codes that achieve optimal rebuilding ratio of $1/r$, for any systematic or parity node erasure. (iii) We present error correction algorithms for zigzag codes, and in particular demonstrate how these codes can be corrected beyond their minimum Hamming distances.

MDR Codes: A New Class of RAID-6 Codes with Optimal Rebuilding and Encoding

As storage systems grow in size, device failures happen more frequently than ever before. Given the commodity nature of hard drives employed, a storage system needs to tolerate a certain number of disk failures while maintaining data integrity, and to recover lost data with minimal interference to normal disk I/O operations. RAID-6, which can tolerate up to two disk failures with the minimum redundancy, is becoming widespread. However, traditional RAID-6 codes suffer from high disk I/O overhead during recovery. In this paper, we propose a new family of RAID-6 codes, the Minimum Disk I/O Repairable (MDR) codes, which achieve the optimal disk I/O overhead for single failure recoveries. Moreover, we show that MDR codes can be encoded with the minimum number of bit-wise XOR operations. Simulation results show that MDR codes help to save about half of disk read operations than traditional RAID-6 codes, and thus can reduce the recovery time by up to 40%.

Rebuild Technology Transfer in the Presence of Remanufacturing Dealer

Product rebuilding requires OEM (Original Equipment Manufacturer) and his dealers to collaborate closely. In this paper, a model is proposed to study the rebuilding technology transfer decisions within an OEM and his authorized dealer who has to invest in technology for remanufacturing key components and rebuild used machines with the rebuilding technologies transferred from OEM. The optimal rebuilding technologies transfer and remanufacturing investment strategies are analyzed. The results highlight the significant effects of discount factor on the optimal strategies of OEM and the dealer. Some tactics for OEM to balance the new and rebuilding market are analysed.

Zigzag Codes: MDS Array Codes With Optimal Rebuilding

Maximum distance separable (MDS) array codes are widely used in storage systems to protect data against erasures. We address the rebuilding ratio problem, namely, in the case of erasures, what is the fraction of the remaining information that needs to be accessed in order to rebuild exactly the lost information? It is clear that when the number of erasures equals the maximum number of erasures that an MDS code can correct, then the rebuilding ratio is 1 (access all the remaining information). However, the interesting and more practical case is when the number of erasures is smaller than the erasure correcting capability of the code. For example, consider an MDS code that can correct two erasures: What is the smallest amount of information that one needs to access in order to correct a single erasure? Previous work showed that the rebuilding ratio is bounded between <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${{1} \over {2}}$</tex></formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${{3} \over {4}}$</tex></formula> ; however, the exact value was left as an open problem. In this paper, we solve this open problem and prove that for the case of a single erasure with a two-erasure correcting code, the rebuilding ratio is <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${{1} \over {2}}$</tex></formula> . In general, we construct a new family of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$r$</tex></formula> -erasure correcting MDS array codes that has optimal rebuilding ratio of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${{1} \over {r}}$</tex></formula> in the case of a single erasure. Our array codes have efficient encoding and decoding algorithms (for the cases <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$r=2$</tex> </formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$r=3$</tex></formula> , they use a finite field of size 3 and 4, respectively) and an optimal update property.

Optimal Rebuilding of a Metapopulation

A contentious issue in recent fisheries management debates has been how to rebuild overfished marine fish stocks. We investigate the economic and ecological nature of rebuilding plans in a metapopulation system. We find “most rapid approach paths” for system‐wide recovery that differ from prototypical paths that might be chosen when populations are assumed independent. For example, moratoria in some patches may be extended in order to speed the recovery of other patches in the system. We also investigate the costs of second‐best policies that depend on the degree of spatial heterogeneity, the nature of the linkages, and the dispersal rates.

Optimal Rebuilding of Fish Stocks in Different Nations: Bioeconomic Lessons for Regulators

Under the rubric of sustainable fisheries, nations are mandated to rebuild overfished stocks. Although rebuilding strategies are almost universally directed by the available biological information, approaches vary depending on fishery laws, management objectives, and technical guidelines. For example, rebuilding schedules in the United States are primarily designed to achieve rapid rebuilding of biomass and spawning stocks consistent with the biological characteristics of the resource. In contrast, New Zealand has greater flexibility in rebuilding stocks in order to consider economic, social, and cultural needs. In this paper we investigate potential economic costs to the fishery that result by limiting the US manager's flexibility in choosing a recovery trajectory. Using numerical models for moderate-and long-lived stocks, the analysis reveals that depending on productivity of the stock and the discount rate, extending the rebuilding timeframe can substantially increase annual harvests and economic benef...