Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This p...Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This paper contains computation of minimum covering Randićenergies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randićenergy are also presented.展开更多
Sustainability describes a broad set of themes centered on current human uses of the planet’s resources.The multiple uses and users of the term have led to a proliferation of salient issues and associated indicators....Sustainability describes a broad set of themes centered on current human uses of the planet’s resources.The multiple uses and users of the term have led to a proliferation of salient issues and associated indicators.We present a new method to systematically link these issues and indicators under two conceptual frameworks of sustainability in order to enable quantitative analyses.We demonstrate this approach with a specific use case focused on the global sourcing of agricultural products.We use the optimization software Marxan in a novel way to develop minimum sets of indicators that provide maximum coverage of sustainability issues.Minimum covering sets were identified and accumulation curves were developed to measure the contribution of each indicator in each set to overall issues coverage.While greater detail in the assessment of each indicator would likely provide more effective sets of indicators,those that were generated provide optimism that this approach can bring better focus to sustainability assessments.展开更多
According to the compound packing problem in ammunition supply system in our army, the non-standard pallet series design model is proposed, and the original problem that can be solved as a set cover problem with a nes...According to the compound packing problem in ammunition supply system in our army, the non-standard pallet series design model is proposed, and the original problem that can be solved as a set cover problem with a nested bin-packing problem, is analyzed, then two heuristic algorithms are applied to solve the problem.展开更多
文摘Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This paper contains computation of minimum covering Randićenergies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randićenergy are also presented.
基金Mars Incorporated and Kraft Foods for their generous funding of this project
文摘Sustainability describes a broad set of themes centered on current human uses of the planet’s resources.The multiple uses and users of the term have led to a proliferation of salient issues and associated indicators.We present a new method to systematically link these issues and indicators under two conceptual frameworks of sustainability in order to enable quantitative analyses.We demonstrate this approach with a specific use case focused on the global sourcing of agricultural products.We use the optimization software Marxan in a novel way to develop minimum sets of indicators that provide maximum coverage of sustainability issues.Minimum covering sets were identified and accumulation curves were developed to measure the contribution of each indicator in each set to overall issues coverage.While greater detail in the assessment of each indicator would likely provide more effective sets of indicators,those that were generated provide optimism that this approach can bring better focus to sustainability assessments.
文摘According to the compound packing problem in ammunition supply system in our army, the non-standard pallet series design model is proposed, and the original problem that can be solved as a set cover problem with a nested bin-packing problem, is analyzed, then two heuristic algorithms are applied to solve the problem.
