Uncertainty measure for the Bellman–Johnson problem with interval processing times

Sotskova, Yu. N.; Matsveichuka, N. M.

doi:10.1007/s10559-012-9445-4

Cited by 6 publications

(4 citation statements)

References 30 publications

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“…As was shown in [21,22], the cardinality |S(T )| of the minimal dominating set S(T ) may be regarded as the measure of uncertainty of the problem 1|p L…”

Section: Methods Based On Optimal Schedule Stabilitymentioning

confidence: 99%

Stability polyhedra of optimal permutation of jobs servicing

Sotskov

2014

Autom Remote Control

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Consideration was given to minimization of the sum of weighted instants of completing servicing of n customers by a single server, provided that the duration of jobs servicing may assume any real value from a given numerical interval. An algorithm of complexity O(n) was developed to construct a polyhedron (parallelepiped) of the optimality of permutation of servicing of n jobs that is contained in the domain of stability of the same permutation and comprises the polyhedron of its stability. For the randomly generated problems, experimental comparison was carried out of the dimensions and relative volumes of the optimality polyhedra and stability of the optimal permutation of servicing n jobs under randomly generated scenarios.

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“…As was shown in [21,22], the cardinality |S(T )| of the minimal dominating set S(T ) may be regarded as the measure of uncertainty of the problem 1|p L…”

Section: Methods Based On Optimal Schedule Stabilitymentioning

confidence: 99%

Stability polyhedra of optimal permutation of jobs servicing

Sotskov

2014

Autom Remote Control

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“…𝜉 ], аnd 𝑛 × 𝑚 is matrix of time intervals of energy transmission by the 𝑖-th source from the 𝑖-th price range, taking into account the parameter 𝜉. Then, if we establish a mutual and unambiguous correspondence between the sources and the requirements for the formation of the energy balance based on seasonal schedules of energy consumption, then the matrix of time intervals of energy transfer [𝑡 𝑖𝑗 𝜉 ], 𝑖 = 1, 𝑛, 𝑗 = 1, 𝑚 will coincide with the matrix of time intervals for the formation of the energy balance structure from selected sources n with characteristics m as a single-route Bellman-Johnson task [21]. Therefore, to calculate the minimum total time 𝑇 ∑ (𝐶, 𝑛, 𝑚, 𝜉) of energy transfer by 𝑛 ≥ 2 heterogeneous distributed competing sources that use 𝑚 ≥ 2 structured flows in a microenergy system with 𝐶 ≥ 2 final consumers, taking into account the parameter 𝜉 > 0, then for our case the Bellman-Johnson functional can be written:…”

Section: If 𝑇 𝜉 = [𝑡 𝑖𝑗mentioning

confidence: 99%

Principles of resource-process modeling of territorial communities combined energy supply in the climate change prevention context

Kaplun

2023

Sist. dosl. energ. (Online)

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The research is devoted to the theoretical and practical substantiation of the principles of formation of systems of combined energy supply with heterogeneous sources to increase the energy efficiency of territorial communities in the conditions of climate change resistance. New approaches and structural models for the formation of local microenergy systems are proposed, which will encourage territorial communities to a new type of activity related to their own energy generation based on the use of local types of fuels and renewable energy sources. The principles of building such local energy supply systems, in general, consist in the rational distribution of resources (renewable sources, sources of combined energy generation using biofuels, energy from external networks) and coordination of the processes of generation, transmission, accumulation, distribution and consumption of energy within the boundaries of a separate territorial community by creating its own high-tech infrastructure assets. The formation of the energy balance in the medium and long term is proposed to be carried out on the basis of a resource-process analysis of the operation of local networks by finding the optimal use of local types of biofuels and renewable sources in the combined generation of electricity and heat, taking into account their current value. The cost of energy for the end consumer is determined by differentiated tariffs of energy supply companies and the use of several heterogeneous sources that participate in the process of decentralized energy production. Mathematical relations are obtained for calculating the values of the time intervals of the execution of a set of parallel processes that arise during the interaction of competing sources of distributed generation with end consumers and establishing the regularities of the formation of the energy balance a micro energy system. The proposed method can be a tool for finding optimal energy efficiency management scenarios of facilities with local energy supply, using operational redistribution of energy flows in the system of combined energy generation and forecasting current costs for energy supply in calculation periods. Such a concept can be a theoretical basis for the formation of principles of energy independence of territorial communities. Keywords: territorial community, combined-heat-and-power-system, renewable energy sources, biofuel, energy balances.

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“…Furthermore, some heuristics are provided by Aydilek et al [8] for the problem F2| LBs i,k ≤ s i,k ≤ UBs i,k | C max and some others are provided by Aydilek et al [9] for the same problem where processing times are uncertain variables as well. For uncertain environments, researchers investigate different scheduling problems by modeling setup/processing times within certain intervals including Braun et al [10], Sotskov et al [23], Matsveichuk et al [21], Sotskov and Matsveichuk [25], and Sotskov and Lai [24].…”

mentioning

confidence: 99%

A better dominance relation and heuristics for Two-Machine No-Wait Flowshops with Maximum Lateness Performance Measure

Allahverdi¹,

Aydilek²,

Aydilek³

et al. 2021

JIMO

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In this paper, we consider a manufacturing system with twomachine no-wait flowshop scheduling problem where setup times are uncertain. The problem with the performance measure of maximum lateness was addressed in the literature (Computational and Applied Mathematics 37, 6774-6794) where dominance relations were proposed. We establish a new dominance relation and show that the new dominance relation is, on average, about 90% more efficient than the existing ones. Moreover, since it is highly unlikely to find optimal solutions for problems of reasonable size by utilizing dominance relations and since there exist no heuristic in the literature for the problem, we propose constructive heuristics to solve real life problems. We conduct extensive computational experiments to evaluate the proposed heuristics. Computational experiments indicate that the performance of the worst proposed heuristic is at least 20% better than a benchmark solution. Furthermore, they also indicate that the best proposed heuristic is about 130% better than the worst one. The average CPU time of the heuristics is significantly less than a second. 2010 Mathematics Subject Classification. 90B36.

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Uncertainty measure for the Bellman–Johnson problem with interval processing times

Cited by 6 publications

References 30 publications

Stability polyhedra of optimal permutation of jobs servicing

Stability polyhedra of optimal permutation of jobs servicing

Principles of resource-process modeling of territorial communities combined energy supply in the climate change prevention context

A better dominance relation and heuristics for Two-Machine No-Wait Flowshops with Maximum Lateness Performance Measure

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