Optimizing Management of Jobs in a Logistic Project Under Conditions of Uncertainty

Koshelev, P. S.; Міщенко, Андрій

doi:10.1134/s1064230721040079

Cited by 9 publications

(3 citation statements)

References 5 publications

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“…Therefore, for some 𝑟𝑟 𝑖𝑖𝑘𝑘𝑘𝑘 ≤ 𝑟𝑟 𝑖𝑖𝑘𝑘𝑘𝑘 0 , equality 𝑔𝑔(𝜏𝜏 𝑘𝑘𝑘𝑘 , 𝑤𝑤 𝑖𝑖 ) = 𝑐𝑐 𝑘𝑘𝑘𝑘 𝑟𝑟 𝑖𝑖𝑘𝑘𝑘𝑘 is fulfilled, i.e., 𝑐𝑐 𝑘𝑘𝑘𝑘 𝑟𝑟 𝑖𝑖𝑘𝑘𝑘𝑘 ≤ 𝑐𝑐 𝑘𝑘𝑘𝑘 𝑟𝑟 𝑖𝑖𝑘𝑘𝑘𝑘 0 and (1) is fulfilled. Further, 𝑔𝑔(𝑢𝑢, 𝜏𝜏 𝑘𝑘𝑘𝑘 ) ≤ 𝑐𝑐 𝑘𝑘𝑘𝑘 𝑅𝑅 𝑘𝑘𝑘𝑘 (11) at all 𝑘𝑘 = 1, 𝐾𝐾, 𝑙𝑙 = 1, 𝐿𝐿. Due to the flow preservation in the nodes 𝜏𝜏 𝑘𝑘𝑘𝑘 , the equalities…”

Section: Necessary and Sufficient Condition For The Existence Of Opti...mentioning

confidence: 99%

“…Remark. It follows from the description of the procedure that the total productivity of performers simultaneously performing job 𝑤𝑤 𝑖𝑖 does not exceed⌈𝑞𝑞 𝑖𝑖𝑗𝑗 /𝛿𝛿 𝑗𝑗 ⌉, where (⌈𝑎𝑎⌉ = 𝑚𝑚𝑚𝑚𝑚𝑚{ 𝑏𝑏 ≥ 𝑎𝑎, 𝑏𝑏 − integer}, and from (11) it follows that this value does not exceed 𝑚𝑚 𝑖𝑖𝑗𝑗 0 . Inequality (12) ensures that the total productivity of performers used in interval Ij does not exceed Mj.…”

Section: Packing Proceduresmentioning

confidence: 99%

“…Then they proposed the new technique. It based on the use of the "branches and bounds" method and the construction of solution stability polyhedra (Koshelev 2021, Gorskii 2022). The authors have studied the problems of allocating both types of resources (Furugyan 2015, Kononov 2019.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Allocation of non-uniform complex of resources in production systems. Scheduling and correction of deadlines

Kononov,

Furugyan

2024

E3S Web Conf.

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The problem of planning a job complex with the use of resources of various types − renewable (performers who can differ with the productivity) and several types of non-renewable is considered. We allow interruptions, and switching from one performer to another and performing one work simultaneously by several performers. The available number of performers at different times is not constant, and their productivity may vary. A developed polynomial algorithm finds the optimal allocation of resources and builds the optimal schedule of jobs. A pseudopolynomial algorithm for finding the optimal allocation of resources of minimal cost has been developed. These algorithms based on building a flow network model and modifying the packing procedure. An algorithm for the optimal allocation of resources and the construction of an optimal schedule for the case of a heterogeneous set of works is proposed.

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Section: Necessary and Sufficient Condition For The Existence Of Opti...mentioning

confidence: 99%

Section: Packing Proceduresmentioning

confidence: 99%