Reduction criteria, upper bounds, and a dynamic programming based heuristic for the max–min $$k_i$$ k i -partitioning problem

Alexander Lawrinenko (), Stefan Schwerdfeger () and Rico Walter ()
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Alexander Lawrinenko: Friedrich-Schiller-University Jena
Stefan Schwerdfeger: Friedrich-Schiller-University Jena
Rico Walter: Friedrich-Schiller-University Jena

Journal of Heuristics, 2018, vol. 24, issue 2, No 3, 173-203

Abstract: Abstract This paper addresses the max–min $$k_i$$ k i -partitioning problem that asks for an assignment of n jobs to m parallel machines so that the minimum machine completion time is maximized and the number of jobs on each machine does not exceed a machine-dependent cardinality limit $$k_i$$ k i $$(i=1,\ldots ,m)$$ ( i = 1 , … , m ) . We propose different preprocessing as well as lifting procedures and derive several upper bound arguments. Furthermore, we introduce suited construction heuristics as well as an effective dynamic programming based improvement procedure. Results of a comprehensive computational study on a large set of randomly generated instances indicate that our algorithm quickly finds (near-)optimal solutions.

Keywords: Parallel machines; Cardinality limits; Preprocessing; Upper bounds; Dynamic programming (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10732-017-9362-9

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