Exact and approximate methods for a one-dimensional minimax bin-packing problem

One-dimensional bin-packing problems require the assignment of a collection of items to bins with the goal of optimizing some criterion related to the number of bins used or the ‘weights’ of the items assigned to the bins. In many instances, the number of bins is fixed and the goal is to assign the...

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Veröffentlicht in:Annals of operations research Jg. 206; H. 1; S. 611 - 626
Hauptverfasser: Brusco, Michael J., Köhn, Hans Friedrich, Steinley, Douglas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.07.2013
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Approximation
Bins
Business and Management
Combinatorial optimization
Combinatorics
Integer programming
Linear programming
Mathematical analysis
Mathematical programming
Methods
Minimax technique
Operations research
Operations Research/Decision Theory
Optimization
Packing problem
Quantitative psychology
Simulated annealing
Simulated annealing (Mathematics)
Software
Software packages
Statistics
Studies
Theory of Computation
United States
Integer programming
One-dimensional bin-packing
Combinatorial optimization
Test splitting
Simulated annealing
ISSN:0254-5330, 1572-9338
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Zusammenfassung:One-dimensional bin-packing problems require the assignment of a collection of items to bins with the goal of optimizing some criterion related to the number of bins used or the ‘weights’ of the items assigned to the bins. In many instances, the number of bins is fixed and the goal is to assign the items such that the sums of the item weights for each bin are approximately equal. Among the possible applications of one-dimensional bin-packing in the field of psychology are the assignment of subjects to treatments and the allocation of students to groups. An especially important application in the psychometric literature pertains to splitting of a set of test items to create distinct subtests, each containing the same number of items, such that the maximum sum of item weights across all bins is minimized. In this context, the weights typically correspond to item statistics derived from difficulty and discrimination indices. We present a mixed zero-one integer linear programming (MZOILP) formulation of this one-dimensional minimax bin-packing problem and develop an approximate procedure for its solution that is based on the simulated annealing algorithm. In two comparisons that focused on 34 practically-sized test problems (up to 6000 items and 300 bins), the simulated annealing heuristic generally provided better solutions than were obtained when using a commercial mathematical programming software package to solve the MZOILP formulation directly.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-012-1175-5