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All Journal International Journal of Industrial Optimization (IJIO)
Song, Myung Soon
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Decision Sciences, Operations Research & Management Engineering Industrial & Manufacturing Engineering

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Filling the gap in weighted set covering problem test instances: implications for both researchers and practitioners Vasko, Francis J.; Lu, Yun; Song, Myung Soon; Rando, Dominic
International Journal of Industrial Optimization Vol. 6 No. 1 (2025)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/ijio.v6i1.10836

Abstract

Since 1990, the quality of approximate solution methods for solving weighted set covering problems (WSCPs) has been measured based on how well they solve 65 WSCPs available in Beasley’s OR-Library.  In a 2024 paper, it has been shown that guaranteed optimal solutions can easily be obtained for 55 weighted set covering problems (WSCPs) in Beasley’s OR-Library using general-purpose integer programming software.  These 55 WSCPs have 500 rows and 5,000 columns or less and were solved in a few seconds on a standard PC.  However, the remaining 10 WSCPs have 1000 rows and 10,000 columns and either required considerably more than 1000 seconds to obtain guaranteed optimums (data set NRG) or no optimums were obtained (NRH).  The purpose of this short paper is to try to quantify the solution times needed to solve WSCPs using general-purpose integer programming software that are larger than 500 rows and 5,000 columns, but less than 1,000 rows and 10,000 columns.  This is important because the size and solution time gap is so large that solution times go from a few seconds for the 55 “smaller” WSCPs to very large solution times for the two largest data sets.  To fill this gap, 40 new WSCP instances are defined and their solution times are analyzed to determine when to expect that WSCPs, based on size and density, can be solved to optimality in a timely manner using general-purpose integer programming software like Gurobi or CPLEX.
The role of mathematical formulation in solving the unbalanced assignment problem Vasko, Francis J.; Lu, Yun; Song, Myung Soon
International Journal of Industrial Optimization Vol. 7 No. 1 (2026)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/ijio.v7i1.12987

Abstract

In a 2019 paper, the authors claim to have developed a modified Hungarian method that performs better than a number of other solution methods for the unbalanced assignment problem (UAP) based on the solution of one UAP instance that has been discussed in the literature. The purpose of this short paper is to demonstrate that the math formulation used in the 2019 paper was not as restrictive as the standard one commonly used in the literature and therefore the comparison is not valid. The commonly used UAP math formulation not only tries to minimize cost, but also tries to level load the jobs onto the machines. The formulation from the 2019 paper allows many jobs to be assigned to a low-cost machine. Hence solutions (not even optimums) to the 2019 formulation can be better than the optimal solution using the standard UAP math formulation. Additionally, it will be shown that the Modified Hungarian method proposed in the 2019 paper does not generate guaranteed optimums to the math formulation used in that paper (let alone the standard UAP formulation). An 8-job and 5-machine assignment problem that appeared in the literature will be used to illustrate the points mentioned above.
Co-Authors Lu, Yun Rando, Dominic Vasko, Francis J.