Set partitioning and packing versus assignment formulations for subassembly matching problems

A Ghoniem and H D Sherali
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A Ghoniem: University of Massachusetts Amherst, Massachusetts, USA
H D Sherali: Virginia Polytechnic Institute and State University, Blacksburg, USA

Journal of the Operational Research Society, 2011, vol. 62, issue 11, 2023-2033

Abstract: This paper addresses alternative formulations and model enhancements for two combinatorial optimization problems that arise in subassembly matching problems. The first problem seeks to minimize the total deviation in certain quality characteristics for the resulting final products from a vector of target values, whereas the second aims at maximizing the throughput under specified tolerance restrictions. We propose set partitioning and packing models in concert with a specialized column generation (CG) procedure that significantly outperform alternative assignment-based formulations presented in the literature, even when the latter are enhanced via tailored symmetry-defeating strategies. In particular, we emphasize the critical importance of incorporating a complementary CG feature to consistently produce near-optimal solutions to the proposed set partitioning and packing models. Extensive computational results are presented to demonstrate the relative effectiveness of the different proposed modelling and algorithmic strategies.

Date: 2011
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