Lexicographic Bin-Packing Optimization for Loading Trucks in a Direct-Shipping System
Katrin Heßler (),
Stefan Irnich (),
Tobias Kreiter () and
Ulrich Pferschy ()
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Katrin Heßler: Johannes Gutenberg-University Mainz, Germany
Stefan Irnich: Johannes Gutenberg-University Mainz, Germany
Tobias Kreiter: scc EDV-Beratung AG
Ulrich Pferschy: University of Graz
No 2009, Working Papers from Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz
We consider a packing problem that arises in a direct-shipping system in the food and beverage industry: Trucks are the containers and products to be distributed are the items. The packing is constrained by two independent quantities, weight (e.g., measured in kg) and volume (number of pallets). Additionally, the products are grouped into the three categories standard, cooled, and frozen (the latter two require refrigerated trucks). Products of different categories can be transported in one truck using separated zones, but the cost of a truck depends on the transported product categories. Moreover, product splitting should be avoided so that (un-)loading is simplified. As a result, we seek for a feasible packing optimizing the following objective functions in a strictly lexicographic sense: minimize the (1) total number of trucks; (2) number of refrigerated trucks; (3) number of refrigerated trucks which contain frozen products; (4) number of refrigerated trucks which also transport standard products; (5) and minimize product splitting. This is a real-world application of a bin-packing problem with cardinality constraints a.k.a. the two-dimensional vector packing problem, with additional constraints. We provide a heuristic and an exact solution approach. The heuristic meta-scheme considers the multi-compartment and item-fragmentation features of the problem and applies various problem-specific heuristics. The exact solution algorithm covering all five stages is based on branch-and-price using stabilization techniques exploiting dual-optimal inequalities. Computational results on real-world and difficult self-generated instances prove the applicability of our approach.
Keywords: bin packing; lexicographic objective; heuristics; column generation; dual-optimal inequalities (search for similar items in EconPapers)
Pages: 34 pages
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