A space-indexed formulation of packing boxes into a larger box
نویسندگان
چکیده
The problem of packing many small boxes into a single larger box underlies a number of cutting, packing, scheduling, and transportation applications. There are a number of heuristic solvers, but the progress in exact solvers, in general, and integer programming solvers, in particular, has been limited. Padberg [Math. Methods Oper. Res., 52(1):1–21, 2000] estimated the integer linear programming formulation of Fasano could cope with “about twenty boxes”. Our computational experiments confirm that the seemingly trivial decision whether twelve unit-cubes can be packed into a box with the unit-base and height eleven, cannot be made within an hour by modern integer programming solvers using this formulation. We present a new, “space-indexed”, linear programming relaxation, which often provides lower bounds within 1 percent of optimality, and allows for integer optima to be computed on instances with 100,000 boxes within an hour. Results of extensive computational tests of both formulations are reported.
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ورودعنوان ژورنال:
- Oper. Res. Lett.
دوره 40 شماره
صفحات -
تاریخ انتشار 2012