Solving robust bin-packing problems with a branch-and-price approach

One-dimensional bin-packing is a well-known combinatorial optimization problem which strongly NP-hard. It consists of allocating given set items different sizes into bins the same capacity to minimize number used. The each bin cannot be exceeded. This paper deals with some variants this take account cases when there are uncertain sizes. goal obtain robust solutions taking possible variations item around their nominal values. First, two approaches considered based on stability radius calculation, ensure that radius, measured either Manhattan or Chebyshev norm, not below threshold. Then, complementary approach applied relative resiliency calculation. To solve optimality these problem, compact 0-1 linear programming formulation, also valid for standard introduced. Dantzig-Wolfe decomposition suggested in order provide set-cover reformulation stronger relaxation, but an exponential columns. Finally, integer optimal solutions, branch-and-price algorithm developed, whose relaxation formulation solved by dynamic column generation. Numerical experiments conducted adapted benchmark sets from literature. performance allows us investigate what protection against uncertainty offered approach, and at cost robustness.