Recently Bansal and Sviridenko [4] proved that for 2-dimensional Orthogonal Rectangle Bin Packing without rotations allowed there is no asymptotic PTAS, unless P = NP. We show that similar approximation hardness results hold for several rectangle packing and covering problems even if rotations by ninety degrees around the axes are allowed. Moreover, for some of these problems we provide explici...

In the generalized budgeted submodular set function maximization problem, we are given a ground of elements and bins. Each bin has its own cost each element depends on associated bin. The goal is to find subset along with an bins such that overall costs both at most budget, profit maximized. We present algorithm guarantees 12(1?1e?)-approximation, where ??1 approximation factor for sub-problem....

in this paper, a robust model presented is developed for hub covering flow problem in which hubs have capacity. this problem has two objective functions converting to a single-objective problem by using weighting method. firstly, the problem will be formulated in a certain case. then, by considering the demand as a non-random variable, it will be modeled by robust optimization. finally, by usin...

the set covering problem (scp) is a well-known combinatorial optimization problem. this paper investigates development of a local branching approach for the scp. this solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. the algorithm parameters are tuned by design of experiments approach. the proposed method is te...

This paper studies a variant of the three-dimensional bin packing problem (3D-BPP), where the bin height can be adjusted to the cartons it packs. The bins and cartons to be packed are assumed rectangular in shape. The cartons are allowed to be rotated into any one of the six positions that keep the carton edges parallel to the bin edges. This greatly increases the difficulty of finding a good s...