We consider a sequential version of the classical bin packing problem in which items are received one by one. Before the size of the next item is revealed, the decision maker needs to decide whether the next item is packed in the currently open bin or the bin is closed and a new bin is opened. If the new item doesn’t fit, it is lost. If a bin is closed, the remaining free space in the bin accou...

In the dual bin packing problem, the objective is to assign items of given size to the largest possible number of bins, subject to the constraint that the total size of the items assigned to any bin is at least equal to 1. We carry out a probabilistic analysis of this problem under the assumption that the items are drawn independently from the uniform distribution on [0, 11 and reveal the conne...

The ordered open-end bin packing problem is a variant of the bin packing problem in which the items to be packed are sorted in a given order and the capacity of each bin can be exceeded by the last item packed into the bin. We present a branch-and-price algorithm for its exact optimization. The pricing subproblem is a special variant of the binary knapsack problem, in which the items are ordere...

ONLINE BIN STRETCHING is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for ONLINE BIN STRETCHING with a stretching factor of 1.5 for any number of bins. We build o...

The 2297 strain of Bacillus sphaericus produces a crystal of the Bin (binary) toxin that is approximately fourfold larger than that of strain 2362, the strain currently used in VectoLex, a commercial mosquito larvicide. Comparison of the regions downstream from the bin operon in these two strains showed that strain 2362 contained a 1.6-kb region with four orf genes not found in strain 2297. Ins...

BACKGROUND Hepatocellular carcinoma is difficult to diagnose early, and most patients are already in the late stages of the disease when they are admitted to hospital. The total 5-year survival rate is less than 5%. Recent studies have showed that brucine has a good anti-tumor effect, but high toxicity, poor water solubility, short half-life, narrow therapeutic window, and a toxic dose that is ...

In this paper, we present an O(n1ogn) algorithm to compute a tighter lower bound for the one-dimensional bin packing problem. We have simulated the algorithm on randomly generated bin packing problems with item sizes drawn uniformly from (a, b], where 0 5 a < b 5 B and B is bin size. Using our lower bound, the average error of BFD is less than 2%. For a + b > B, the error is less than 0.003%. K...

Following the work of Anily et al., we consider a variant of bin packing, called BIN PACKING WITH GENERAL COST STRUCTURES (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic bin packing problem, a set of one-dimensional items is to be assigned to subsets of total size at most 1, that is, to be packed into unit sized bins. However,...

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of 1.5 for any number of bins. We build o...

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as the optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of 1.5 for any number of bins. We also s...