More on ordered open end bin packing

We consider the Ordered Open End Bin Packing problem. Items of sizes in (0, 1] are presented one by one, to be assigned bins this order. An item can any bin for which current total size is strictly below 1. This means also that overloaded its last packed item. improve lower and upper bounds on asymptotic competitive ratio online case. Specifically, we design first algorithm whose 2, value close bound. contrast best possible absolute ratio, equal 2. study offline problem where sequence items known advance, while still based their order sequence. For scenario, an polynomial time approximation scheme.