Çatışmalarla açık uçlu kutulama problemi

In this thesis study, we focus on a new variant of the famous Bin Packing Problem (BPP) called the Open-End Bin Packing Problem with Conflicts (OEBPPC) which combines the Open-End Bin Packing Problem (OEBPP) and the Bin Packing Problem with Conflicts (BPPC). In OEBPPC, the aim is to pack a set of items into the least number of bins. However, the bin capacity is allowed to be exceeded only by the last item packed into the bin, and there exist conflicts between some item pairs; they cannot be packed into the same bin. We introduce a mathematical formulation and propose lower bounding procedures for our problem. We propose a metaheuristic algorithm, namely Variable Neighborhood Search (VNS), to approach the optimal solution through systematic changes and improvements in the solution. We generate different sets of instances by adapting some instances from the literature to our problem. We compare the performance of our metaheuristic algorithm both against the best lower bound and other algorithms we adapted from the literature as benchmark algorithms. We observe that our proposed metaheuristic outperforms the best benchmark algorithm in 74% of the instances with varying features.