Abstract—we consider a special class of the bin packing problems having the following distinctive feature; items are grouped based on their subset of elements. Splitting of group is to be minimized while compatibility of items placed in same bins is of utmost priority.

The problem, denoted as the fragmentable group and item bin packing with Item compatibility preferences, has a very interesting structure and models real life application ranging from industrial, educational and the financial sectors.

According to our knowledge, the FGIBPCP has never been tackled in the literature. In this paper we addressed if for the first time. We examined the theoretical properties which has some resemblance to some seen in the literature. Then we elaborate it to dense a mathematical model.

A new offline heuristic we referred to as RHEMA 1 heuristic was proposed and was used to search for solution and implemented manually for small size problem. It yielded a better result than that of an online algorithm. Further experimentation with will be carried out to analyze the performance of the solution in the future research.

Keywords— Bin packing; heuristic; group; item compatibility; subset.