Approximate solution scheme for inverse bin-packing problem subject to decision making preferences

The problem of packing maximal number of items in the given set of equal capacity bins while taking into account DM’s preferences is under consideration. The solution of this problem must satisfy to the following conditions: (1) the total weight of items in each been is not greater than its capacity, and (2) for each unpacked item there is none packed items less preferable for DM instead of which it may be packed without violation the capacity constraint. The approximate solution scheme for this problem based on modified First Fit Decreasing algorithm is proposed.