Approximate Solution Scheme for Inverse Bin-Packing Problem Subject to Decision Maker’s Preferences

Abstract

The problem of packing a maximal number of items in the given set of equal capacity bins subject to Decision Maker’s (DM’s) preferences over the items is under consideration. The solution of this problem must satisfy the following conditions: (1) the total weight of items in a bin is not to be greater than the bin capacity; and (2) for each unpacked item there are no packed items less preferable for DM, instead of which it may be packed without violating the capacity limit. The approximate solution scheme for this problem based on modified First Fit Decreasing algorithm is proposed.