Developing column generation approach to solve the rectangular two-dimensional single knapsack problem

The rectangular two-dimensional single knapsack problem (skp) consists of packing a fixed rectangular space (so-called pallet) with a subset of smaller rectangular shapes (so-called pieces) of different dimensions and without rotation. pieces have different values. the objective is to maximize the sum of the values of the pieces packed. this paper proposes a new method for solving rectangular two-dimensional skp based on the column generation approach. the mathematical formulation of the proposed model is the simplest of all present mathematical formulations in the the state-of-the art. the computational performance indicates that it is an effective method based on quality of solution.