Sharif University of Technology Scientia Iranica 1026-3098 24 6 2017 12 01 Developing Column Generation Approach to Solve the Rectangular Two-dimensional Single Knapsack Problem 3287 3296 4401 10.24200/sci.2017.4401 EN Mohammad Ali Hatefi Department of Economics & Energy Management, Petroleum University of Technology (PUT) Sattarkhan Ave., Khosrow Jonoubi St., Tehran, Iran Journal Article 2014 08 20 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. Mathematical formulation of the proposed model is simplest than the present mathematical formulations in the state-of-the art. The computational performance indicates that it is an effective method in the view of quality of solution. https://scientiairanica.sharif.edu/article_4401_7bdf3d25f09bf54b4efe58558bc41422.pdf