From time representation in scheduling to the solution of strip packing problems

We propose two mixed-integer linear programming based approaches for the 2-D orthogonal strip packing problem. Using knowledge from the alternative forms of time representation in scheduling formulations, we show how to efficiently combine three different concepts into the xand ydimensions. One model features a discrete representation on the x-axis (strip width) and a continuous representation with general precedence variables on the y-axis (strip height). The other features a full continuous-space representation with the same approach for the y-axis and a single non-uniform grid made up of slots for the x-axis. Through the solution of a set of twenty nine instances from the literature, we show that the former is a better approach, even when compared to three alternative MILP models ranging from a pure discrete-space to a pure continuous-space with precedence variables in both dimensions. All models are available in www.minlp.org.