A MILP model for N-dimensional allocation

This paper presents a Mixed Integer Linear Programming (MILP) model for the solution of N-dimensional allocation problems. The applicability of the model is presented and demonstrated through some illustrative examples with different numbers of dimensions. Several problems, previously presented in the literature, are solved using the proposed model, such as, one-dimensional scheduling problems, two-dimensional cutting problems, as well as plant layout problems and three-dimensional packing problems. Additionally, some problems in four dimensions are presented and solved using the considered model. The presented model is applicable to a wide variety of allocation problems as it offers a general framework for modelling allocation problems with any given number of continuous or discrete dimensions. The presented problems are formulated as MILP problems where the first four dimensions usually are continuous spatial and time dimensions. Additional dimensions are often of a discrete nature.