Giorgio Fasano This chapter examines the problem of packing tetris-like items, orthogonally, with the possibility of rotations, into a convex domain, in the presence of additional conditions. An MILP (Mixed Integer Linear Programming) and an MINLP (Mixed Integer Nonlinear Programming) models, previously studied by the author, are surveyed. An efficient formulation of the objective function, aimed at … Read more
The International Space Station poses very challenging issues from the logistic point of view. Its on-orbit stay is to be significantly extended in the near future and ever increasing experimental activity in microgravity is expected, giving rise to a renewed interest in the related optimization aspects. A permanent logistic support is necessary to guarantee its … Read more
This work is inspired by very challenging issues arising in space logistics. The problem of scheduling a number of activities, in a given time elapse, optimizing the resource exploitation is discussed. The available resources are not constant, as well as the request, relative to each job. The mathematical aspects are illustrated, providing a time-indexed MILP … Read more
The search for a better understanding of complex systems calls for quantitative model development. Within this development process, model fitting to observational data (calibration) often plays an important role. Traditionally, local optimization techniques have been applied to solve nonlinear (as well as linear) model calibration problems numerically: the limitations of such approaches in the nonlinear … Read more
This article extends a previous work focused on a mixed integer programming (MIP) based heuristic approach, aimed at solving non-standard three-dimensional problems with additional conditions. The paper that follows considers a mixed integer non-linear (MINLP) reformulation of the previous model, to improve the former heuristic, based on linear relaxation. The approach described herewith is addressed, … Read more
This paper is the continuation of a previous work (Fasano 2004), dedicated to a MIP formulation for non-standard three-dimensional packing issues, with additional conditions. The Single Bin Packing problem (Basic Problem) is considered and its MIP formulation shortly surveyed, together with some possible extensions, including balancing, tetris-like items and non-standard domains. A MIP-based heuristic is … Read more
This paper considers packing problems with balancing conditions and items consisting of clusters of parallelepipeds (mutually orthogonal, i.e. tetris-like items). This issue is quite frequent in space engineering and a real-world application deals with the Automated Transfer Vehicle project (funded by the European Space Agency), at present under development. A Mixed Integer Programming (MIP) approach … Read more