Caractérisation, modélisation et algorithmes pour des problèmes de découpe guillotine

This thesis focuses on a two-dimensional cutting stock problem where guillotine constraint is required. Despite the fact that guillotine constraint was introduced at the very beginning of the cutting stock and bin packing research, no mathematical definition has been given. Then the purpose of the thesis is to characterize and model the guillotine constraint and to propose efficient algorithms to solve variants of the two-dimensional cutting stock. We first give a necessary and sufficient condition for a cutting pattern to be guillotine. And consequently we propose a polynomial algorithm to check this condition for any given pattern. Then we give a linear program that describes explicitly the guillotine constraint by means of the previous condition. Thereafter, we are interested in strip packing problem which consists of packing rectangular items of predetermined sizes into a strip of fixed width and infinite height. The aim is to find cutting pattern that minimizes the total height used and where guillotine constraint is required. Two constructive heuristics are proposed and tested on a great number of instances. The originality lies in the way of filling the shelves and of determining their heights. In the last part, we deal with a variant of the two-dimensional cutting stock, in which, we have an infinite number of rectangular sheets of raw material having identical width. The aim is to cut off a given set of items while minimizing the waste. One of the heuristics proposed previously was generalized and tested on a great number of instances