### Title: Combined cutting stock and scheduling: a matheuristic approach

Authors: Nuno Braga; Cláudio Alves; Rita Macedo; José Valério De Carvalho

Addresses: Centro Algoritmi, Escola de Engenharia, Universidade do Minho, 4710-057 Braga, Portugal ' Centro Algoritmi, Escola de Engenharia, Universidade do Minho, 4710-057 Braga, Portugal ' Laboratoire LEM, Université Lille-3, 59653 Villeneuve d'Ascq cedex, France ' Centro Algoritmi, Escola de Engenharia, Universidade do Minho, 4710-057 Braga, Portugal

Abstract: The efficient solution of practical problems combining both cutting stock and scheduling aspects has motivated the development of several approaches described recently in the literature. These problems consist in determining a cutting plan that minimises both the waste generated by cutting the stock rolls and the tardiness related to the delivery of items later than their specified due date. In this paper, we review two exact formulations proposed recently, which differ essentially on their strength and size. The first one is a compact model, which can be strengthened using knapsack-based inequalities. The other is a pseudo-polynomial model based on arc flows. Additionally, we explore a matheuristic approach based on a variant of the arc flow model that proved to be effective for solving medium scale instances. Computational results are provided and discussed at the end of the paper.

Keywords: combinatorial optimisation; integer programming; cutting stock; scheduling; integrated optimisation; matheuristics; compact formulations; pseudo-poynomial formulations; valid inequalities; computational experiments; cutting planning; waste generation; stock rolls; tardiness; due dates; knapsack-based inequalities; arc flows.

International Journal of Innovative Computing and Applications, 2016 Vol.7 No.3, pp.135 - 146

Available online: 01 Sep 2016 *