Intl. Trans. in Op. Res. 00 (2019) 1–41 DOI: 10.1111/itor.12687 INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH Constrained two-dimensional guillotine cutting problem: upper-bound review and categorization Mauro Russo a , Maurizio Boccia b , Antonio Sforza a and Claudio Sterle a,b a Department of Electrical Engineering and Information Technology, University “Federico II” of Naples, Naples 80138, Italy b Istituto di analisi dei sistemi ed informatica Antonio Ruberti, Consiglio Nazionale delle Ricerche, Rome 00185, Italy E-mail: ma.russo@unina.it [Russo]; maurizio.boccia@unina.it [Boccia]; sforza@unina.it [Sforza]; claudio.sterle@unina.it [Sterle] Received 13 December 2018; received in revised form 2 May 2019; accepted 14 May 2019 Abstract In the two-dimensional (2D) cutting (2DC) problem, a large rectangular sheet has to be dissected into smaller rectangular pieces with the aim of maximizing the total profit associated with the extracted pieces. When the number of copies of each piece to be extracted is bounded, it is referred to as constrained 2DC (C2DC) problem. The C2DC has been widely studied by the operations research community for its applications and theoretical issues. In this work, we recall the best exact and heuristic solving approaches for the C2DC and we provide a review and a categorization of the available upper bounds. We also discuss improvements and combinations of these upper bounds and give directions for their effective exploitation. Finally, we demonstrate the loss of accuracy of several exact methods present in literature because of the effect of the used antiredundancy strategies on the implemented bounding criteria. This work, based on more than 90 contributions, has a twofold target. For researchers working in C2DC, it provides a useful insight on the topic. For expert practitioners, it represents a systematic collection of the main findings and achievements, posing also the basis for future research. Keywords: cutting problems; cutting stock; combinatorial optimization; integer programming; literature review; upper- bound categorization; bounding strategies 1. Introduction In the wide class of cutting and packing (C&P) problems, a strong interest has been shown in the operations research community for the two-dimensional (2D) cutting (2DC) problem according to the huge number of real applications, mainly in the production of primary goods such as glass, wood, metal, paper, and plastic, but also in Very Large Scale Integration (VLSI) circuits, resource scheduling, transportation, and others. Besides, 2DC has been also largely combined with other C  2019 The Authors. International Transactions in Operational Research C  2019 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA.