Other Publications

Articles in Books

1. L. Galli & A.N. Letchford: Convex hulls for non-convex mixed-integer quadratic programs in the McCormick space. To appear in G. Fasano et al. (eds) Optimization and Decision Science for Sustainability. Accepted subject to minor revision June 2026. Revised July 2026.
2. L. Galli & A.N. Letchford (2026) On a hierarchy of polytopes for integer quadratic programming. In M. Barbato, N. Bianchessi & A. Boggio Tomasaz (eds) Mathematics, Algorithms and the Art and Science of Decision-Making. Cham: Springer.
3. R.W. Eglese & A.N. Letchford (2024) Arc routing problems. In P.M. Pardalos & O.A. Prokopyev (eds.) Encyclopedia of Optimization (3rd edn). Cham: Springer.
4. A.N. Letchford (2022) The Boolean quadric polytope. In A.P. Punnen (ed.) The Quadratic Unconstrained Binary Optimization Problem: Theory, Algorithms and Applications, pp. 97–120. Cham: Springer.
5. A.N. Letchford, Q. Ni & Z. Zhong (2018) A heuristic for maximising energy efficiency in OFDMA systems with QoS constraints. In J. Lee, G. Rinaldi & A.R. Mahjoub (eds.) Combinatorial Optimization: 5th International Symposium, pp. 303–312. Lecture Notes in Computer Science, vol. 10856. Berlin: Springer. (PDF)
6. A.N. Letchford, F. Marzi, F. Rossi & S. Smriglio (2016) Strengthening Chvátal-Gomory cuts for the stable set problem. In R. Cerulli, S. Fujishige & A.R. Mahjoub (eds.), Combinatorial Optimization: 4th International Symposium, pp. 201–212. Lecture Notes in Computer Science, vol. 9849. Berlin: Springer. (PDF)
7. L. Galli, K. Kaparis & A.N. Letchford (2012) Gap inequalities for the max-cut problem: a cutting-plane algorithm. In A.R. Mahjoub, V. Markakis, I. Milis & V.T. Paschos (eds.) Combinatorial Optimization: 2nd International Symposium, pp. 178–188. Lecture Notes in Computer Science, vol. 7422. Berlin: Springer. (PDF)
8. M. Giandomenico, A.N. Letchford, F. Rossi & S. Smriglio (2011) A new approach to the stable set problem based on ellipsoids. In O. Günlük & G.J. Woeginger (eds.) Integer Programming and Combinatorial Optimization XV, pp. 223–234. Lecture Notes in Computer Science, vol. 6655. Heidelberg: Springer. (PDF)
9. K. Kaparis & A.N. Letchford (2010) Cover inequalities. In J.J. Cochran et al. (eds.) Encyclopedia of Operations Research and Management Science, vol. 2, pp. 1074–1080. New York: Wiley. (PDF)
10. A.N. Letchford & A. Lodi (2010) Mathematical programming approaches to the traveling salesman problem. In J.J. Cochran et al. (eds.) Encyclopedia of Operations Research and Management Science, vol. 5, pp. 3125–3132. New York: Wiley. (PDF)
11. A.N. Letchford (2010) Integer quadratic quasi-polyhedra. In F. Eisenbrand & B. Shepherd (eds.) Integer Programming and Combinatorial Optimization XIV, pp. 258–270. Lecture Notes in Computer Science, vol. 6080. Berlin: Springer. (PDF)
12. R.W. Eglese & A.N. Letchford (2009) The general routing problem. In C.H. Floudas & P.M. Pardalos (eds.) Encyclopedia of Optimization (2nd edn), pp. 1252–1254. Boston, MA: Springer. (PDF)
13. A.N. Letchford & M.M. Sørensen (2008) Binary positive semidefinite matrices and associated integer polytopes. In A. Lodi, A. Panconesi & G. Rinaldi (eds.) Integer Programming and Combinatorial Optimization XIII, pp. 125–139. Lecture Notes in Computer Science, vol. 5035. Berlin: Springer. (PDF)
14. A.N. Letchford, G. Reinelt & D.O. Theis (2004) A faster exact separation algorithm for blossom inequalities. In G. Nemhauser & D. Bienstock (eds.) Integer Programming and Combinatorial Optimization X, pp. 196–205. Lecture Notes in Computer Science, vol. 3064. Berlin: Springer. (PDF)
15. A.N. Letchford & A. Lodi (2003) An augment-and-branch-and-cut framework for mixed 0-1 programming. In M. Jünger, G. Reinelt & G. Rinaldi (eds.) Combinatorial Optimization: Eureka, You Shrink!, pp. 119–133. Lecture Notes in Computer Science, vol. 2570. Berlin: Springer. (PDF)
16. A.N. Letchford & A. Lodi (2002) Polynomial-time separation of simple comb inequalities. In W.J. Cook & A.S. Schulz (eds.) Integer Programming and Combinatorial Optimization IX, pp. 93–108. Lecture Notes in Computer Science, vol. 2337. Berlin: Springer. (PDF)
17. R.W. Eglese & A.N. Letchford (2001) The general routing problem. In C.H. Floudas & P.M. Pardalos (eds.) Encyclopedia of Optimization, pp. 746–747. Dordrecht: Kluwer. (PDF)
18. R.W. Eglese & A.N. Letchford (2000) Polyhedral theory for arc routing problems. In M. Dror (ed.) Arc Routing: Theory, Solutions and Applications, pp. 199–230. Dordrecht: Kluwer. (PDF)
19. A. Caprara, M. Fischetti & A.N. Letchford (1999) On the separation of maximally violated mod-k cuts. In G. Cornuéjols, R.E. Burkard & G.J. Woeginger (eds.) Integer Programming and Combinatorial Optimization VII, pp. 87–98. Lecture Notes in Computer Science, vol. 1610. Berlin: Springer. (PDF)

Editorials

• A.N. Letchford, J.B. Lasserre, P.A. Parrilo & D. Steurer (2015) Polynomial optimisation (Editorial). Math. Program., 151(2), 375–377. (PDF)
• A. Clark, R.W. Eglese, A.N. Letchford & M.B. Wright (2008) Combinatorial optimisation (Editorial). Discr. Appl. Math., 156(3), 289–290. (PDF)
• J. Lee & A.N. Letchford (2007) Mixed integer programming (Editorial). Discr. Optim., 4(1), 1–2. (PDF)

Book Reviews

• A.N. Letchford & J. Mareček (2015) Review of "Integer Programming" by Conforti et al. In: Interfaces, 45(5), 481–482. (PDF)
• A.N. Letchford (2012) Review of "The Linear Ordering Problem: Exact and Heuristic Methods in Combinatorial Optimization" by Martí & Reinelt. Interfaces, 42(3), 324–325. (PDF)
• A.N. Letchford & A. Lodi (2007) Review of "The Traveling Salesman Problem: A Computational Study" by Applegate et al. In: 4OR: Quart. J. Oper. Res., 5(4), 315–317. (PDF)
• A.N. Letchford (2004) Review of "Introduction to the Theory of Cooperative Games" by Peleg & Sudholter. J. Oper. Res. Soc., 55(7), 787–788. (PDF)
• A.N. Letchford (2004) Review of "The Vehicle Routing Problem" by Toth & Vigo. Oper. Res. Lett., 32, 392–393. (PDF)
• A.N. Letchford (2002) Review of "Approximation Algorithms" by Vazirani. J. Oper. Res. Soc., 53(7), 807–808. (PDF)
• A.N. Letchford (2000) Review of "Model Building in Mathematical Programming" by Williams. J. Oper. Res. Soc., 51(10), 1212–1213. (PDF)
• A.N. Letchford (2000) Review of "Theory of Linear and Integer Programming" by Schrijver. J. Oper. Res. Soc., 51(7), 892–893. (PDF)

Mathematical Reviews

• #2828758 (2012): Projecting systems of linear inequalities with binary variables.
• #2828758 (2012): The Chvátal-Gomory closure of a strictly convex body.
• #2764343 (2011): Orbital branching.
• #2560536 (2011): On the Chvátal rank of linear relaxations of the stable set polytope.
• #2679998 (2011): On the dominant of the s-t cut polytope: vertices, facets and adjacency.
• #2609619 (2010): Extended formulations in combinatorial optimization.
• #2600658 (2010): Minimal inequalities for an infinite relaxation of integer programs.
• #2573497 (2010): Gear composition of stable set polytopes and G-perfection.
• #2533755 (2010): Coefficient strengthening: a tool for reformulating mixed-integer programs.
• #2511722 (2010): Applying mod-k-cuts for solving linear ordering problems.
• #2520406 (2009): MIR closures of polyhedral sets.
• #2505741 (2009): Generalized mixed integer rounding inequalities: facets for infinite group polyhedra.
• #2469128 (2009): A note on the continuous mixing set.
• #2437266 (2009): Local cuts revisited.
• #2411399 (2008): FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension.
• #2375482 (2008): Projected Chvátal-Gomory cuts for mixed integer linear programs.
• #2363379 (2008): On clique separators, nearly chordal graphs, and the maximum weight stable set problem.
• #2348000 (2008): A branch-and-cut algorithm for a resource-constrained scheduling problem.
• #2317860 (2008): New cutting-planes for the time and/or precedence-constrained ATSP and directed VRP.
• #2333324 (2007): Using critical sets to solve the maximum independent set problem.
• #2320128 (2007): Optimization with binet matrices.
• #2299689 (2007): A new min-cut max-flow ratio for multicommodity flows.
• #2292489 (2007): Using mixed-integer programming to solve power grid blackout problems.
• #2289774 (2007): Integer programming formulations for the two 4-hop constrained paths problem.

Miscellaneous

• P. Date, A.N. Letchford, D. Onkal, A.-L. Sachs & A. Syntetos (2025) Mathematics of operational research conference. Mathematics Today, 61(4), 101.
• D. Tilley, A.N. Letchford, A. Syntetos, R. Misener & K. Liu (2023) The 4th IMA and OR Society conference on the mathematics of operational research: thoughts from the committee. IFORS Newsletter, 18(3), 35–37.
• A.N. Letchford, K. Liu, R. Misener, A. Syntetos & D. Tilley (2023) The mathematics of operational research. Mathematics Today, 59(4), 103.
• J. Fliege, A.N. Letchford & D. Tilley (2021) Maths of OR — reflections from the committee. Mathematics Today, 57(4), 115.
• A.N. Letchford (2016) NATCOR: Ten years of doctoral training in OR. IFORS Newsletter, 10(4), 10–11.
• N. Bansal et al. (2013) Alberto Caprara (1968-2012): Scientific Contributions. Optima (Newsletter of the Mathematical Optimization Society), 91, 1–11. (PDF)
• M. Giandomenico, A.N. Letchford, F. Rossi & S. Smriglio (2013) Approximating the Lovász theta function with the subgradient method. Elec. Notes in Discr. Math., 41, 157–164. (Special issue devoted to INOC 2013.) (PDF)
• A. Caprara, A.N. Letchford & J.J. Salazar (2010) Lower bounds for the minimum linear arrangement of a graph. Elec. Notes in Discr. Math., 36, 843–849. (Special issue devoted to ISCO 2010.)
• A.R.S. Amaral, A. Caprara, A.N. Letchford & J.J. Salazar (2008) A new lower bound for the minimum linear arrangement of a graph. Elec. Notes in Discr. Math., 30, 87–92. (Special issue devoted to LAGOS 2007.)
• D.D. Clarke & A.N. Letchford (1995) Rules from behaviour: the use of a computational 'rule-finder' as a tool for social psychology. Newsletter of the British Psychological Society, Social Psychology Section, 33, 4–13.

PhD Thesis:

Polyhedral Results for Some Constrained Arc-Routing Problems.

Awarded at Lancaster University on 31st January 1997. Examines integer programming formulations, valid inequalities and algorithms for four 'Arc Routing Problems'. (PDF)

Last update: July 2026.

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