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 August 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: August 2026.

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