Williams, Paul

Williams, H. Paul (2016) The dependency diagram of a mixed integer linear programme Journal of the Operational Research Society. ISSN 0160-5682

Williams, H. Paul (2016) The Red River Godrevy Press . ISBN 9781533177964

Williams, H. Paul (2013) Model building in mathematical programming 5th, Wiley. ISBN 9781118443330

Williams, H. P. (2013) The dependency diagram of a mixed integer linear programme Working paper, LSEOR 13.139. Management Science Group, Department of Management, The London School of Economics and Political Science, London, UK.

Williams, H. P. (2013) The general solution of a mixed integer linear programme over a cone Working paper, LSEOR 13.140. Management Science Group, Department of Management, The London School of Economics and Political Science, London, UK.

Yan, Hong and Williams, H. Paul (2007) Convex hull representations of the at least predicate of constraint satisfaction Operational Research working papers, LSEOR 07.97. Operational Research Group, London School of Economics and Political Science, London, UK. ISBN 9780853280538

Williams, H. Paul (2007) A method for finding all solutions of a Linear Complementarity Problem Operational Research working papers, LSEOR 07.96. Operational Research Group, Department of Management, London School of Economics and Political Science, London, UK. ISBN 9780853280521

Orman, A. J. and Williams, H. Paul (2006) A survey of different integer programming formulations of the travelling salesman problem In: Kontoghiorghes, Erricos John and Gatu, Cristian, (eds.) Optimisation, Econometric and Financial Analysis. Advances in computational management science, 9 (9). Springer, Berlin, Germany, 93-108. ISBN 9783540366256

Williams, H. Paul and Butler, Martin (2006) The allocation of shared fixed costs European Journal of Operational Research, 170 (2). 391-397. ISSN 0377-2217

Appa, Gautam and Argyris, N. and Williams, H. Paul (2006) A methodology for cross-evaluation in DEA Operational Research working papers, LSEOR 06.81. Operational Research Group, Department of Management, London School of Economics and Political Science, London, UK. ISBN 0753017032

Appa, Gautam and Williams, H. Paul (2006) A new framework for the solution of DEA models European Journal of Operational Research, 172 (2). 604-615. ISSN 0377-2217

Appa, Gautam and Williams, H. Paul (2002) A formula for the solution of DEA models Operational Research working papers, LSEOR 02.49. Department of Operational Research, London School of Economics and Political Science, London, UK.

Williams, H. Paul and Munford, A. G. (1999) Formulae for the L0, L1 and L∞ norms Journal of Statistical Computation and Simulation, 63 (2). 121-141. ISSN 0094-9655

Williams, H. Paul (1998) Recent developments in combinatorial optimisation In: OR Keynote Papers 1998. The Operational Research Society, Birmingham, UK.

Williams, H. Paul and Wilson, John M. (1998) Connections between integer linear programming and constraint logic programming: an overview and introduction to the cluster of articles Informs Journal on Computing, 10 (3). 261-264. ISSN 1091-9856

Williams, H. Paul (1997) The splitting of variables and constraints in the formulation of integer programming models European Journal of Operational Research, 100 (3). 623-628. ISSN 0377-2217

Williams, H. Paul (1997) Integer programming and pricing revisited IMA Journal of Mathematics Applied in Business and Industry, 8 (3). 203-213. ISSN 0953-0061

Butler, Martin and Williams, H. Paul and Yarrow, Leslie-Ann (1997) The two-period travelling salesman problem applied to milk collection in Ireland Computational Optimization and Applications, 7 (3). 291-306. ISSN 0926-6003

Williams, H. Paul and Brailsford, S. C. (1996) Computational logic and integer programming In: Beasley, J. E., (ed.) Advances in Linear and Integer Programming . Oxford lecture series in mathematics and its applications (4). Oxford University Press, Oxford, UK, 249-281. ISBN 9780198538561

Williams, H. Paul (1996) The equivalence of two theorems of integer programming Bulletin of the London Mathematical Society, 28 (3). 311-316. ISSN 0024-6093

Williams, H. Paul (1996) Duality in mathematics and linear and integer programming Journal of Optimization Theory and Applications, 90 (2). 257-278. ISSN 0022-3239

Williams, H. Paul (1996) Constructing the value function for an Integer Linear Programme over a Cone Computational Optimization and Applications, 6 (1). 15-26. ISSN 0926-6003

Brailsford, S. C. and Hubbard, P. M. and Smith, B. M. and Williams, H. Paul (1996) Organizing a social event: a difficult problem of combinatorial optimization Computers and Operations Research, 23 (9). 845-856. ISSN 0305-0548

Rhodes, Frank and Williams, H. Paul (1995) Discrete subadditive functions as Gomory functions Mathematical Proceedings of the Cambridge Philosophical Society, 117 (03). 559-574. ISSN 0305-0041

Williams, H. Paul (1995) Logic applied to integer programming and integer programming applied to logic European Journal of Operational Research, 81 (3). 605-616. ISSN 0377-2217

Smith, Barbara M. and Brailsford, Sally C. and Hubbard, Peter M. and Williams, H. Paul (1995) The progressive party problem: integer linear programming and constraint programming compared In: Montanari, Ugo and Rossi, Francesca, (eds.) Principles and Practice of Constraint Programming: Proceedings of First International Conference, Cp '95, Cassis, France, Septem. Lecture notes in computer science (976). Springer, Berlin, Germany, 36-52. ISBN 9783540602996

Williams, H. Paul (1994) An alternative explanation of disjunctive formulations European Journal of Operational Research, 72 (1). 200-203. ISSN 0377-2217

Williams, H. Paul (1993) How long is the coast of Cornwall? Mathematics Review, 3. 2-5. ISSN 0957-1280

Williams, H. Paul (1992) The elimination of integer variables Journal of the Operational Research Society, 43 (5). 387-393. ISSN 0160-5682

Williams, H. Paul (1990) How important are models to operational research? IMA Journal of Mathematics Applied in Business and Industry, 2. 189-195. ISSN 0953-0061

Williams, H. Paul (1989) Mathematical programming modelling In: Shahani, Arjan K. and Stainton, Roy, (eds.) Tutorial Papers in Operational Research. Operational Research Society, Birmingham, UK, 41-56.

McKinnon, K. I. M. and Williams, H. Paul (1989) Constructing integer programming models by the predicate calculus Annals of Operations Research, 21. 227-245. ISSN 0254-5330

Williams, H. Paul (1987) Linear and integer programming applied to the propositional calculus Systems Research and Information Science, 2. 81-100. ISSN 0882-3014

Williams, H. Paul (1987) A note: orthogonality in linear congruence duality Faculty of Mathematical Studies working papers , OR9. University of Southampton, Southampton, UK.

Williams, H. Paul (1987) Evolution, games theory and polyhedra Journal of Mathematical Biology, 25 (4). 393-409. ISSN 0303-6812

Williams, H. Paul (1986) Optimisation is best. In: Inaugural lecture as Professor of Operational Research, Nov 1986, University of Southampton

Day, R. E. and Williams, H. Paul (1986) MAGIC: The design and use of an interactive modelling language for mathematical programming IMA Journal of Management Mathematics, 1 (1). 53-65. ISSN 1471-678X

Williams, H. Paul (1984) Restricted vertex generation applied as a CRASHing procedure for linear programming Computers and Operations Research, 11 (4). 401-407. ISSN 0305-0548

Cheshire, M. and McKinnon, K. I. M. and Williams, H. Paul (1984) The efficient allocation of private contractors to public works Journal of the Operational Research Society, 35 (8). 705-709. ISSN 0160-5682

Williams, H. Paul (1983) A reduction procedure for linear and integer programming models In: Karwan, M. H. and Lotfi, V. and Telgen, J. and Zionts, S., (eds.) Redundancy in Mathematical Programming: a State-Of-The-Art Survey. Lecture notes in economics and mathematical systems (206). Springer-Verlag, Berlin, Germany, 87-107. ISBN 0387115528

Williams, H. Paul (1983) A characterisation of all feasible solutions to an integer program Discrete Applied Mathematics, 5 (1). 147-155. ISSN 0166-218X

Williams, H. Paul (1981) Reallocating the cost of dependent decisions Applied Economics, 13 (1). 89-98. ISSN 0003-6846

Williams, H. Paul (1980) Integer programming In: Lederman, Walter and Vajda, Steven, (eds.) Handbook of Applicable Mathematics: Vol. 1, Algebra. Wiley, Chichester, UK, 339-390. ISBN 0471277045

Williams, H. Paul (1979) The economic interpretation of duality for practical mixed integer programming models In: Prékopa, A., (ed.) Survey of Mathematical Programming : Proceedings of the 9th International Mathematical Programming Symposium, Budapest, August 2. North Holland, Amsterdam, The Netherlands, 567-586. ISBN 0444850333

Williams, H. Paul (1978) The reformulation of two mixed integer programming problems Mathematical Programming, 14 (1). 325-331. ISSN 0025-5610

Williams, H. Paul (1976) Fourier-Motzkin elimination extension to integer programming problems Journal of Combinatorial Theory, Series A, 21 (1). 118-123. ISSN 0097-3165

Brearley, A. L. and Mitra, G. and Williams, H. Paul (1975) Analysis of mathematical programming problems prior to applying the simplex algorithm Mathematical Programming, 8 (1). 54-83. ISSN 0025-5610

Williams, H. Paul (1974) Three integer programming models ACM Sigmap Bulletin, 16. 35-41. ISSN 1931-1184

Williams, H. Paul and Redwood, A. C. (1974) A structured linear programming model in the food industry Operational Research Quarterly, 25 (4). 517-527. ISSN 0030-3623

Williams, H. Paul (1973) Decision procedures in formal logic and mathematical programming algorithms Research report, 73-5. Operational Research Group, University of Sussex, Brighton, UK.