LSE creators

Number of items: 94.
Article
  • Williams, H. Paul (2017). The dependency diagram of a mixed integer linear programme. Journal of the Operational Research Society, 68(7), 829-833. https://doi.org/10.1057/jors.2016.45
  • Williams, H. Paul, Hooker, J. N. (2016). Integer programming as projection. Discrete Optimization, 22(B), 291-311. https://doi.org/10.1016/j.disopt.2016.08.004
  • Williams, H. Paul (2015). The dependency diagram of a linear programme. Journal of the Operational Research Society, 67(3), 450-456. https://doi.org/10.1057/jors.2015.72
  • Hooker, J. N., Williams, H. Paul (2012). Combining equity and utilitarianism in a mathematical programming model. Management Science, 58(9), 1682-1693. https://doi.org/10.1287/mnsc.1120.1515
  • Williams, H. Paul (2011). The problem with integer programming. IMA Journal of Management Mathematics, 22(3), 213-230. https://doi.org/10.1093/imaman/dpq014
  • Williams, H. Paul (2007). Stanley Skewes and the Skewes number. Journal of the Royal Institution of Cornwall, 70-75.
  • Appa, Gautam, Williams, H. Paul (2006). A new framework for the solution of DEA models. European Journal of Operational Research, 172(2), 604-615. https://doi.org/10.1016/j.ejor.2004.09.051
  • Williams, H. Paul, Butler, Martin (2006). The allocation of shared fixed costs. European Journal of Operational Research, 170(2), 391-397. https://doi.org/10.1016/j.ejor.2004.07.046
  • Williams, H. Paul (2005). George B Dantzig, 1914–2005. Journal of the Operational Research Society, 56(12), 1349-1350. https://doi.org/10.1057/palgrave.jors.2602056
  • Butler, Martin, Williams, H. Paul (2002). Fairness versus efficiency in charging for the use of common facilities. Journal of the Operational Research Society, 53(12), 1324-1329. https://doi.org/10.1057/palgrave.jors.2601456
  • Williams, H. Paul, Yan, Hong (2001). Representations of the 'all_different' predicate of constraint satisfaction in integer programming. Informs Journal on Computing, 13(2), 96-103.
  • Williams, H. Paul (2000). The dual of a logical linear programme. Journal of Global Optimization, 18(2), 129-141. https://doi.org/10.1023/A:1008328500933
  • Williams, H. Paul, Munford, A. G. (1999). Formulae for the L0, L1 and L∞ norms. Journal of Statistical Computation and Simulation, 63(2), 121-141. https://doi.org/10.1080/00949659908548521
  • Williams, H. Paul, 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.
  • 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. https://doi.org/10.1016/S0377-2217(96)00236-6
  • Williams, H. Paul (1997). Integer programming and pricing revisited. IMA Journal of Mathematics Applied in Business and Industry, 8(3), 203-213. https://doi.org/10.1093/imaman/8.3.203
  • Williams, H. Paul, Kirby, D. (1997). Representing integral monoids by inequalities. Journal of Combinatorial Mathematics and Combinatorial Computing, 23, 87-95.
  • Butler, Martin, Williams, H. Paul, Yarrow, Leslie-Ann (1997). The two-period travelling salesman problem applied to milk collection in Ireland. Computational Optimization and Applications, 7(3), 291-306. https://doi.org/10.1023/A:1008608828763
  • Brailsford, S. C., Hubbard, P. M., Smith, B. M., Williams, H. Paul (1996). Organizing a social event: a difficult problem of combinatorial optimization. Computers and Operations Research, 23(9), 845-856. https://doi.org/10.1016/0305-0548(96)00001-9
  • Williams, H. Paul (1996). Duality in mathematics and linear and integer programming. Journal of Optimization Theory and Applications, 90(2), 257-278. https://doi.org/10.1007/BF02189998
  • Williams, H. Paul (1996). Constructing the value function for an Integer Linear Programme over a Cone. Computational Optimization and Applications, 6(1), 15-26. https://doi.org/10.1007/BF00248007
  • Williams, H. Paul (1996). The equivalence of two theorems of integer programming. Bulletin of the London Mathematical Society, 28(3), 311-316. https://doi.org/10.1112/blms/28.3.311
  • Williams, H. Paul (1995). Logic applied to integer programming and integer programming applied to logic. European Journal of Operational Research, 81(3), 605-616. https://doi.org/10.1016/0377-2217(93)E0359-6
  • Williams, H. Paul (1995). The Cornish caveman mathematician. Mathematical Intelligencer, 17(1), 34, 64. https://doi.org/10.1007/BF03024715
  • Rhodes, Frank, Williams, H. Paul (1995). Discrete subadditive functions as Gomory functions. Mathematical Proceedings of the Cambridge Philosophical Society, 117(03), 559-574. https://doi.org/10.1017/S0305004100073370
  • Williams, H. Paul (1994). An alternative explanation of disjunctive formulations. European Journal of Operational Research, 72(1), 200-203. https://doi.org/10.1016/0377-2217(94)90341-7
  • Williams, H. Paul (1993). How long is the coast of Cornwall? Mathematics Review, 3, 2-5.
  • Williams, H. Paul (1992). Solving systems of linear inequalities. Mathematical Medley, 20(1), 59-67.
  • Williams, H. Paul (1992). The elimination of integer variables. Journal of the Operational Research Society, 43(5), 387-393. https://doi.org/10.1057/jors.1992.65
  • Baston, V. J. D., Rahmouni, M. K., Williams, H. Paul (1991). The practical conversion of linear programmes to network flow models. European Journal of Operational Research, 50(3), 325-334. https://doi.org/10.1016/0377-2217(91)90264-V
  • Williams, H. Paul (1990). How important are models to operational research? IMA Journal of Mathematics Applied in Business and Industry, 2, 189-195.
  • Williams, H. Paul (1990). Optimisation and operational research. Bulletin of the Institute of Mathematics and Its Applications, 26, 76-85.
  • McKinnon, K. I. M., Williams, H. Paul (1989). Constructing integer programming models by the predicate calculus. Annals of Operations Research, 21, 227-245.
  • Williams, H. Paul (1987). Evolution, games theory and polyhedra. Journal of Mathematical Biology, 25(4), 393-409. https://doi.org/10.1007/BF00277164
  • Williams, H. Paul (1987). Linear and integer programming applied to the propositional calculus. Systems Research and Information Science, 2, 81-100.
  • Williams, H. Paul (1986). Fourier's method of linear programming and its dual. American Mathematical Monthly, 93(9), 681-695.
  • Day, R. E., 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. https://doi.org/10.1093/imaman/1.1.53
  • Williams, H. Paul (1984). A duality theorem for linear congruences. Discrete Applied Mathematics, 7(1), 93-103. https://doi.org/10.1016/0166-218X(84)90116-1
  • Williams, H. Paul (1984). Restricted vertex generation applied as a CRASHing procedure for linear programming. Computers and Operations Research, 11(4), 401-407. https://doi.org/10.1016/0305-0548(84)90041-8
  • Cheshire, M., McKinnon, K. I. M., Williams, H. Paul (1984). The efficient allocation of private contractors to public works. Journal of the Operational Research Society, 35(8), 705-709. https://doi.org/10.1057/jors.1984.146
  • Williams, H. Paul (1983). A characterisation of all feasible solutions to an integer program. Discrete Applied Mathematics, 5(1), 147-155. https://doi.org/10.1016/0166-218X(83)90024-0
  • Williams, H. Paul (1982). Models with network duals. Journal of the Operational Research Society, 33(2), 161-169. https://doi.org/10.1057/jors.1982.28
  • Williams, H. Paul (1981). Reallocating the cost of dependent decisions. Applied Economics, 13(1), 89-98. https://doi.org/10.1080/00036848100000039
  • Williams, H. Paul (1981). Mathematical modelling in management. Bulletin of the Institute of Mathematics and Its Applications, 17, 51-52.
  • Williams, H. Paul, Thomas, P. G. (1980). The Open University interactive system for integer programming. IUCC Bulletin, 2,
  • Williams, H. Paul (1979). Four examples of artless modelling. Omega, 7(2), 163-165. https://doi.org/10.1016/0305-0483(79)90104-X
  • Williams, H. Paul (1978). The reformulation of two mixed integer programming problems. Mathematical Programming, 14(1), 325-331. https://doi.org/10.1007/BF01588974
  • Williams, H. Paul (1977). Logical problems and integer programming. Bulletin of the Institute of Mathematics and Its Applications, 13, 18-20.
  • Williams, H. Paul (1976). Fourier-Motzkin elimination extension to integer programming problems. Journal of Combinatorial Theory, Series A, 21(1), 118-123. https://doi.org/10.1016/0097-3165(76)90055-8
  • Brearley, A. L., Mitra, G., Williams, H. Paul (1975). Analysis of mathematical programming problems prior to applying the simplex algorithm. Mathematical Programming, 8(1), 54-83. https://doi.org/10.1007/BF01580428
  • Williams, H. Paul (1975). The formulation of mathematical programming models. Omega, 3(5), 551-556. https://doi.org/10.1016/0305-0483(75)90028-6
  • Williams, H. Paul, Redwood, A. C. (1974). A structured linear programming model in the food industry. Operational Research Quarterly, 25(4), 517-527.
  • Williams, H. Paul (1974). Three integer programming models. ACM Sigmap Bulletin, 16, 35-41. https://doi.org/10.1145/1217031.1217038
  • Williams, H. Paul (1969). A formalisation of the arithmetic of the ordinals less than Wω. Notre Dame Journal of Formal Logic, 10(1), 77-89. https://doi.org/10.1305/ndjfl/1093893588
  • Williams, H. Paul (1968). The synthesis of logical nets consisting of NOR units. Computer Journal, 11(2), 173-176. https://doi.org/10.1093/comjnl/11.2.173
    • Book
  • Williams, H. Paul (2016). The Red River. Godrevy Press.
  • Williams, H. Paul (2013). Model building in mathematical programming. John Wiley & Sons.
  • Williams, H. Paul (2009). Logic and integer programming. Springer Berlin / Heidelberg.
  • Appa, Gautam, Pitsoulis, Leonidas, Williams, H. Paul (Eds.) (2006). Handbook on modelling for discrete optimization. Springer Berlin / Heidelberg.
  • Williams, H. Paul (1999). Model building in mathematical programming. John Wiley & Sons.
  • Williams, H. Paul (1993). Model solving in mathematical programming. John Wiley & Sons.
    • Chapter
  • Orman, A. J., Williams, H. Paul (2006). A survey of different integer programming formulations of the travelling salesman problem. In Kontoghiorghes, Erricos John, Gatu, Cristian (Eds.), Optimisation, Econometric and Financial Analysis (pp. 93-108). Springer Berlin / Heidelberg.
  • Williams, H. Paul (1998). Recent developments in combinatorial optimisation. In OR Keynote Papers 1998 . Operational Research Society (Great Britain).
  • Williams, H. Paul, Brailsford, S. C. (1996). Computational logic and integer programming. In Beasley, J. E. (Ed.), Advances in Linear and Integer Programming (pp. 249-281). Oxford University Press.
  • Smith, Barbara M., Brailsford, Sally C., Hubbard, Peter M., Williams, H. Paul (1995). The progressive party problem: integer linear programming and constraint programming compared. In Montanari, Ugo, Rossi, Francesca (Eds.), Principles and Practice of Constraint Programming: Proceedings of First International Conference, Cp '95, Cassis, France, Septem (pp. 36-52). Springer Berlin / Heidelberg. https://doi.org/10.1007/3-540-60299-2
  • Williams, H. Paul (1994). The contractor allocation problem: an integer programming problem that wasn't. In Ciriani, T., Leachman, R. (Eds.), Optimisation in Industry (pp. 25-32). John Wiley & Sons.
  • Williams, H. Paul (1989). Mathematical programming modelling. In Shahani, Arjan K., Stainton, Roy (Eds.), Tutorial Papers in Operational Research (pp. 41-56). Operational Research Society (Great Britain).
  • Williams, H. Paul (1987). Recent developments in mathematical programming. In Thomas, L. C. (Ed.), Recent Developments in Operational Research (pp. 33-44). Pergamon Press (Oxford, England).
  • Williams, H. Paul (1985). Model building in linear and integer programming. In Schittkowski, K. (Ed.), Proceedings of Nato Advanced Study Institute on Mathematical Programming (pp. 25-35). Springer Berlin / Heidelberg.
  • Williams, H. Paul (1983). A reduction procedure for linear and integer programming models. In Karwan, M. H., Lotfi, V., Telgen, J., Zionts, S. (Eds.), Redundancy in Mathematical Programming: a State-Of-The-Art Survey (pp. 87-107). Springer Berlin / Heidelberg.
  • Williams, H. Paul (1980). Integer programming. In Lederman, Walter, Vajda, Steven (Eds.), Handbook of Applicable Mathematics: Vol. 1, Algebra (pp. 339-390). John Wiley & Sons.
  • 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 (pp. 567-586). North-Holland.
  • Williams, H. Paul (1974). Experiments in the formulation of integer programming problems. In Balinski, M. L. (Ed.), Approaches to Integer Programming (pp. 180 - 197). Springer Berlin / Heidelberg. https://doi.org/10.1007/BFb0120686
    • Conference or Workshop Item
  • Williams, H. Paul (1998-07-01) Tutorials and recent reviews [Other]. 16th EURO Conference on Operational Analysis, Brussels, Belgium, BEL.
  • Williams, H. Paul (1986-11-01) Optimisation is best [Other]. Inaugural lecture as Professor of Operational Research, Southampton, United Kingdom, GBR.
  • Williams, H. Paul (1978-01-01) Model building in management science: is the model more important than the mathematics? [Other]. Inaugural lecture as Professor of Management Science, Edinburgh, United Kingdom, GBR.
    • Report
  • Williams, H. Paul (1973). Decision procedures in formal logic and mathematical programming algorithms. (Research report 73-5). Operational Research Group, University of Sussex.
  • Williams, H. Paul (1973). Simplifying linear programming problems. (Research report 73-2). Operational Research Group, University of Sussex.
    • Other
  • Williams, H. Paul (1976). Linear programming II: Open University unit for numerical computation course M351.
    • Online resource
  • Williams, H. Paul (1996). Obituary of Professor Steven Vajda.
    • Working paper
  • Williams, H. Paul, Hooker, J. N. (2014). Integer programming as projection. (Working Paper LSEOR 13.143). Management Science Group, Department of Management, The London School of Economics and Political Science.
  • Williams, H. Paul (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.
  • Williams, H. Paul (2013). The dependency diagram of a linearprogramme. (Working paper LSEOR 13.138). London School of Economics and Political Science.
  • Williams, H. Paul (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.
  • Williams, H. Paul (2010). What lies between + and x (and beyond)? (Operational Research working papers LSEOR 10.119). London School of Economics and Political Science.
  • Yan, Hong, 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.
  • 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.
  • Appa, Gautam, Argyris, N., 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.
  • Appa, Gautam, 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.
  • Williams, H. Paul (1989). A method of finding all equilibrium solutions of a 2-person matrix game. (Faculty of Mathematical Studies working papers OR22). Southampton University.
  • Williams, H. Paul (1988). An alternative form of the value function of an integer programme. (Faculty of Mathematical Studies working papers OR16). Faculty of Mathematical Studies, University of Southampton.
  • Williams, H. Paul (1987). A note: orthogonality in linear congruence duality. (Faculty of Mathematical Studies working papers OR9). University of Southampton.
  • Williams, H. Paul (1983). A duality relationship for integer programmes. (Department of Business Studies working papers 1/83). Department of Business Studies, University of Edinburgh.
  • Williams, H. Paul (1970). An algorithm for the solution of linear programming problems. (IBM working papers). IBM.