Abstract
The main objective of this chapter is to discuss the formulation of an optimization problem the solution of which leads to the identification of robust decisions. In Chapter 1 we formally defined the Robustness Approach to Decision Making. According to our discussion, three different robustness criteria can be used for the selection of the robust decision.
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References
Brandeau, M.L. and S.S. Chiu (1989), “An Overview of Representative Problems in Location Research,” Management Science, 35, 6, 645–674.
Chen, B. and C.S. Lin (1995), “Robust One Median Location Problem”. Working Paper, Department of Management and Systems, Washington State University, Pullman, Washington.
Chvatal, V. (1983), Linear Programming. W.H. Freeman and Company, New York.
Daniels, R.L. and P. Kouvelis (1995), “Robust Scheduling to Hedge Against Processing Time Uncertainty in Single-Stage Production,” Management Science, 41, 2, 363–376.
Dijkstra, E.W. (1959), “A Note on Two Problems in Connection with Graphs,” Numerische Mathematik, l, 269–271.
Efroymson, M.A. and T.L. Ray (1966), “A Branch and Bound Algorithm for Plant Location,” Operations Research, 14, 361–368.
Erlenkotter, D. (1978), “A Dual-Based Procedure for Uncapacitated Facility Location,” Operations Research, 26, 992–1009.
Federgruen, A. and M. Tzur (1991), “A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time,” Management Science, 37, 909–925.
Florian, M. and M. Klein (1970), “Deterministic Production Planning with Concave Costs and Capacity Constraints,” Management Science, 18, 1, 12–20.
Francis, R.L., L.F. McGinnis and J.A. White (1992), Facility Layout and Location: An Analytical Approach, Prentice Hall, Englewood Cliffs, New Jersey.
Gallego, G. and I. Moon (1993), “The Distribution Free Newsboy Problem: Review and Extensions,” Journal of Operational Research Society, 44, 8, 825–834.
Gavish, B. (1982), “Topological Design of Centralized Computer Networks — Formulations and Algorithms,” Networks, 12, 355–377.
Gutierrez, G.J., P. Kouvelis and A.A. Kurawarwala (1996), “A Robustness Approach to Uncapacitated Network Design Problems,” European Journal of Operational Research, forthcoming.
Harris, R.S. (1913), “How Many Parts to Make at Once,” Factory, The Magazine of Management, 10, 2, 135–136.
Hillier, F.S. and G.J. Lieberman (1990), Introduction to Mathematical Programming, McGraw Hill, New York.
Ibaraki, T. and N. Katoh (1988), Resource Allocation Problems: Algorithmic Approaches, the MIT Press, Cambridge, Massachusetts.
Johnson, S.M. (1954), “Optimal Two- and Three-Stage Production Schedules with Setup Times Included,” Naval Research Logistics Quarterly, 1, 61–68.
Karabati, S., P. Kouvelis and G. Yu (1996), “A Min-Max-Sum Resource Allocation Problem and Its Applications,” Working Paper, Fuqua School of Business, Duke University.
Khumawala, B.M. (1972), “A Branch and Bound Algorithm for Plant Location,” Management Science, 18, 718–731.
Kouvelis, P., A.A. Kurawarwala and G.J. Gutiérrez (1992), “Algorithms for Robust Single and Multiple Period Layout Planning for Manufacturing Systems,” European Journal of Operational Research, 63, 287–303.
Kouvelis, P., R.L. Daniels and G. Vairaktarakis (1996), “Robust Scheduling of a Two-Machine Flow Shop with Uncertain Processing Times,” Working Paper, Fuqua School of Business, Duke University (to appear in Naval Research Logistics).
Kouvelis, P., G. Vairaktarakis and G. Yu (1996), “Robust 1-Median Location on a Tree in the Presence of Demand and Transportation Cost Uncertainty,” Working Paper, Fuqua School of Business, Duke University.
Kouvelis, P. and G. Yu (1995), “Robust Discrete Optimization and Its Applications,” Working Paper, Department of MSIS, Graduate School of Business, The University of Texas at Austin.
Kruskal, J.B. (1956), “On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem,” in Proceedings of the American Mathematical Society, 7, 48–50.
Larson, R.C. and A.R. Odoni (1981), Urban Operations Research, Prentice Hall, Englewood Cliffs, New Jersey.
Lee, H.L. and S. Nahmias (1993), “Single-Product, Single Location Models,” Handbooks in Operations Research and Management Science, Vol. 4, edited by S.C. Graves, A.H.G. Rinnooy Kan and P.H. Zipkin, Elsevier Science Publishers B.V., 3–55.
Magnanti, T.L. and Wong, R.T. (1984), “Network Design and Transportation Planning: Models and Algorithms,” Transportation Science, 18, 1, 1–55.
Moon, I. and G. Gallego (1994), “Distribution Free Procedures for Some Inventory Models,” Journal of the Operational Research Society, 45, 6, 651–658.
Murty, K.G. (1983), Linear Programming, Wiley, New York.
Prim, R.C. (1957), “Shortest Connection Networks and Some Generalizations,” Bell System Technical Journal, 36, 1389–1401.
Rosenhead, M.J., M. Elton and S.K. Gupta (1972), “Robustness and Optimally as Criteria for Strategic Decisions,” Operational Research Quarterly, 23, 4, 413–430.
Scarf, H. (1958), “A Min-Max Solution of an Inventory Problem,” in Studies in the Mathematical Theory of Inventory and Production,” K. Arrow, S. Karlin and H. Scarf (Eds.), Stanford University Press, 201–209.
Silver, E.A. and R. Peterson (1985), Decision Systems for Inventory Management and Production Planning,” Wiley, New York.
Tansel, B.C., R.L. Francis and T.J. Lowe (1983), “Location on Networks: A Survey — Part II, Exploiting Tree Network Structure,” Management Science, 29, 498–511.
Toth, P. (1980), “Dynamic Programming Algorithms for the Zero-one Knapsack Problem,” Computing, 25, 29–45.
Vairaktarakis, G.(1995), “Robust Solutions for Multi-Item Newsboy Models with a Budget Constraint and Uncertain Demand,” Working Paper, College of Business Administration, Marquette University, Milwaukee.
Vairaktarakis, G. and P. Kouvelis (1996), “Incorporating Dynamic Aspects and Uncertainty in 1-Median Location Problems,” Working Paper, College of Business Administration, Marquette University, Milwaukee.
Van Roy, T.J. and D. Erlenkotter (1982), “A Dual-Based Procedure for Dynamic Facility Location,” Management Science, 28, 10, 1091–1105.
Wagelmans, A., S. Van Hoesel and A. Kolen (1992), “Economic Lot Sizing: an O(n logn) Algorithm that runs in Linear Time in the Wagner-Whitin Case,” Operations Research, 40, 5145–5156.
Wagner, H.M. and T.M. Whitin (1958), “Dynamic Version of the Economic Lot Size Model,” Management Science, 5, 89–96.
Wilson, R.H. (1934), “A Scientific Routine for Stock Control,” Harvard Business Review 13, 116–128.
Yu, G. (1994), “Robust Shortest Path Problem in Layered Networks,” Working Paper, Department of MSIS, University of Texas at Austin.
Yu, G. (1996a), “Robust Economic Order Quantity Models,” European Journal of Operational Research, forthcoming.
Yu, G. (1996b), “On the Max-min 0–1 Knapsack Problem with Robust Optimization Applications,” Operations Research, 44, 2, 407–415.
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Kouvelis, P., Yu, G. (1997). A Robust Discrete Optimization Framework. In: Robust Discrete Optimization and Its Applications. Nonconvex Optimization and Its Applications, vol 14. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2620-6_2
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DOI: https://doi.org/10.1007/978-1-4757-2620-6_2
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