Abstract
We propose a multiobjective local search metaheuristic for a mean-risk multistage capacity investment problem with irreversibility, lumpiness and economies of scale in capacity costs. Conditional value-at-risk is considered as a risk measure. Results of a computational study are presented and indicate that the approach is capable of producing high-quality approximations to the efficient sets with a modest computational effort. The best results are achieved with a new hybrid approach, combining Tabu Search and Variable Neighbourhood Search.
Similar content being viewed by others
References
Ahmed, M.A., Alkhamis, T.M.: Simulation-based optimization using simulated annealing with ranking and selection. Comput. Oper. Res. 29(4), 387–402 (2002)
Ahmed, S.: Convexity and decomposition of mean-risk stochastic programs. Math. Program. 106(3), 433–446 (2006)
Ahmed, S., Sahinidis, N.V.: An approximation scheme for stochastic integer programs arising in capacity expansion. Oper. Res. 51(3), 461–471 (2003)
Ahmed, S., King, A., Parija, G.: A multi-stage stochastic integer programming approach for capacity expansion under uncertainty. J. Glob. Optim. 26(1), 3–24 (2003)
Alrefaei, M.H., Andradottir, S.: A simulated annealing algorithm with constant temperature for discrete stochastic optimization. Manag. Sci. 45(5), 748–764 (1999)
Barahona, F., Bermon, S., Günlük, O., Hood, S.: Robust capacity planning in semiconductor manufacturing. Nav. Res. Logist. 52(5), 459–468 (2005)
Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. R. Stat. Soc. 57(1), 289–300 (1995)
Çakanyildirim, M., Roundy, R.O.: Optimal capacity expansion and contraction under demand uncertainty. Working paper. University of Texas at Dallas (2002)
Chang, T.J., Meade, N., Beasley, J.E., Sharaiha, Y.M.: Heuristics for cardinality constrained portfolio optimisation. Comput. Oper. Res. 27(13), 1271–1302 (2000)
Chen, Z.-L., Li, S., Tirupati, D.: A scenario-based stochastic programming approach for technology and capacity planning. Comput. Oper. Res. 29(7), 781–806 (2002)
Cheng, L.F., Subrahmanian, E., Westerberg, A.W.: Multi-objective decisions on capacity planning and production - inventory control under uncertainty. Ind. Eng. Chem. Res. 43(9), 2192–2208 (2004)
Claro, J., Sousa, J.P.: An object-oriented framework for multiobjective local search. In: J.P. Sousa, (ed.) MIC’2001 4th Metaheuristics Int. Conf., Porto, Portugal, pp. 231–236 (2001)
Costa, D., Silver, E.A.: Tabu search when noise is present: An illustration in the context of cause and effect analysis. J. Heuristics 4(1), 5–23 (1998)
Crama, Y., Schyns, M.: Simulated annealing for complex portfolio selection problems. Eur. J. Oper. Res. 150(3), 546–571 (2003)
Czyzak, P., Jaszkiewicz, A.: Pareto simulated annealing—a metaheuristic technique for multiple-objective combinatorial optimization. J. Multi-Criteria Decis. Anal. 7(1), 34–47 (1998)
Das, I.: Robustness optimization for constrained nonlinear programming problems. Eng. Optim. 32(5), 585–618 (2000)
Deb, K., Gupta, H.: Introducing robustness in multiobjective optimization. Report No. 2004016, Kanpur Genetic Algorithms Laboratory (KanGAL), Indian Institute of Technology, Kanpur, India (2004)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Dixit, A.K., Pindyck, R.S.: Investment Under Uncertainty. Princeton University Press, Princeton (1994)
Ehrgott, M., Gandibleux, X.: A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spectrum 22(4), 425–460 (2000)
Ehrgott, M., Gandibleux, X.: Approximative solution methods for multiobjective combinatorial optimization. TOP 12(1), 1–90 (2004). (Spanish journal of operations research)
Ehrgott, M., Klamroth, K., Schwehm, C.: An MCDM approach to portfolio optimization. Eur. J. Oper. Res. 155(3), 752–770 (2004)
Eichhorn, A., Romisch, W.: Polyhedral risk measures in stochastic programming. SIAM J. Optim. 16(1), 69–95 (2005)
Eppen, G.D., Martin, R.K., Schrage, L.: A scenario approach to capacity planning. Oper. Res. 37(4), 517–527 (1989)
Gandibleux, X., Ehrgott, M.: 1984–2004—20 years of multiobjective metaheuristics. but what about the solution of combinatorial problems with multiple objectives? In: Coello, C.A.C., Aguirre, A.H., Zitzler, E. (eds.) Evol. Multi-Criterion Optim. Lect. Notes Comput. Sci., vol. 3410, pp. 33–46. Springer, Berlin (2005)
Gandibleux, X., Mezdaoui, N., Freville, A.: A multiobjective tabu search procedure to solve combinatorial optimization problems. In: Caballero, R., Ruiz, F. (eds.) Adv. Mult. Objective Goal Program. Lect. Notes Econ. Math. Syst., vol. 445, pp. 291–300. Springer, Berlin (1997)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
Gutjahr, W.J.: A converging ACO algorithm for stochastic combinatorial optimization. In: Albrecht, A., Steinhöfel, K. (eds.) Stoch. Alg.: Found. Appl. Lect. Notes Comput. Sci., vol. 2827, pp. 10–25. Springer, Berlin (2003)
Hansen, M.P.: Tabu search for multiobjective combinatorial optimization: TAMOCO. Control Cybern. 29(3), 799–818 (2000)
Haugen, K.K., Lokketangen, A., Woodruff, D.L.: Progressive hedging as a meta-heuristic applied to stochastic lot-sizing. Eur. J. Oper. Res. 132(1), 116–122 (2001)
Huang, K., Ahmed, S.: The value of multi-stage stochastic programming in capacity planning under uncertainty. (2005, submitted for publication)
Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments—a survey. IEEE Trans. Evol. Comput. 9(3), 303–317 (2005)
Jin, Y.C., Sendhoff, B.: Trade-off between performance and robustness: An evolutionary multiobjective approach. In: Goos, G., Hartmanis, J., van Leeuwen, J. (eds.) Evol. Multi-Criterion Optim., Proc. Lect. Notes Comput. Sci., vol. 2632, pp. 237–251. Springer, Berlin (2003)
Jones, D.F., Mirrazavi, S.K., Tamiz, M.: Multi-objective meta-heuristics: An overview of the current state-of-the-art. Eur. J. Oper. Res. 137(1), 1–9 (2002)
Jorion, P.: Risk2: Measuring the risk in value-at-risk. Financ. Anal. J. 52(6), 47–56 (1996)
Julka, N., Baines, T., Tjahjono, B., Lendermann, P., Vitanov, V.: A review of multi-factor capacity expansion models for manufacturing plants: Searching for a holistic decision aid. Int. J. Prod. Econ. 106(2), 607–621 (2007)
Knowles, J., Corne, D.: The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation. Proc. 1999 Cong. Evol. Comput., CEC ’99, vol. 1, pp. 98–105 (1999)
Luss, H.: Operations research and capacity expansion problems: A survey. Oper. Res. 30(5), 907–947 (1982)
Malakooti, B., Wang, J., Tandler, E.C.: A sensor-based accelerated approach for multi-attribute machinability and tool life evaluation. Int. J. Prod. Res. 28(12), 2373–2392 (1990)
Medaglia, A.L., Graves, S.B., Ringuest, J.L.: A multiobjective evolutionary approach for linearly constrained project selection under uncertainty. Eur. J. Oper. Res. 179(3), 869–894 (2007)
Narongwanich, W., Duenyas, I., Birge, J.R.: Optimal portfolio of reconfigurable and dedicated capacity under uncertainty. Preprint. University of Michigan (2002)
Rajagopalan, S., Swaminathan, J.M.: A coordinated production planning model with capacity expansion and inventory management. Manag. Sci. 47(11), 1562–1580 (2001)
Ray, T.: Constrained robust optimal design using a multiobjective evolutionary algorithm. In: Proc. 2002 Cong. Evol. Comput., 2002, CEC ’02, vol. 1, pp. 419–424 (2002)
Rockafellar, R.T., Uryasev, S.: Conditional value-at-risk for general loss distributions. J. Bank. Finance 26(7), 1443–1471 (2002)
Rockafellar, R.T., Wets, R.J.B.: Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16(1), 119–147 (1991)
Rosen, S.L., Harmonosky, C.M.: An improved simulated annealing simulation optimization method for discrete parameter stochastic systems. Comput. Oper. Res. 32(2), 343–358 (2005)
Rudberg, M., Olhager, J.: Manufacturing networks and supply chains: an operations strategy perspective. Omega 31(1), 29–39 (2003)
Ruszczynski, A., Shapiro, A.: Optimization of convex risk functions. Math. Oper. Res. 31(3), 433–452 (2006)
Schaffer, J.D.: Multiple objective optimization with vector evaluated genetic algorithms. J.J. Grefenstette (ed.) Gen. Alg. Appl.: Proc. First Int. Conf. Gen. Alg., pp. 92–100, Lawrence Erlbaum (1985)
Schlottmann, F., Seese, D.: A hybrid heuristic approach to discrete multi-objective optimization of credit portfolios. Comput. Stat. Data Anal. 47(2), 373–399 (2004)
Schultz, R.: Stochastic programming with integer variables. Math. Program. 97(1–2), 285–309 (2003)
Schultz, R., Tiedemann, S.: Conditional value-at-risk in stochastic programs with mixed-integer recourse. Math. Program. 105(2–3), 365–386 (2006)
Serafini, P.: Simulated annealing for multiple objective optimization problems. In: Proc. Tenth Int. Conf. Mult. Criteria Decision Making, pp. 87–96, Taipei, Taiwan (1992)
Snow, D.C., Wheelwright, S.C., Wagonfeld, A.B.: Genentech—Capacity Planning. Harvard Business School Case Series, 9-606-052 (2006)
Steuer, R.E.: Multiple Criteria Optimization: Theory, Computation, and Optimization. Wiley, New York (1986)
Swaminathan, J.M.: Tool capacity planning for semiconductor fabrication facilities under demand uncertainty. Eur. J. Oper. Res. 120(14), 545–558 (2000)
Tomlin, B., Wang, Y.: On the value of mix flexibility and dual sourcing in unreliable newsvendor networks. Manuf. Serv. Oper. Manag. 7(1), 37–57 (2005)
Ulungu, E.L., Teghem, J., Fortemps, P.H., Tuyttens, D.: MOSA method: a tool for solving multiobjective combinatorial optimization problems. J. Multi-Criteria Decis. Anal. 8(4), 221–236 (1998)
Van Mieghem, J.A.: Capacity management, investment, and hedging: Review and recent developments. Manuf. Serv. Oper. Manag. 5(4), 269–302 (2003)
Van Mieghem, J.A.: Risk mitigation in newsvendor networks: Resource diversification, flexibility, sharing, and hedging. Manag. Sci. 53(8), 1269–1288 (2007)
Wheelwright, S.C.: Reflecting corporate strategy in manufacturing decisions. Bus. Horiz. 21(1), 57–66 (1978)
Wu, S.D., Erkoc, M., Karabuk, S.: Managing capacity in the high-tech industry: A review of literature. Eng. Econ. 50(2), 125–158 (2005)
Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms—a comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.P. (eds.) Parallel Problem Solving from Nature—PPSN V. Lect. Notes Comput. Sci., vol. 1498, pp. 292–301. Springer, Berlin (1998)
Author information
Authors and Affiliations
Corresponding author
Additional information
The work reported in this paper has been partially supported by FCT project POCI/EGE/61362/2004.
Rights and permissions
About this article
Cite this article
Claro, J., de Sousa, J.P. A multiobjective metaheuristic for a mean-risk multistage capacity investment problem. J Heuristics 16, 85–115 (2010). https://doi.org/10.1007/s10732-008-9090-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-008-9090-2