Skip to main content
Log in

A multiobjective metaheuristic for a mean-risk multistage capacity investment problem

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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)

    Article  MATH  Google Scholar 

  • Ahmed, S.: Convexity and decomposition of mean-risk stochastic programs. Math. Program. 106(3), 433–446 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Ahmed, S., Sahinidis, N.V.: An approximation scheme for stochastic integer programs arising in capacity expansion. Oper. Res. 51(3), 461–471 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    Article  MATH  MathSciNet  Google Scholar 

  • Alrefaei, M.H., Andradottir, S.: A simulated annealing algorithm with constant temperature for discrete stochastic optimization. Manag. Sci. 45(5), 748–764 (1999)

    Article  Google Scholar 

  • Barahona, F., Bermon, S., Günlük, O., Hood, S.: Robust capacity planning in semiconductor manufacturing. Nav. Res. Logist. 52(5), 459–468 (2005)

    Article  MATH  Google Scholar 

  • 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)

    MATH  MathSciNet  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Crama, Y., Schyns, M.: Simulated annealing for complex portfolio selection problems. Eur. J. Oper. Res. 150(3), 546–571 (2003)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Das, I.: Robustness optimization for constrained nonlinear programming problems. Eng. Optim. 32(5), 585–618 (2000)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Dixit, A.K., Pindyck, R.S.: Investment Under Uncertainty. Princeton University Press, Princeton (1994)

    Google Scholar 

  • Ehrgott, M., Gandibleux, X.: A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spectrum 22(4), 425–460 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Ehrgott, M., Gandibleux, X.: Approximative solution methods for multiobjective combinatorial optimization. TOP 12(1), 1–90 (2004). (Spanish journal of operations research)

    Article  MATH  MathSciNet  Google Scholar 

  • Ehrgott, M., Klamroth, K., Schwehm, C.: An MCDM approach to portfolio optimization. Eur. J. Oper. Res. 155(3), 752–770 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Eichhorn, A., Romisch, W.: Polyhedral risk measures in stochastic programming. SIAM J. Optim. 16(1), 69–95 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Eppen, G.D., Martin, R.K., Schrage, L.: A scenario approach to capacity planning. Oper. Res. 37(4), 517–527 (1989)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Google Scholar 

  • Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  • 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)

    Google Scholar 

  • Hansen, M.P.: Tabu search for multiobjective combinatorial optimization: TAMOCO. Control Cybern. 29(3), 799–818 (2000)

    MATH  Google Scholar 

  • 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)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Chapter  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Jorion, P.: Risk2: Measuring the risk in value-at-risk. Financ. Anal. J. 52(6), 47–56 (1996)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Rockafellar, R.T., Wets, R.J.B.: Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16(1), 119–147 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    MATH  MathSciNet  Google Scholar 

  • Rudberg, M., Olhager, J.: Manufacturing networks and supply chains: an operations strategy perspective. Omega 31(1), 29–39 (2003)

    Article  Google Scholar 

  • Ruszczynski, A., Shapiro, A.: Optimization of convex risk functions. Math. Oper. Res. 31(3), 433–452 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    Article  MATH  MathSciNet  Google Scholar 

  • Schultz, R.: Stochastic programming with integer variables. Math. Program. 97(1–2), 285–309 (2003)

    MATH  MathSciNet  Google Scholar 

  • Schultz, R., Tiedemann, S.: Conditional value-at-risk in stochastic programs with mixed-integer recourse. Math. Program. 105(2–3), 365–386 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    MATH  Google Scholar 

  • Swaminathan, J.M.: Tool capacity planning for semiconductor fabrication facilities under demand uncertainty. Eur. J. Oper. Res. 120(14), 545–558 (2000)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • Van Mieghem, J.A.: Capacity management, investment, and hedging: Review and recent developments. Manuf. Serv. Oper. Manag. 5(4), 269–302 (2003)

    Article  Google Scholar 

  • Van Mieghem, J.A.: Risk mitigation in newsvendor networks: Resource diversification, flexibility, sharing, and hedging. Manag. Sci. 53(8), 1269–1288 (2007)

    Article  Google Scholar 

  • Wheelwright, S.C.: Reflecting corporate strategy in manufacturing decisions. Bus. Horiz. 21(1), 57–66 (1978)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to João Claro.

Additional information

The work reported in this paper has been partially supported by FCT project POCI/EGE/61362/2004.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-008-9090-2

Keywords

Navigation