Skip to main content
SpringerLink
Log in

Advances in the decision-making of set covering models under uncertainty

  • Original Research
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The Set Covering Problem (SCP) has been an extensively studied NP-hard problem in the field of combinatorial optimization since 1970. Over the past five decades, a significant amount of research has led to the development of a diverse set of covering models to support decision-making in various areas. However, the SCPs related to real-world applications are often too complex to solve using existing algorithms due to uncertain problem parameters. Thus, given the diversity of new developments, there is a pressing need to know both the current solution approaches and the advanced strategies for studying the uncertain SCP. This study summarizes the various modeling and solution approaches to the SCP when the model parameters are uncertain. Further, this study discusses some promising future research directions of the uncertain SCP that will impact new investigations of decisions on complex and competitive real-world issues.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ahmed, S., & Papageorgiou, D. J. (2013). Probabilistic set covering with correlations. Operations Research, 61(2), 438–452.

    Article  Google Scholar 

  • Aly, A. A., & White, J. A. (1978). Probabilistic formulation of the emergency service location problem. Journal of the Operational Research Society, 29(12), 1167–1179.

    Article  Google Scholar 

  • Bandara, D., Mayorga, M., & McLay, M. (2012). Optimal dispatching strategies for emergency vehicles to increase patient survivability. International Journal of Operational Research, 15(2), 195–214.

    Article  Google Scholar 

  • Bélanger, V., Ruiz, A., & Soriano, P. (2019). Recent optimization models and trends in location, relocation, and dispatching of emergency medical vehicles. European Journal of Operational Research, 272(1), 1–23.

    Article  Google Scholar 

  • Benveniste, R. (1982). A note on the set covering problem. Journal of Operational Research Society, 33, 261–265.

    Article  Google Scholar 

  • Beraldi, P., & Ruszczyński, A. (2002). A branch and bound method for stochastic integer problems under probabilistic constraints. Optimization Methods and Software, 17(3), 359–382.

    Article  Google Scholar 

  • Beraldi, P., & Ruszczyński, A. (2002). The probabilistic set-covering problem. Operations Research, 50(6), 956–967.

    Article  Google Scholar 

  • Beraldi, P., & Ruszczyński, A. (2005). Beam search heuristic to solve stochastic integer problems under probabilistic constraints. European Journal of Operational Research, 167(1), 35–47.

    Article  Google Scholar 

  • Bettinelli, A., Ceselli, A., & Righini, G. (2014). A branch-and-price algorithm for the multi-depot heterogeneous-fleet pickup and delivery problem with soft time windows. Mathematical Programming Computation, 6(2), 171–197.

    Article  Google Scholar 

  • Borrás, F., & Pastor, J. T. (2002). The ex-post evaluation of the minimum local reliability level: An enhanced probabilistic location set covering model. Annals of Operations Research, 111(1), 51–74.

    Article  Google Scholar 

  • Cabeza, M., Araújo, M. B., Wilson, R. J., Thomas, C. D., Cowley, M. J., & Moilanen, A. (2004). Combining probabilities of occurrence with spatial reserve design. Journal of Applied Ecology, 41(2), 252–262.

    Article  Google Scholar 

  • Chvatal, V. (1979). A greedy heuristic for the set-covering problem. Mathematics of Operations Research, 4(3), 233–235.

    Article  Google Scholar 

  • Coco, A. A., Santos, A. C., & Noronha, T. F. (2022). Robust min–max regret covering problems. Computational Optimization and Applications, 83(1), 111–141.

    Article  Google Scholar 

  • Daskin, M. S., & Stern, E. H. (1981). A hierarchical objective set covering model for emergency medical service vehicle deployment. Transportation Science, 15(2), 137–152.

    Article  Google Scholar 

  • Deb, K., & Kumar, A. (2007). Light beam search based multi-objective optimization using evolutionary algorithms. In 2007 IEEE congress on evolutionary computation (pp. 2125–2132). IEEE.

  • Degel, D., & Lutter, P. (2013). A robust formulation of the uncertain set covering problem. Technical report, Ruhr-University Bochum.

  • Ding, S., Zhang, Q., & Yuan, Z. (2020). An under-approximation for the robust uncertain two-level cooperative set covering problem. In 2020 59th IEEE conference on decision and control (CDC) (pp. 1152–1157). IEEE.

  • Farahani, R. Z., Asgari, N., Heidari, N., Hosseininia, M., & Goh, M. (2012). Covering problems in facility location: A review. Computers & Industrial Engineering, 62(1), 368–407.

    Article  Google Scholar 

  • Fischetti, M., & Monaci, M. (2012). Cutting plane versus compact formulations for uncertain (integer) linear programs. Mathematical Programming Computation, 4(3), 239–273.

    Article  Google Scholar 

  • Florios, K., & Mavrotas, G. (2014). Generation of the exact pareto set in multi-objective traveling salesman and set covering problems. Applied Mathematics and Computation, 237, 1–19.

    Article  Google Scholar 

  • Grossman, T., & Wool, A. (1997). Computational experience with approximation algorithms for the set covering problem. European Journal of Operational Research, 101(1), 81–92.

    Article  Google Scholar 

  • Haight, R. G., Revelle, C. S., & Snyder, S. A. (2000). An integer optimization approach to a probabilistic reserve site selection problem. Operations Research, 48(5), 697–708.

    Article  Google Scholar 

  • Hammer, P. L., & Bonates, T. O. (2006). Logical analysis of data: An overview: From combinatorial optimization to medical applications. Annals of Operations Research, 148(1), 203–225.

    Article  Google Scholar 

  • Hwang, H.-S. (2002). Design of supply-chain logistics system considering service level. Computers & Industrial Engineering, 43(1–2), 283–297.

    Article  Google Scholar 

  • Jaszkiewicz, A. (2003). Do multiple-objective metaheuristics deliver on their promises? A computational experiment on the set-covering problem. IEEE Transactions on Evolutionary Computation, 7(2), 133–143.

    Article  Google Scholar 

  • Kohl, N., & Karisch, S. E. (2004). Airline crew rostering: Problem types, modeling, and optimization. Annals of Operations Research, 127(1–4), 223–257.

    Article  Google Scholar 

  • Lemke, C. E., Salkin, H., & Spielberg, K. (1971). Set covering by single-branch enumeration with linear-programming subproblems. Operations Research, 19(4), 998–1022.

    Article  Google Scholar 

  • Lowerre, B. T. (1976). The harpy speech recognition system. Pittsburgh: Carnegie Mellon University.

    Google Scholar 

  • Lutter, P., Degel, D., Büsing, C., Koster, A. M., & Werners, B. (2017). Improved handling of uncertainty and robustness in set covering problems. European Journal of Operational Research, 263(1), 35–49.

    Article  Google Scholar 

  • Marchiori, E., & Steenbeek, A. (2000). An evolutionary algorithm for large scale set covering problems with application to airline crew scheduling. In 41st Annual symposium on real-world applications of evolutionary computation, workshops (pp. 370–384). Berlin: Springer.

  • Marchiori, E., & Steenbeek, A. (2000b). An evolutionary algorithm for large scale set covering problems with application to airline crew scheduling. In Workshops on real-world applications of evolutionary computation (pp 370–384). Springer.

  • Marianov, V., & Revelle, C. (1994). The queuing probabilistic location set covering problem and some extensions. Socio-Economic Planning Sciences, 28(3), 167–178.

    Article  Google Scholar 

  • Marsten, R. E., & Shepardson, F. (1981). Exact solution of crew scheduling problems using the set partitioning model: Recent successful applications. Networks, 11(2), 165–177.

    Article  Google Scholar 

  • McDonnell, M. D., Possingham, H. P., Ball, I. R., & Cousins, E. A. (2002). Mathematical methods for spatially cohesive reserve design. Environmental Modeling and Assessment, 7(2), 107–114.

    Article  Google Scholar 

  • NETLIB. (2013). http://www.netlib.org/lp/data/.

  • ORLIB. (1990). http://people.brunel.ac.uk/~mastjjb/jeb/info.html.

  • Pereira, J., & Averbakh, I. (2013). The robust set covering problem with interval data. Annals of Operations Research, 207(1), 217–235.

    Article  Google Scholar 

  • Powell, W. B. (2019). A unified framework for stochastic optimization. European Journal of Operational Research, 275(3), 795–821.

    Article  Google Scholar 

  • Prins, C., Prodhon, C., & Calvo, R. W. (2006). Two-phase method and Lagrangian relaxation to solve the bi-objective set covering problem. Annals of Operations Research, 147(1), 23–41.

    Article  Google Scholar 

  • ReVelle, C., & Hogan, K. (1989). The maximum availability location problem. Transportation science, 23(3), 192–200.

    Article  Google Scholar 

  • ReVelle, C., & Marianov, V. (1991). A probabilistic fleet model with individual vehicle reliability requirements. European Journal of Operational Research, 53(1), 93–105.

    Article  Google Scholar 

  • Sabuncuoglu, I., & Bayiz, M. (1999). Job shop scheduling with beam search. European Journal of Operational Research, 118(2), 390–412.

    Article  Google Scholar 

  • Saxena, A., Goyal, V., & Lejeune, M. A. (2010). MIP reformulations of the probabilistic set covering problem. Mathematical Programming, 121(1), 1–31.

    Article  Google Scholar 

  • Saxena, R. R., & Arora, S. (1981). Exact solution of crew scheduling problems using the set partitioning model: Recent successful applications. Optimization, 11(2), 165–177.

    Google Scholar 

  • Schilling, D. A. (1993). A review of covering problems in facility location. Location Science, 1, 25–55.

    Google Scholar 

  • Slavík, P. (1996). A tight analysis of the greedy algorithm for set cover. In Proceedings of the twenty-eighth annual ACM symposium on theory of computing (pp. 435–441).

  • Soyster, A. L. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 21(5), 1154–1157.

    Article  Google Scholar 

  • Toregas, C., Swain, R., ReVelle, C., & Bergman, L. (1971). The location of emergency service facilities. Operations Research, 19(6), 1363–1373.

    Article  Google Scholar 

  • Wang, W., Wu, S., Wang, S., Zhen, L., & Qu, X. (2021). Emergency facility location problems in logistics: Status and perspectives. Transportation Research Part E: Logistics and Transportation Review, 154, 102465.

    Article  Google Scholar 

  • Weerasena, L. (2020). Algorithm for generalised multi-objective set covering problem with an application in ecological conservation. International Journal of Mathematical Modelling and Numerical Optimisation, 10(2), 167–186.

    Article  Google Scholar 

  • Weerasena, L., & Wiecek, M. M. (2019). A tolerance function for the multiobjective set covering problem. Optimization Letters, 13(1), 3–21.

    Article  Google Scholar 

  • Weerasena, L., Shier, D., & Tonkyn, D. (2014). A hierarchical approach to designing compact ecological reserve systems. Environmental Modeling & Assessment, 19(5), 437–449.

    Article  Google Scholar 

  • Weerasena, L., Wiecek, M. M., & Soylu, B. (2017). An algorithm for approximating the pareto set of the multiobjective set covering problem. Annals of Operations Research, 248(1), 493–514.

    Article  Google Scholar 

  • Weerasena, L., Ebiefung, A., & Skjellum, A. (2022). Design of a heuristic algorithm for the generalized multi-objective set covering problem. Computational Optimization and Applications, 1–35.

  • Wu, H.-H., & Kucukyavuz, S. (2019a). Chance-constrained combinatorial optimization with a probability oracle and its application to probabilistic partial set covering. SIAM Journal on Optimization, 1–37.

  • Wu, H.-H., & Kucukyavuz, S. (2019). Probabilistic partial set covering with an oracle for chance constraints. SIAM Journal on Optimization, 29(1), 690–718.

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Science Foundation under Grant #2137622.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN, 37403-2598, USA

    Lakmali Weerasena & Chathuri Aththanayake

  2. Gary W. Rollins College of Business, 615 McCallie Avenue, Chattanooga, TN, 37403, USA

    Damitha Bandara

Authors
  1. Lakmali Weerasena
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chathuri Aththanayake
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Damitha Bandara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lakmali Weerasena.

Ethics declarations

Conflict of interest

None.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Weerasena, L., Aththanayake, C. & Bandara, D. Advances in the decision-making of set covering models under uncertainty. Ann Oper Res (2024). https://doi.org/10.1007/s10479-024-05915-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10479-024-05915-8

Keywords

Search

Navigation