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A scenario-based framework for supply planning under uncertainty: stochastic programming versus robust optimization approaches

Author

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  • Francesca Maggioni

    (University of Bergamo)

  • Florian A. Potra

    (University of Maryland)

  • Marida Bertocchi

    (University of Bergamo)

Abstract

In this paper we analyze the effect of two modelling approaches for supply planning problems under uncertainty: two-stage stochastic programming (SP) and robust optimization (RO). The comparison between the two approaches is performed through a scenario-based framework methodology, which can be applied to any optimization problem affected by uncertainty. For SP we compute the minimum expected cost based on the specific probability distribution of the uncertain parameters related to a set of scenarios. For RO we consider static approaches where random parameters belong to box or ellipsoidal uncertainty sets in compliance with the data used to generate SP scenarios. Dynamic approaches for RO, via the concept of adjustable robust counterpart, are also considered. The efficiency of the methodology has been illustrated for a supply planning problem to optimize vehicle-renting and procurement transportation activities involving uncertainty on demands and on buying costs for extra-vehicles. Numerical experiments through the scenario-based framework allow a fair comparison in real case instances. Advantages and disadvantages of RO and SP are discussed.

Suggested Citation

  • Francesca Maggioni & Florian A. Potra & Marida Bertocchi, 2017. "A scenario-based framework for supply planning under uncertainty: stochastic programming versus robust optimization approaches," Computational Management Science, Springer, vol. 14(1), pages 5-44, January.
    • Handle: RePEc:spr:comgts:v:14:y:2017:i:1:d:10.1007_s10287-016-0272-3
    DOI: 10.1007/s10287-016-0272-3
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    5. Fanzeres, Bruno & Ahmed, Shabbir & Street, Alexandre, 2019. "Robust strategic bidding in auction-based markets," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1158-1172.
    6. Rodrigues, Filipe & Agra, Agostinho & Christiansen, Marielle & Hvattum, Lars Magnus & Requejo, Cristina, 2019. "Comparing techniques for modelling uncertainty in a maritime inventory routing problem," European Journal of Operational Research, Elsevier, vol. 277(3), pages 831-845.
    7. Snoeck, André & Winkenbach, Matthias, 2020. "The value of physical distribution flexibility in serving dense and uncertain urban markets," Transportation Research Part A: Policy and Practice, Elsevier, vol. 136(C), pages 151-177.
    8. Sesini, Marzia & Giarola, Sara & Hawkes, Adam D., 2021. "Strategic natural gas storage coordination among EU member states in response to disruption in the trans Austria gas pipeline: A stochastic approach to solidarity," Energy, Elsevier, vol. 235(C).

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