On risk management of a two-stage stochastic mixed 0–1 model for the closed-loop supply chain design problem

Susana Baptista, Ana Paula Barbosa-Póvoa, Laureano F. Escudero, Maria Isabel Gomes, Celeste Pizarro

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


In this work, the design and operation planning of a multi-period, multi-product closed-loop supply chain is addressed. Recovered end-of-life products from customers are evaluated in disassembly centers and accordingly are sent back to factories for remanufacturing, or leave the network either by being sold to third parties or by being sent to disposal. Typical uncertain parameters are product demand, production cost, and returned product volume and evaluation, among others. So, stochastic optimization approaches should be used for problem solving, where different topology decisions on the timing, location and capacity of some entities (factories, and distribution and sorting centers) are to be considered along a time horizon. A two-stage multi-period stochastic mixed 0–1 bilinear optimization model is introduced, where the combined definition of the available entities at the periods and the products’ flow among the entities, maximizes the net present value of the expected total profit along the time horizon. A version of the mixture of chance-constrained and second order stochastic dominance risk averse measures is considered for risk management at intermediate periods of the time horizon. Given the high dimensions of the model it is unrealistic to look for the optimality of the solution in an affordable computing effort for current hardware and optimization software resources. So, a decomposition approach is considered, namely a Fix-and-Relax decomposition algorithm. For assessing the computational validation of the modeling and algorithmic proposals, pilot cases are taken from a real-life glass supply chain network whose main features are retained.

Original languageEnglish
Pages (from-to)91-107
JournalEuropean Journal of Operational Research
Issue number1
Publication statusPublished - 1 Apr 2019


  • Closed-loop
  • Design and production planning
  • Risk averse strategy
  • Supply chain management
  • Two-stage stochastic optimization


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