A case-oriented approach to a lead/acid battery closed-loop supply chain network design under risk and uncertainty

• A stochastic and possibilistic MILP model for lead/acid battery CLSC network.
• A multi-objective model with several financial and collection risk measures.
• Maximization of collection of used batteries based on maximal coverage problem.
• Inclusion of different uncertainty categories such as randomness and fuzziness.
• Formulating some risk measures where target values are stated as fuzzy.

A new scenario based stochastic and possibilistic mixed integer programming model for a multi-objective closed-loop supply chain network design problem by considering financial and collection risks is proposed. Uncertainties in the form of randomness and fuzziness are handled together for a better reflection of the problem. Different risk measures such as “variability index”, “downside risk” and “conditional value at risk” are integrated within the proposed model. Particularly, for the downside risk measure, target/threshold values are considered as fuzzy and described by their own possibility distribution. The proposed hybrid model is applied to an illustrative example inspired by the lead/acid industry in Turkey. Computational results of applying the different risk measures suggest that using downside risk model with fuzzy targets is found to be an appropriate choice for the stated closed-loop supply chain network design problem in terms of “computational efficiency”, “handling uncertainty” and “solution quality”