{'fraction_non_alphanumeric': 0.009582477754962354, 'fraction_numerical': 0.0, 'mean_word_length': 5.706422018348624, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An enhanced possibilistic programming approach for reliable closed-loop supply chain network design

Most of current logistics network design models in the literature typically assume that facilities are always available and absolutely reliable while in practice, they are always subject to several operational and disruption risks. This paper proposes a reliable closed-loop supply chain network design model, which accounts for both partial and complete facility disruptions as well as the uncertainty in the critical input data. The proposed model is of mixed integer possibilistic linear programming type that aims to minimise simultaneously the total cost of opening new facilities and the expected cost of disruption scenarios. An enhanced possibilistic programming approach is proposed to deal with the epistemic uncertainty in input data. Furthermore, the p-robustness criterion is used to limit the cost of disruption scenarios and protect the designed network against random facility disruptions. Several numerical experiments along with sensitivity analyses on uncertain parameters are conducted to illustrate the significance and applicability of the developed model as well as the effectiveness of the proposed solution approach. Our results demonstrate that operational and disruption risks considerably affect the whole structure of the designed network and they must be taken into account when designing a reliable closed-loop logistics network.