A fuzzy-budgeted robust optimization model for joint network design-pricing problem in a forward−reverse supply chain: the viewpoint of third-party logistics

Abstract

The increasing opportunities for cost savings and customer satisfaction have propelled third-party logistics providers (3PLs) to get involved in the forward and reverse logistics operations. The forward−reverse supply chain network design (FRSCND) for 3PLs have been somehow studied under various conditions, so far. However, some very common business configurations and real-world concerns such as pricing and uncertainty are less investigated in the literature. Accordingly, this paper proposes a novel robust model for the design of a 3PL’s logistics network and pricing decisions. Since the value of uncertainty budget parameter in the robust model is an epistemic uncertain one, the fuzzy-robust model regarding the uncertainty budget parameter as a fuzzy number is also developed. The results of numerical examples show that the proposed models outperform the deterministic model regarding solution robustness and computational time. Considering the robust sensitivity analysis, the effects of uncertain parameters on total cost, based on their conservatism levels are analyzed. In addition, the conducted sensitivity analysis over penalty values for constraints violation reveal that for the medium- and large-size problems, the proposed models are more cost-effective for high penalty values, while the models’ performance is related to the problem size, for their low amounts.