We develop a robust optimization model for designing a three-echelon supply chain network that consists of manufacturers, distribution centers, and retailers under both demand uncertainty and supply disruptions. The market demands are assumed to be random variables with known distribution and the supply disruptions caused by some of the facilities faults or connection links interruptions are formulated by several scenarios with unknown occurrence probabilities. In particular, we assume the probabilities that the disruption scenarios happen belong to the two predefined uncertainty sets, named box and ellipsoid uncertainty sets, respectively. Through mathematical deductions, the proposed robust SCN design models can be transformed into the tractable linear program for box uncertainty and into second-order cone program for ellipsoid uncertainty. We further offer propositions with proof to show the equivalence of the transformed problems with the original ones. The applications of the proposed models together with solution approaches are investigated in a real case to design a tea supply chain network and validate their effectiveness. Numerical results obtained from model implementation and sensitivity analysis arrive at important practical insights.

Purpose: This work examines the joint pricing and ordering (JPO) decisions for a loss-averse retailer with quantity-oriented reference point (RP) effect under demand uncertainty.Design/methodology/approach: The demand is assumed to be uncertain with the mean and variance as the only known information. The prospect theory is used to model the retailer's expected utility. An expected utility maximization model in the distribution-free approach (DFA) is then developed. Using duality theory, the expected utility under the worst-case distribution is transformed into tractable piece-wise functions. To examine the effectiveness of the DFA in coping with the demand uncertainty, a stochastic programming model is developed and its solutions are used as benchmarks.Findings: The proposed model and solution approach can effectively hedge against the demand uncertainty. The JPO decisions are significantly influenced by the LA coefficient and the reference level. The LA has a stronger influence than the reference level does on the expected utility. An excessive LA is detrimental while an appropriate reference level is beneficial to the retailer.Practical implications: The results of this work are applicable to loss-averse retailers with the quantity-oriented RP when making JPO decisions with difficulty in predicting the demands.Originality/value: The demand is assumed to be uncertain in this work, but a certain demand distribution is usually assumed in the existing literature. The DFA is used to study JPO decisions for the loss-averse retailer with quantity-oriented RP effect under the uncertain demand.

The problem of designing a multi-product, multi-period green supply chain network under uncertainties in carbon price and customer demand is studied in this paper. The purpose of this study is to develop a robust green supply chain network design model to minimize the total cost and to effectively cope with uncertainties. A scenario tree method is applied to model the uncertainty, and a green supply chain network design model is developed under the p-robustness criterion. Furthermore, the solution method for determining the lower and upper bounds of the relative regret limit is introduced, which is convenient for decision-makers to choose the corresponding supply chain network structure through the tradeoff between risk and cost performance. In particular, to overcome the large scale of the model caused by a high number of uncertain scenarios and reduce the computational difficulty, a scenario reduction technique is applied to filter the scenarios. Numerical calculations are executed to analyze the influence of relevant parameters on the performance of the designed green supply chain network. The results show that the proposed p-robust green supply chain network design model can effectively deal with carbon and demand uncertainties while ensuring cost performance, and can offer more choices for decision-makers with different risk preferences.