Unpredictable disruptions (e.g., accidents, traffic conditions, among others) in supply chains (SCs) encourage the development of decision tools that allow designing resilient routing strategies. The transportation problem, for which a model is proposed in this paper, consists of minimizing the stochastic transportation time and the deterministic freight rate. This paper extends a stochastic multi-objective minimum cost flow (SMMCF) model by proposing a novel simulation-based multi-objective optimization (SimMOpt) solution procedure. A real case study, consisting of the road transportation of perishable agricultural products from Mexico to the United States, is presented and solved using the proposed SMMCF-Continuous/SimMOpt solution framework. In this case study, time variability is caused by the inspection of products at the U.S.-Mexico border ports of entry. The results demonstrate that this framework is effective and overcomes the limitations of the multi-objective stochastic minimum cost flow problem (which becomes intractable for large-scale instances).

Effective planning of a transportation network influences tactical and operational activities and has a great impact on business. Planning typically considers multiple aspects such as variable transportation costs, various levels of customer service offered, security of goods, and traveling time. These aspects often vary with time. Although the minimum cost flow problem is a widely seen approach to configure a transportation network, there is no much work considering variations on arcs; even more, the problem with varying nodes has hardly been addressed. In this work is developed a mathematical model for the multi-objective minimum cost flow problem, applied in networks with varying attributes on arcs. The model finds the set of non-dominated solutions for a multi-objective stochastic network having variations in attributes of its arcs and nodes, such as cost or transportation time. A modified version of the two-stage method was used to address the stochastic nature of the problem combined with the epsilon-constraint method, which is used for building the set of non-dominated solutions. This paper presents the main features of the model, the theoretical bases and a computational implementation. Experiments were applied in a transport network for the exportation market of ornamental flowers as perishable goods from Mexico to the United States, which considered variations in border crossing times.