Efficient Frontier for Multi-Objective Stochastic Transportation Networks in International Market of Perishable Goods

Abstract

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.

Simulation-based multi-objective model for supply chains with disruptions in transportation

“…To incorporate the inherent uncertainties of disruptive events into the complex supply chain design optimization process, this paper presents a model that extends previous research work (SMMCF-Discrete model for solving the discrete stochastic MMCF [6] There are many real applications that can be modeled as a stochastic minimum cost flow problem. For example, in real situations, the freight rate, which is assumed deterministic by the general SMMCF, follows a probability distribution.…”

“…The SMMCF-Discrete model considers randomness related to inspection time by including into the objective function the possible values of the stochastic attributes, for each scenario determined with the ε-constraint method [6]. The values of these stochastic attributes are assumed to follow discrete probability distributions.…”

“…For this reason, goal programming weights method is used to find a set of initial solutions. effort and convergence to the global-optima of the discrete version obtained by using the SMMCF-Discrete [6]. The configurations of the schedules are described in Section 8.…”

“…The real system was simplified so that the stochastic attributes were considered as values of discrete probability distributions followed by the times required for the inspection of cargo. Bustos et al [6] shows the Pareto frontier for the non-dominated solutions for the discrete stochastic problem solved with the SMMCF-Discrete. It is statistically demonstrated that the Pareto frontiers from the discrete stochastic version of the case study and from a deterministic version based on expected values are differently distributed.…”

Design of an inventory management system in an agricultural supply chain considering the deterioration of the product: The case of small citrus producers in a developing country

“…Taking into account the results presented above and considering the defi ned planning horizon (one month), it is possible to formulate the inventory control policy for each echelon belonging to the supply chain, thus responding to the three fundamental questions: Frequency of revision, moment of ordering and quantity to order. According to [20]in the case of perishable goods, since they have a limited lifetime, in order to be able to complying with the shelf life time, the length time in the supply chain should not exceed the lifetime value, as each unit of time that is exceeded in the supply chain represent deterioration in the products condition. In this sense the inventory level revisionshould be defi ned as continuous in each echelon.…”