lp relaxation

This paper considers the reliable multi-product multi-vehicle multi-type link logistics network design problem (RMLNDP) with system disruptions, which is concerned with facilities locating, transshipment links constructing, and also allocating them to the customers in order to satisfy their demand on minimum expected total cost (including locating costs, link constructing costs, and also expected transshipment costs in normal and disruption conditions). The motivating application of this class of problem is in multi-product, multi-vehicle, and multi-type link logistics network design regarding to system disruptions simultaneously. In fact, the decision makers in this area are not only concerned with the facility locating costs, link constructing costs, and logistical costs of the system but also by focusing on the several system disruptions states in order to be able to provide a reliable sustainable multi configuration logistic network system. All of the facility location plan, link construction plan and also link transshipment plan of the demands in the problem must be efficiently determined while considering the several system disruptions. The problem was modeled as a MIP. Also, a hybrid heuristic, based on LP relaxation approach, is proposed. Computational experiments illustrate that the provided algorithm will able to substantially outperform the proposed integer programming model in terms of both finding and verifying the efficient optimal (or near optimal) solution at a reasonable processing time.

Proposing a robust designed facility location is one of the most effective ways to hedge against unexpected disruptions and failures in a transportation network system. This paper considers the combined facility location/network design problem with regard to transportation link disruptions and develops a mixed integer linear programming formulation to model it. With respect to the probability of link disruptions, the objective function of the model minimizes the total costs, including location costs, link construction costs and also the expected transportation costs. An efficient hybrid algorithm based on LP relaxation and variable neighbourhood search metaheuristic is developed in order to solve the mathematical model. Numerical results demonstrate that the proposed hybrid algorithm has suitable efficiency in terms of duration of solution time and determining excellent solution quality.