The heterogeneous open vehicle routing problem with release and due dates : a case on spare parts industry


In this paper, we introduce the Heterogeneous Open Vehicle Routing Problem with Release and Due Dates (HOVRP-RDD). This problem is inspired by a real delivery operation of a company that buys and imports spare parts from different vendors. The parts arrive to a depot and then are delivered to a set of customers, so they can perform corrective maintenance. The objective of HOVRP-RDD is to design a set of routes for visiting all the customers, in a way that: each customer’s product has a ready time at the depot; each customer has a due date and importance weight; and the total delivery cost does not exceed a maximum budget. To transport the products, the company hires a heterogeneous fleet, in which every vehicle finishes its route at the last customer. For the HOVRP-RDD, the objective function is to minimize the total weighted tardiness, considering that the customers need the parts to carry on their operations. For solving this problem, we propose a Mixed-Integer linear programming (MILP) formulation. For improving the performance of the MILP formulation running on a commercial solver, we propose a set of valid inequalities and an approach to reduce the cardinality of a set of vehicles. To test the MILP formulation, we present a computational experiment using 40 instances based on a real operation from a company in the spare parts industry. The results show that the MILP formulation has an acceptable performance given the size of the real instances from the company that motivates the HOVRP-RDD.


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