The inventory routing problem (IRP) arises in the joint practices of vendor-managed inventory (VMI) and vehicle routing problem (VRP), aiming to simultaneously optimize the distribution, inventory and vehicle routes. This paper studies the multi-vehicle multi-compartment inventory routing problem with stochastic demands (MCIRPSD) in the context of fuel delivery. The problem with maximum-to-level (ML) replenishment policy is modeled as a two-stage stochastic programming model with the purpose of minimizing the total cost, in which the inventory management and routing decisions are made in the first stage while the corresponding resource actions are implemented in the second stage. An acceleration strategy is incorporated into the exact single-cut Benders decomposition algorithm and its multi-cut version respectively to solve the MCIRPSD on the small instances. Two-phase heuristic approaches based on the single-cut decomposition algorithm and its multi-cut version are developed to deal with the MCIRPSD on the medium and large-scale instances. Comparing the performance of the proposed algorithms with the Gurobi solver within limited time, the average objective value obtained by the proposed algorithm has decreased more than 7.30% for the medium and large instances, which demonstrates the effectiveness of our algorithms. The impacts of the instance features on the results are further analyzed, and some managerial insights are concluded for the manager.

The set covering problem is to find the minimum cardinality set of locations to site the facilities which cover all of the demand points in the network. In this classical problem, it is assumed that the potential facility locations and the demand points are limited to the set of vertices. Although this problem has some applications, there are some covering problems in which the facilities can be located along the edges and the demand exists on the edges, too. For instance, in the public service environment the demand (population) is distributed along the streets. In addition, in many applications (like bus stops), the facilities are not limited to be located at the vertices (intersections), rather they are allowed to be located along the edges (streets). For the first time, this paper develops a novel integer programming formulation for the set covering problem wherein the demand and facility locations lie continuously along the edges. In order to find good solutions in a reasonable time, a matheuristic algorithm is developed which iteratively adds dummy vertices along the edges and solves a simpler problem which does not allow non-nodal facility locations. Finally, a Benders decomposition reformulation of the problem is developed and the lower bounds generated by the Benders algorithm are used to evaluate the quality of the heuristic solutions. Numerical results show that the Benders lower bounds are tight and the matheuristic algorithm generates good quality solutions in short time.

Globalization and increasing competition in global markets have forced businesses to provide a high level of service to their customers. Time-sensitive transportation systems which are used in transportation of perishable goods, express mail delivery, and emergency services are playing a very important role in this regard. This paper addresses the problem of uncapacitated multiple allocation p-hub center problem (UMApHCP) which is fundamental in proper functioning of time-sensitive transportation systems. A mixed-integer programming formulation is proposed for the problem and a highly efficient Benders decomposition algorithm is developed for solving it. The proposed algorithm is capable of solving large-scale instances of the problem to optimality in order of seconds.