A \emph{general branch-and-bound tree} is a branch-and-bound tree which is allowed to use general disjunctions of the form $\pi^{\top} x \leq \pi_0 \,\vee\, \pi^{\top}x \geq \pi_0 + 1$, where $\pi$ is an integer vector and $\pi_0$ is an integer scalar, to create child nodes. We construct a packing instance, a set covering instance, and a … Read more
We study the polyhedral convex hull structure of a mixed-integer set which arises in a class of cardinality-constrained concave submodular minimization problems. This class of problems has an objective function in the form of $f(a^\top x)$, where $f$ is a univariate concave function, $a$ is a non-negative vector, and $x$ is a binary vector of … Read more
This work addresses an operational problem of a logistics service provider that consists of finding an optimal route for a vehicle carrying customer parcels from a central depot to selected facilities, from where autonomous devices like robots are launched to perform last-mile deliveries. The objective is to minimize a tardiness indicator based on the customer … Read more
We consider the capacitated multi-trip vehicle routing problem with time windows (CMTVRPTW), where vehicles are allowed to make multiple trips. The ability to perform multiple trips is necessary for some real-world applications where the vehicle capacity, the trip duration, or the number of drivers or vehicles is limited. However, it substantially increases the solution difficulty … Read more
Decision making problems are typically concerned with maximizing efficiency. In contrast, we address problems where there are multiple stakeholders and a centralized decision maker who is obliged to decide in a fair manner. Different decisions give different utility to each stakeholder. In cases where these decisions are made repeatedly, we provide efficient mathematical programming formulations … Read more
In this work, we suggest concepts and solution methodologies for a series of strategic network design problems that find application in highly data-sensitive industries, such as, for instance, the high-tech, governmental, or military sector. Our focus is on the installation of widely used cost-efficient tree-structured communication infrastructure. As base model we use the well-known Steiner … Read more
This paper examines the Inventory Routing Problem (IRP) with Maximum Level inventory policy. The IRP is a broad class of hard to solve problems with numerous practical applications in the field of freight transportation and logistics. A supplier is responsible for determining the timing and the quantity of replenishment services offered to a set of … Read more
Branch-and-bound is the workhorse of all state-of-the-art mixed integer linear programming (MILP) solvers. These implementations of branch-and-bound typically use variable branching, that is, the child nodes are obtained by fixing some variable to an integer value v in one node and to v + 1 in the other node. Even though modern MILP solvers are … Read more
We consider the class of 2-partition inequalities for the clique partitioning problem associated with complete graphs. We propose a heuristic separation algorithm for the inequalities and evaluate its usefulness in a cutting-plane algorithm. Our computational experiments fall into two parts. In the first part, we compare the LP objective values obtained by the proposed separator … Read more
The tourist trip design problem is an extension of the orienteering problem applied to tourism. The problem consists in selecting a subset of locations to visit from among a larger set while maximizing the benefit for the tourist. The benefit is given by the sum of the rewards collected at each location visited. We consider … Read more