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 a single machine scheduling problem to minimize the completion time variance of n jobs. This problem is known to be NP-hard and our contribution is to establish a novel bounding condition for a characterization of an optimal sequence. Specifically, we prove a necessary and sufficient condition (which can be verified in O(n\log n)) … 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
This paper introduces the production routing problem for perishable products with fixed shelf life and gradual decay, where the age of products impacts the price that can be obtained when satisfying customer demands. In this problem, a single supplier is responsible for the production and distribution of perishable products to a set of customers. Fixed … Read more
In this paper we introduce the selective maximum coverage and the selective maximum set packing problem and variants of them. Both problems are strongly related to well studied problems such as maximum coverage, set packing, and (bipartite) hypergraph matching. The two problems are given by a collection of subsets of a ground set and index … Read more
This paper introduces the heterogeneous multicrew scheduling and routing problem (MCSRP) in road restoration. The MCSRP consists of identifying the schedule and route of heterogeneous crews that must perform the restoration of damaged nodes used in the paths to connect a source node to demand nodes in a network affected by extreme events. The objective … 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
The concept of balance plays an important role in many combinatorial optimization problems. Yet there exist various ways of expressing balance, and it is not always obvious how best to achieve it. In this methodology-focused paper, we study three cases where its integration is deficient and analyze the causes of these inadequacies. We examine the … Read more
We introduce the ratio-cut polytope defined as the convex hull of ratio-cut vectors corresponding to all partitions of $n$ points in $\R^m$ into at most $K$ clusters. This polytope is closely related to the convex hull of the feasible region of a number of clustering problems such as K-means clustering and spectral clustering. We study … Read more
All feasible flows in potential-driven networks induce an orientation on the undirected graph underlying the network. Clearly, these orientations must satisfy two conditions: they are acyclic and there are no “dead ends” in the network, i.e. each source requires outgoing flows, each sink requires incoming flows, and each transhipment vertex requires both an incoming and … Read more