This paper describes and evaluates alternative branch-and-price decompositions (B&P-Ds) of the multi-dimensional knapsack problem with generalized upper bound constraints both analytically and computationally. As part of our theoretical analysis we compare the bounds available from B&P-Ds with three alternative relaxations (Lagrangean relaxation, Lagrangean decomposition, and Surrogate relaxati...

We review several linear programming (LP) formulations for the one-dimensional cutting stock and bin packing problems, namely, the models of Kantorovich, Gilmore–Gomory, onecut models, as in the Dyckhoff–Stadtler approach, position-indexed models, and a model derived from the vehicle routing literature. We analyse some relations between the corresponding LP relaxations, and their relative stren...

The efficient management of nursing personnel is of critical importance in a hospital’s environment comprising a vast share of the hospital’s operational costs. The nurse scheduling process affects highly the nurses’ working conditions, which are strongly related to the provided quality of care. In this paper, we consider the rostering over a mid-term period that involves the construction of du...

In this paper, we consider a deterministic multi-attribute vehicle routing problem derived from a real-life milk collection system. This problem is characterized by the presence of a heterogeneous fleet of vehicles, multiple depots, and several resource constraints. A branch-and-price methodology is proposed to tackle the problem. In this methodology, different branching strategies, adapted to ...

We describe models and exact solutions approaches for an integrated aircraft fleeting and routing problem arising at TunisAir. Given a schedule of flights to be flown, the problem consists of determining a minimum cost route assignment for each aircraft so as to cover each flight by exactly one aircraft while satisfying maintenance activity constraints. We investigate two tailored approaches fo...

Managing, recruiting, keeping the right staff, and deploying resources efficiently are key challenges for the healthcare industry in the coming decennia due to the increasing elder population and the corresponding increasing demand for care and caring personnel ([16]). Since the quality of care ultimately depends on the quality and motivation of health human resources, personnel problems should...

We consider a Two-Dimensional Cutting Stock Problem (2DCSP) where stock of different sizes is available, and a set of rectangular items has to be obtained through two-stage guillotine cuts. We propose and computationally compare three Mixed-Integer Programming models for the 2DCSP developing formulations from the literature. The first two models have a polynomial and pseudo-polynomial number of...

This paper studies location routing and scheduling problems, a class of problems in which the decisions of facility location, vehicle routing, and route assignment are optimized simultaneously. For a version with capacity and time restrictions, two formulations are presented, one graph-based and one set-partitioning-based. For the set-partitioning-based formulation, valid inequalities are ident...

with an Application to the Multicommodity Fixed Charge Network Flow Problem Mike Hewitt Department of Industrial and Systems Engineering, Rochester Institute of Technology, Rochester, NY 14623, USA, [email protected], George Nemhauser H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA, [email protected], Martin W.P...

Given a bipartite graph G = (S, T, E), the k-clustering Minimum Biclique Completion Problem (k-MinBCP) consists of finding k bipartite subgraphs (clusters), such that each vertex i of S appears in exactly one subgraph, every vertex j in T appears in each cluster in which at least one of its neighbors appears, and the total number of edges that would complete each subgraph into a complete bipart...