We compare two branch-and-price approaches for the cutting stock problem. Each algorithm is based on a different integer programming formulation of the column generation master problem. One formulation results in a master problem with 0–1 integer variables while the other has general integer variables. Both algorithms employ column generation for solving LP relaxations at each node of a branch-...

Submitted Abstract We use column generation and a specialized branching technique for solving constrained clustering problems. We also develop and implement an innovative com-binatorial method for solving the pricing subproblems. Computational experiments comparing the resulting branch-and-price method to competing methodologies in the literature are presented and suggest that our technique yie...

In the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows, the set of customers is the union of delivery customers and pickup customers. A fleet of identical capacitated vehicles based at the depot must perform all deliveries and profitable pickups while respecting time windows. The objective is to minimize routing costs, minus the revenue associated with the pickups. T...

The Multicommodity Flow Problem (MCFP) considers the efficient routing of commodities from their origins to their destinations, subject to capacity restrictions and edge costs. This paper studies the NP-hard Minimum Cost Multicommodity k-splittable Flow Problem in which each commodity may use at most k paths between its origin and its destination. The problem has applications in transportation ...

W study the problem of (re)designing the regional network by which cadaveric livers are allocated. Whereas prior research focused mainly on maximizing a measure of efficiency of the network that was based on aggregate patient survival, we explicitly account for the trade-off between efficiency and a measure of geographical equity in the allocation process. To this end, we extend earlier optimiz...

In this paper we study the capacitated team orienteering problem where split deliveries are allowed. A set of potential customers is given, each associated with a demand and a profit. The set of customers to be served by a fleet of capacitated vehicles has to be identified in such a way that the profit collected is maximized, while satisfying constraints on the maximum time duration of each rou...

In the Bin Packing Problem with Conflicts (BPPC), we are given a set V = {1, 2, . . . , n} of items, each item i having a non-negative weight wi, and an infinite number of identical bins of weight capacity W . We are also given a conflict graph G = (V,E), where E is a set of edges such that (i, j) ∈ E when i and j are in conflict. Items in conflict cannot be assigned to the same bin. The aim of...

Several very effective exact algorithms have been developed for vehicle routing problems with time windows. Unfortunately, most of these algorithms cannot be applied to instances that are defined on road networks, because they implicitly assume that the cheapest path between two customers is equal to the quickest path. Garaix and coauthors proposed to tackle this issue by first storing alternat...

We investigate the two-stage guillotine two-dimensional cutting stock problem. This problem commonly arises in the industry when small rectangular items need to be cut out of large stock sheets. We propose an integer programming formulation that extends the well-known Gilmore and Gomory model by explicitly considering solutions that are obtained by both slitting some stock sheets down their wid...

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