In this paper we propose a Branch and Price algorithm for solving multi-period single-sourcing problems. In particular, we generalize a Branch and Price algorithm that was developed for the Generalized Assignment Problem (GAP) to a class of convex assignment problems. We then identify an important subclass of problems, containing many variants of the multi-period single-sourcing problem (MPSSP)...

Given a directed graph with weights on the vertices and on the arcs, a θ-improper k-coloring is an assignment of at most k different colors to the vertices of G such that the weight of every vertex v is greater, by a factor 1 θ , than the sum of the weights on the arcs (u, v) entering v with the head u of the same color as v. For a given real number θ, we consider the problem of determining the...

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles’ capacity and customer time windows. The delivery request of a customer is discrete since it consists of several items that cannot be split further. The problem belongs to the c...

The multi-depot pickup and delivery problem with heterogeneous fleet and soft time windows (MDPDPHSTW) requires to find a minimum cost routing for a fleet vehicles with different capacities and based at different depots, satisfying a given set of customers. A customer request is associated with two locations: a source where a certain demand must be picked up and a destination where this demand ...

We present a column-generation model and branch-and-price-and-cut algorithm for origin-destination integer multicommodity flow problems. The origin-destination integer multicommodity flow problem is a constrained version of the linear multicommodity flow problem in which flow of a commodity (defined in this case by an origin-destination pair) may use only one path from origin to destination. Br...

This paper describes a methodology for the case mix problem at the strategic level in the health care sector. Aiming to maximize hospital profits under the given resource capacity, a mathematical model is developed to produce an optimal case mix pattern and a corresponding resource allocation scheme. Two exact methods, integer linear programming and branch-and-price, are deployed to solve the c...

In this paper we address branch-and-price algorithms for the unsplittable multicommodity flow problem. This problem is defined over a capacitated network in which we intend to route a set of commodities, each one with a given origin, destination and demand, at minimal cost, without exceeding the arc capacities. Furthermore, the flow of each commodity must be routed using a single path. Formulat...

Branch-and-price is a well established technique for solving large scale integer programming problems. This method combines the standard branch-and-bound framework of solving integer programming problems with Column Generation. In each node of the branch-and-bound tree, the bound is calculated by solving the LP relaxation. The LP relaxation is solved using Column Generation. In this report, we ...