François Vanderbeck

University of Bordeaux · College of Science and Technology

Given the emergence of two-echelon distribution systems in several practical contexts, this paper tackles, at the strategic level, a distribution network design problem under uncertainty. This problem is defined as the two-echelon stochastic multi-period capacitated location-routing problem (2E-SM-CLRP). It considers a network partitioned into two...

This document presents a user guide for BaPCod version 0.66, a C++ library implementing a generic branch-cut-and-price solver. We give guidelines for installing BaPCod, using its modelling language, BaPCod parameterization, retrieving BaPCod statistics, and understanding BaP-Cod output. We also present the VRPSolver extension of BaPCod which allows...

Optimizing nuclear unit outages is of significant economic importance for the French electricity company EDF, as these outages induce a substitute production by other more expensive means to fulfill electricity demand. This problem is quite challenging given the specific operating constraints of nuclear units, the stochasticity of both the demand a...

More than ever, data networks have demonstrated their central role in the world economy, but also in the well-being of humanity that needs fast and reliable networks. In parallel, with the emergence of Network Function Virtualization (NFV) and Software Defined Networking (SDN), efficient network algorithms considered too hard to be put in practice...

Capacitated vehicle routing problems are widely studied combinatorial optimization problems, and branch-and-cut-and-price algorithms can solve instances harder than ever before. These models, however, neglect that demands volumes are often not known with precision when planning the vehicle routes, thus incentivizing decision makers to significantly...

Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a...

This paper proposes a comprehensive methodology for the stochastic multi-period two-echelon distribution network design problem (2E-DDP) where product flows to ship-to-points are directed from an upper layer of primary warehouses to distribution platforms (DPs) before being transported to the ship-to-points. A temporal hierarchy characterizes the d...

In the two-dimensional guillotine cutting-stock problem, the objective is to minimize the number of large plates used to cut a list of small rectangles. We consider a variant of this problem, which arises in glass industry when different bills of order (or batches) are considered consecutively. For practical organization reasons, leftovers are not...

Math heuristics have become an essential component in mixed integer programming (MIP) solvers. Extending generic MIP heuristics, our study outlines generic procedures to build primal solutions in the context of a Branch-and-Price approach and reports on their performance. Rounding the linear relaxation solution of the Dantzig-Wolfe reformulation, w...

Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cut-and-Price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a...

The convergence of a column generation algorithm can be improved in practice by using so-called stabilization techniques. Proximal methods based on penalising the deviation from the incumbent dual solution have become standards of the domain. However, the analysis of such methods is important to understand the mechanism on which they rely, to appre...

The two-dimensional knapsack problem consists in packing a set of small rectangular items into a given large rectangle while maximizing the total reward associated with selected items. We restrict our attention to packings that emanate from a k-stage guillotine-cut process. We introduce a generic model where a knapsack solution is represented by a...

This work presents the application of branch-and-price approaches to the automatic version of the Software Clustering Problem. To tackle this problem, we apply the Dantzig–Wolfe decomposition to a formulation from the literature. Given this, we present two Column Generation (CG) approaches to solve the linear programming relaxation of the resulting...

This work presents the application of branch-and-price approaches to the automatic version of the Software Clustering Problem. To tackle this problem, we apply the Dantzig-Wolfe decomposition to a formulation from literature. Given this, we present two Column Generation (CG) approaches to solve the linear programming relaxation of the resulting ref...

Stabilization procedures for column generation can be viewed as cutting plane strategies in the dual. Exploiting the link between in-out separation strategies and dual price smoothing techniques for column generation, we derive a generic bound convergence property for algorithms using a smoothing feature. Such property adds to existing in-out asymp...

Working in an extended variable space allows one to develop tighter reformu-lations for mixed integer programs. However, the size of the extended formulation grows rapidly too large for a direct treatment by a MIP-solver. Then, one can work with inner approximations defined and improved by generating dynamically vari-ables and constraints. When the...

Primal heuristics have become an essential component in mixed integer programming (MIP). Generic heuristic paradigms of the literature remain to be extended to the context of a column generation so-lution approach. As the Dantzig-Wolfe reformulation is typically tighter than the original compact formulation, techniques based on rounding its linear...

The bin packing problem with conflicts consists in packing items in a minimum number of bins of limited capacity while avoiding joint assignments of items that are in conflict. Our study demonstrates the comparatively good performance of a generic Branch-and-Price algorithm for this problem. We made use of our black-box solver BaPCod, relying on it...

Working in an extended variable space allows one to develop tight reformulations for mixed integer programs (MIP). However, the size of the extended formulation grows rapidly too large for a direct treatment by a MIP-solver. When the extended formulation stems from a decomposition principle, as typical in practice, a column generation procedure tha...

Inventory routing problems combine the optimization of product deliveries (or pickups) with inventory control at customer sites. Our application concerns the planning of single product pickups over time; each site accumulates stock at a deterministic rate; the stock is emptied on each visit. At the tactical planning stage considered here, our objec...

We examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover reformulations based on decomposition, such as Lagrangean relaxation, the Dantzig-Wolfe ref...

Train operations will be greatly enhanced with the development of new decision support systems. However, when considering problems such as online rescheduling of trains, experience shows a pitfall in the communication between the different elements that compose them, namely simulation software (in charge of projection, conflict detection, validatio...

In the past decade, significant progress has been achieved in developing generic primal heuristics that made their way into commercial mixed integer programming (MIP) solver. Extensions to the context of a column generation solution approach are not straightforward. The Dantzig-Wolfe decomposition principle can indeed be exploited in greedy, local...

We consider a multi-layer network design model arising from a real-life telecommunication application where traffic routing decisions imply the installation of expensive nodal equipment. Customer requests come in the form of bandwidth reservations for a given origin destination pair. Bandwidth demands are expressed as a multiple of nominal granular...

Knapsack problems with setups find their application in many concrete industrial and financial problems. Moreover, they also arise as subproblems in a Dantzig–Wolfe decomposition approach to more complex combinatorial optimization problems, where they need to be solved repeatedly and therefore efficiently. Here, we consider the multiple-class integ...

The traffic grooming, routing and wavelength assignment (GRWA) problem in wavelength division multiplexed (WDM) networks has been the focus of many studies over the past years. Under fixed grooming ratio and ring network topology assumptions, researchers have been able to provide exact or near optimal solutions. However, all practical cases in mesh...

We consider a telecommunication optical network design problem where traffic routing decisions imply the installation of expensive equipment at nodes. Customer requests come in the form of bandwidth reservations for a given origin destination pair. Capacity reservations are expressed as a multiple of nominal granularities. Each nominal granularity...

In this paper, we address the Grooming, Routing and Wavelength Assignment (GRWA) problem under the minimization of the total number of optical ports. Even if many studies have been conducted on this problem under potentially restrictive assumptions, its difficulty only allows producing solutions that are not proved optimal and that may be far from...

When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear programming community as the cutting-plane algorithm of Kelley and Cheney-Goldstein. However, more...

unavailable

The periodic vehicle routing problem (PVRP) consists in establishing a planning of visits to clients over a given time horizon so as to satisfy some service level while optimizing the routes used in each time period. The tactical planning model considered here restricts its attention to scheduling visits and assigning them to vehicles while leaving...

The Dantzig–Wolfe reformulation principle is presented based on the concept of generating sets. The use of generating sets allows for an easy extension to mixed integer programming. Moreover, it provides a unifying framework for viewing various column generation practices, such as relaxing or tightening the column generation subproblem and introduc...

Periodic Vehicle Routing Problem: classification and heuristic for tactical planning. The Periodic Vehicle Routing Problem (PVRP) consists in assigning customer visits to vehicle routes in some periods of a time horizon so as to satisfy some service level requirements that can take the form of frequency of visit, constraint on time lag between visi...

We review the main issues that arise when implementing a column generation approach to solve a mixed integer program: setting-up the Dantzig-Wolfe reformulation, adapting standard MIP techniques to the context of column generation (branching, preprocessing, primal heuristics), and dealing with issues specific to column generation (initialization, s...

Developing a branching scheme that is compatible with the column generation procedure can be challenging. Application specific and generic schemes have been proposed in the literature, but they have their drawbacks. One generic scheme is to implement standard branching in the space of the compact formulation to which the Dantzig-Wolfe reformulation...

. The bounded multiple-class binary knapsack problem is a variant of the knapsack problem where the items are partitioned into classes and the item weights in each class are a multiple of a class weight. Thus, each item has an associated multiplicity. The constraints consists of an upper bound on the total item weight that can be selected and upper...

We consider the cutting of rectangular order pieces into stock pieces of specified width and length. The cutting process involves three stages of orthogonal guillotine cutting: Stock pieces are cut into sections that are cut into slits that are cut into order pieces. Restrictions imposed on the cutting process make the combinatorial structure of th...

The cutting stock problem is that of finding a cutting of stock material to meet demands for small pieces of prescribed dimensions while minimising the amount of waste. Because changing over from one cutting pattern to another involves significant setups, an auxiliary problem is to minimise the number of different patterns that are used. The patter...

Dantzig-Wolfe decomposition as applied to an integer program is a specific form of problem reformulation that aims at providing a tighter linear programming relaxation bound. The reformulation gives rise to an integer master problem, whose typically large number of variables is dealt with implicitly by using an integer programming column generation...

This paper reports on our attempt to design an efficient exact algorithm based on column generation for the cutting stock problem. The main focus of the research is to study the extend to which standard branch-and-bound enhancement features such as variable fixing, the tightening of the formulation with cutting planes, early branching, and rounding...

We study a problem that has arisen recently in the design of telecommunications transmission networks at France Telecom. Given a set of centers in a city or conglomeration linked together on a ring architecture, given the expected demands between the centers and an essentially unlimited availability of rings of fixed capacity on the network, assign...

Many practical applications of lot-sizing and scheduling problems involve start-up times. Operations research literature contains but few studies of lot-sizing models that take start-up times explicitly into account. Here, we review some of these studies, discuss the models and their complexity, and we propose further models. We consider in particu...

An exact column generation algorithm for integer programs with a large (implicit) number of columns is presented. The family of problems that can be treated includes not only standard partitioning problems such as bin packing and certain vehicle routing problems in which the columns generated have 0–1 compenents and a right-hand side vector of 1's,...

Thesis (doctoral)--Université catholique de Louvain, 1994.

Utilizing the automatic assembly machines effectively is critical for electronics assembly operations. This paper develops an optimization model and methodology to assign product families to parallel placement machines in a high mix, low volume environment. Unlike strategic and operational models that emphasize either workload balancing or setup op...

We consider a very simple integer program involving production of a single item and start-up costs for the standard machines first studied by Lasdon and Terjung. Solving directly as an integer program leads to prohibitively large branch and bound trees. Here, we show how using a simple family of valid inequalities and a heuristic procedure to choos...

This paper presents effective heuristics to solve GRWA problem where the objective is to minimize network cost. We present our greedy, tabu search and rounding off column generation based heuristics and we test them on some instances to make some comparison.

We consider an application of the inventory routing problem. A ∞eet of vehicles is devoted to collecting a single product from geographically dis- persed sites. Each site has its own accumulation rate and stock capacity. On each visit, the vehicle empties the stock of accumulated product. In the tactical planning phase, we search for a periodic sol...

The paper deals with a two layer optical network design problem: The virtual layer where nodes are logically connected by optical hops and the physical layer where optical hops have to be routed. The optical hops are used to route a very large number of commodities that direct approaches have difficulties to handle efficiently. We propose a hierarc...

Mots-clefs : heuristiques primales, génération de colonnes, tournées de véhicules, planification, problème industriel. 1 Heuristiques basées sur la génération de colonnes Les heuristiques classiques de type glouton, de recherche locale ou d'arrondi de la solution continue, peuvent être adaptées dans le cadre d'une approche de génération de colonnes...