Fatma Gzara

A cutting plane approach for bilevel hazardous material transport network design

Abstract We consider the network design problem for hazardous material transportation that is modeled as a bilevel multi-commodity network flow model. We study a combinatorial bilevel formulation of the problem and present results on its solution space. We propose a family of valid cuts and incorporate them within an exact cutting plane algorithm. Numerical testing is performed using real as well as random data sets. The results show that the cutting plane method is faster than other methods in the literature on the same formulation.

Telecommunications network design with multiple technologies

In this paper we consider a telecommunications network design problem allowing for multiple technologies. The problem arises in wide-area network and metro-area network design for which a combination of technologies may be necessary due to high traffic volumes, long-distance transmission, and design restrictions. The network design problem builds the best network to channel traffic between a set of origins and destinations, which requires selecting links, equipping them with fiber, deciding on the type of technology, and locating switches. The goal is to minimize the total cost of the network, which accounts for the flow cost, the fiber and technology costs, and the switch-location cost. We model the problem using a multicommodity network design formulation with side constraints. We apply Benders decomposition to the problem and develop a two-phase solution method that uses a number of improvements over the basic Benders algorithm. We present promising results on randomly generated test problems.

Linear location-inventory models for service parts logistics network design

We present two integrated network design and inventory control problems in service-parts logistics systems. Such models are complicated due to demand uncertainty and highly nonlinear time-based service level constraints. Exploiting unique properties of the nonlinear constraints, we provide an equivalent linear formulation under part-warehouse service requirements, and an approximate linear formulation under part service requirements. Computational results indicate the superiority of our approach over existing approaches in the literature.

Facility location with economies and diseconomies of scale: models and column generation heuristics

Most of the literature on facility location assumes a fixed setup and a linear variable cost. It is known, however, that as volume increases cost savings are achieved through economies of scale, but when the volume exceeds a certain level, diseconomies of scale occur and marginal costs start to increase. This is best captured by an inverse S-shaped cost function that is initially concave and then turns convex. This article studies such a class of location problems and solution methods are proposed that are based on Lagrangian relaxation, column generation, and branch-and-bound methods. A nonlinear mixed-integer programming formulation is introduced that is decomposable by environment type; i.e., economies or diseconomies of scale. The resulting concave and convex subproblems are then solved efficiently as piecewise convex and concave bounded knapsack problems, respectively. A heuristic solution is found based on dual information from the column generation master problems and the solution of the subproblems. Armed with the Lagrangian lower bound and the heuristic solution, the procedure is embedded in a branch-and-price-type algorithm. Unfortunately, due to the nonlinearity of the problem, global optimality is not guaranteed, but high-quality solutions are achieved depending on the amount of branching performed. The methodology is tested on three function types and four cost settings. Solutions with an average gap of 1.1% are found within an average of 20 minutes.

The robust crew pairing problem: model and solution methodology

We present a new robust formulation for the crew pairing problem where flight and connection times are random and vary within an interval. The model protects against infeasibility with a specified level of uncertainty and minimizes crew cost in the worst case. The resulting robust terms in the objective function and in the resource constraints are nonlinear. We apply Lagrangian relaxation to separate the nonlinear terms in the subproblem leading to a new robust formulation of the shortest path problem with resource constraints. We show that the nonlinear subproblem can be solved as a series of linear auxiliary problems. The proposed solution methodology was successful to solve industry instances in very competitive times and led to more robust crew pairing solutions as shown by simulation experiments.

Characterizing the optimality gap and the optimal packings for the bin packing problem

We provide properties for the bin packing problem based on Lagrangian relaxation and column generation. We characterize the columns that are likely to be in an optimal solution, explicitly quantify the gap for any feasible solution, and provide a new set partitioning formulation. These properties are then used to design a column generation heuristic that solves a reduced set covering problem containing a selected set of columns. The heuristic is tested on benchmark instances from the literature, and is found to perform extremely well. It is able to find optimal solutions for

Logic-based Benders decomposition for an inventory-location problem with service constraints☆

70\, \%

Linear integrated location-inventory models for service parts logistics network design

70% out of the 1,617 instances tested, and to find feasible solutions that are one bin away from the optimal for an additional