Adriana F. Gabor

A new approximation algorithm for the multilevel facility location problem

In this paper we propose a new integer programming formulation for the multilevel facility location problem and a novel 3-approximation algorithm based on LP-rounding. The linear program that we use has a polynomial number of variables and constraints, thus being more efficient than the one commonly used in the approximation algorithms for these types of problems.

A Wide Coverage Positioning System (WPS) for Underwater Localization

Underwater localization is challenging as its efficacy is affected by propagation delays, motion-induced doppler shift, phase and amplitude fluctuations, multipath interference etc that are inherent in underwater acoustic channels. In this paper, we consider a recently proposed Underwater Positioning Scheme, which offers unique localization only in a finite region. We quantify the conditions for unique localization and propose a variant that offers unique localization with high probability regardless of the reference and unknown node deployment. We demonstrate the trade-offs between both schemes in terms of localizability space, localization latency and energy consumption.

The Time Window Assignment Vehicle Routing Problem

In many distribution networks, it is vital that time windows in which deliveries are made are assigned to customers for the long term. However, at the moment of assigning time windows demand is not known. In this paper we introduce the time window assignment vehicle routing problem, the TWAVRP. In this problem time windows have to be assigned before demand is known. Next the realization of demand is revealed and an optimal vehicle routing schedule has to be made that satisfies the time window constraints. We assume that different scenarios of demand realizations are known, as well as their probability distribution. The TWAVRP is the problem of assigning time windows such that the expected traveling costs are minimized. We propose a formulation of the TWAVRP and develop two variants of a column generation algorithm to solve the LP relaxation of this formulation. Numerical experiments show that these algorithms provide us with very tight LP-bounds to instances of moderate size in reasonable computation time. We incorporate the column generation algorithm in a branch and price algorithm and find optimal integer solutions to small instances of the TWAVRP. In our numerical experiments, the branch and price algorithm typically finds the optimal solution very early in the branching procedure and spends most time on proving optimality.

The vehicle rescheduling problem

The capacitated vehicle routing problem (CVRP) is the problem of finding a routing schedule to satisfy demand by supplying goods stored at the depot, such that the traveling costs are minimized. For operational purposes, in many practical applications a long term routing schedule is made, often based on average demand. When demand substantially differs from the average, constructing a new schedule is beneficial. The vehicle rescheduling problem (VRSP) is the problem of finding a new schedule that not only minimizes the total traveling costs but also minimizes the costs of deviating from the original schedule. In this paper a mathematical programming formulation of the rescheduling problem is presented as well as a heuristic solution method referred to as the two-phase heuristic. We provide sufficiency conditions for which it produces the optimal solution. Finally, we perform computational experiments to study the performance of the two-phase heuristic.

An approximation algorithm for the k-level stochastic facility location problem

We consider the k-level stochastic facility location problem. For this, we present an LP rounding algorithm that is 3-approximate. This result is achieved by a novel integer linear programming formulation that exploits the stochastic structure.

An Approximate Policy for a Dual-Sourcing Inventory Model with Positive Lead Times and Binomial Yield

This paper studies the inventory system of a retailer who orders his products from two supply sources, a local one that is responsive and reliable, but expensive, and a global one that is low-cost but less reliable. The deliveries from the global source only partially satisfy the quality requirements. We model this situation with a dual-sourcing inventory model with positive lead times and random yield. We propose a dual-index order-up-to policy (DOP) based on approximating the inventory model with an unreliable supplier by a sequence of dual-sourcing models with reliable suppliers and suitably modified demand distributions. Numerical results show that the performance of this heuristic is close to that of the optimal DOP. Moreover, we extend the heuristic to models with advance yield information and study its impact on the total inventory costs.

Maximizing revenue with allocation of multiple advertisements on a Web banner

The problem addressed in this paper is the allocation of multiple advertisements on a Web banner, in order to maximize the revenue of the allocated advertisements. It is essentially a two-dimensional, single, orthogonal, knapsack problem, applied to pixel advertisement. As this problem is known to be NP-hard, and due to the temporal constraints that Web applications need to fulfill, we propose several heuristic algorithms for generating allocation patterns. The heuristic algorithms presented in this paper are the left justified algorithm, the orthogonal algorithm, the GRASP constructive algorithm, and the greedy stripping algorithm. We set out an experimental design using standard banner sizes, and primary and secondary sorting criteria for the set of advertisements. We run two simulations, the first simulation compares the heuristics with an optimal solution found using brute force search, and the second simulation compares the heuristic algorithms to gain a better insight into their performance. Finding a suitable pattern generating algorithm is a trade-off between effectiveness and efficiency. Results indicate that allocating advertisements with the orthogonal algorithm is the most effective. In contrast, allocating advertisements using the greedy stripping algorithm is the most efficient. Furthermore, the best settings per algorithm for each banner size are given.

Performance Analysis of Data Delivery Schemes for a Multi-Sink Wireless Sensor Network

Wireless sensor networks are expected to be deployed in harsh environments characterised by extremely poor and fluctuating channel conditions. With the commonly adopted single-sink architecture, such conditions are exemplified by contention near the sink as a result of multipath delivery. This may be reduced by deploying multiple sinks spatially- apart e.g., along the edges of the network such that multiple spatially diverse paths that diverge like a starburst from each node towards these sinks can be set-up. Such an architecture opens up new challenges to the data delivery scheme, which determines the performance of the network. Since the compactness of sensors with limited energy resources restrict the use of sophisticated mechanisms, we consider simple data delivery schemes suited for such a multi-sink architecture. We optimise a single-path data delivery scheme with simple ARQ for a spatially-invariant environment, and demonstrate that its optimality over a spatially-diverse multipath scheme extends to spatially-variant environments. We also verify our analysis with simulations obtained using the Qualnet simulator.

A Tabu Search Algorithm for application placement in computer clustering

This paper presents and analyzes a model for the problem of placing applications on computer clusters (APP). In this problem, organizations requesting a set of software applications have to be assigned to computer clusters such that the costs of opening clusters and installing the necessary applications are minimized. This problem is related to known OR problems such as the multiproduct facility location problem and the generalized bin packing problem. We show that APP is NP-hard, and then propose a simple Tabu Search heuristic to solve it. The performance of the Tabu Search heuristic is assessed via extensive computational experiments, which indicate the promise of the proposed Tabu Search.

How * not * to solve a Sudoku

We prove the NP-hardness of a consistency checking problem that arises in certain elimination strategies for solving Sudoku-type problems.