Mihiro Sasaki

On the selection of hub airports for an airline hub-and-spoke system

We consider the 1-stop multiple allocation p-hub median problem. We formulate the problem as a p-median problem and propose a branch-and-bound algorithm and a greedy-type heuristic algorithm. We report computational results for problems with airline passenger interactions between 25 US cities in 1970 evaluated by the Civil Aeronautics Board. For further investigation, we made computational experiments with some random data. The obtained results also show that the proposed algorithms work better than the well-known nested-dual algorithm, particularly for relatively small problems.

A Stackelberg hub arc location model for a competitive environment

In this paper, we consider the design of large-scale multiple allocation hub-and-spoke transportation networks in a competitive environment. We adopt a generic hub arc location model that locates arcs with discounted transport costs connecting pairs of hub facilities. Two firms compete for customers in a Stackelberg framework where the leader firm locates hub arcs to maximize its revenue, given that the follower firm will subsequently locate its own hub arcs to maximize its own revenue. We present an optimal solution algorithm that allocates traffic between the two firms based on the relative utility of travel via the competing hub networks. Results for each competing firm with up to three hub arcs show the important role of competition in designing hub-based transportation systems.

Exact optimal solutions of the minisum facility and transfer points location problems on a network

We consider hierarchical facility location problems on a network called Multiple Location of Transfer Points (MLTP) and Facility and Transfer Points Location Problem (FTPLP), where q facilities and p transfer points are located and each customer goes to one of the facilities directly or via one of the transfer points. In FTPLP, we need to find an optimal location of both the facilities and the transfer points while the location of facilities is given in MLTP. Although good heuristics have been proposed for the minisum MLTP and FTPLP, no exact optimal solution has been tested due to the size of the problems. We show that the minisum MLTP can be formulated as a p-median problem, which leads to obtaining an optimal solution. We also present a new formulation of FTPLP and an enumeration-based approach to solve the problems with a single facility.

An LP-based heuristic algorithm for the node capacitated in-tree packing problem

In this paper, we deal with the node capacitated in-tree packing problem. The input consists of a directed graph, a root node, a node capacity function and edge consumption functions for heads and tails. The problem is to find a subset of rooted spanning in-trees and their packing numbers, where the packing number of an in-tree is the number of times it is packed, so as to maximize the sum of packing numbers under the constraint that the total consumption of the packed in-trees at each node does not exceed the capacity of the node. This problem is known to be NP-hard.We propose a two-phase heuristic algorithm for this problem. In the first phase, it generates candidate spanning in-trees to be packed. The node capacitated in-tree packing problem can be formulated as an IP (integer programming) problem, and the proposed algorithm employs the column generation method for the LP (linear programming) relaxation problem of the IP to generate promising candidate in-trees. In the second phase, the algorithm computes the packing number of each in-tree. Our algorithm solves this second-phase problem by first modifying feasible solutions of the LP relaxation problem and then improving them with a greedy algorithm. We analyze upper and lower bounds on the solution quality of such LP-based algorithms for this problem.We conducted computational experiments on graphs used in related papers and on randomly generated graphs. The results indicate that our algorithm has a better performance than other existing methods. Highlights? Introducing node capacities to a spanning arborescence packing problem on digraphs. ? Generating in-trees by the column generation method. ? Solving the minimum weight rooted arborescence problem as the pricing problem. ? Packing in-trees by a greedy algorithm with efficient data structures. ? The approximation guarantee of LP-based algorithms.

A heuristic method for clustering a large-scale sensor network

We present a new heuristic method for a clustering problem of sensor networks. The heuristic method is using the uncapacitated facility location problem formulation for the clustering problem of sensor networks. It is an iterative method based on the Voronoi diagram. We also propose a parallel version of the heuristics to reduce the time to obtain a solution. The proposed algorithms are investigated for the quality of their approximate solutions and computational time to obtain them. By comparing the approximate solutions to the exact solutions for examples of one hundred sensors, we found that the quality of the approximate solutions is almost the same as that of the exact ones. The computational time to obtain the approximate solutions is a thousandth of that of obtaining the exact solution. For examples of ten thousand sensors, the computational time to obtain a solution is about 9.1 seconds by the sequential algorithm and about 6.0 seconds by our parallel algorithm with six computers.

The complexity of the node capacitated in-tree packing problem

This article describes a node capacitated in-tree packing problem. The input consists of a directed graph, a root node, a node capacity function, and edge consumption functions. The problem is to find the maximum number of rooted in-trees, such that the total consumption of in-trees at each node does not exceed the capacity of the node. The problem is one of the network lifetime problems that are among the most important issues in the context of sensor networks. We establish the computational complexity of the problem under various restrictions on consumption functions and graphs. For example, we consider general graphs, acyclic graphs, and complete graphs embedded in the d -dimensional space \input amssym

New formulation for scheduling problem in multi-hop wireless sensor networks

{\Bbb{R}}^d

STACKELBERG HUB LOCATION PROBLEM

having edge consumption functions depending only on distances between end nodes.

ON THE HUB-AND-SPOKE MODEL WITH ARC CAPACITY CONATRAINTS

In this paper, we consider a multi-hop sensor network, where the network topology is a tree, TDMA is employed as medium access control, and all data generated at sensor nodes are delivered to a sink node located on the root of the tree through the network. It is reported that if a transmission schedule that avoids interference between sensor nodes completely can be computed, TDMA is preferable to CSMA/CA in performance. However, solving the scheduling problem for TDMA is difficult, especially, in large-scale multi-hop sensor networks. In this paper, to formulate the scheduling problem for TDMA, we propose min-max model and min-sum model. While the min-max model yields the shortest schedule under the constraints, the min-sum model does not guarantee providing the shortest schedule. Numerical examples show that the min-sum model can provide good schedules in a reasonable CPU time, even when the min-max model fails to compute the shortest schedule in a reasonable CPU time.