Dong-wan Tcha

Prioritized channel assignment in a cellular radio network

Dimensioning procedures for prioritized channel assignment in a cellular radio network are considered. Under the cutoff priority discipline, the prioritized channel assignment procedures for a single cell and multicell system are formulated as nonlinear discrete capacity allocation problems. Exact incremental algorithms which efficiently solve the proposed problems are devised. They are based on the properties of the blocking probabilities of new calls and handoff calls. Given the number of available frequency channels together with the arrival rates and the grade of service (GOS) for both types of calls in each cell, algorithm SP1 generates an optimal channel assignment which ensures priority for handoff calls. Given the arrival rates and distinct GOSs for new and handoff calls, algorithm SP2 finds the minimum number of channels required in each cell. Algorithm MP extends algorithm SP1 to a multicell system and provides the prioritized channel assignment for all calls in the system. The algorithms are very fast and are appropriate for the fair allocation of frequency channels among cells. >

A column generation approach to the heterogeneous fleet vehicle routing problem

We consider a vehicle routing problem with a heterogeneous fleet of vehicles having various capacities, fixed costs and variable costs. An approach based on column generation (CG) is applied for its solution, hitherto successful only in the vehicle routing problem with time windows. A tight integer programming model is presented, the linear programming relaxation of which is solved by the CG technique. A couple of dynamic programming schemes developed for the classical vehicle routing problem are emulated with some modifications to efficiently generate feasible columns. With the tight lower bounds thereby obtained, the branch-and-bound procedure is activated to obtain an integer solution. Computational experience with the benchmark test instances confirms that our approach outperforms all the existing algorithms both in terms of the quality of solutions generated and the solution time.

On the generalized minimum spanning tree problem

This paper considers the Generalized Minimum Spanning Tree Problem (GMSTP). Given an undirected graph whose nodes are partitioned into mutually exclusive and exhaustive node sets, The GMSTP is then to find a minimum-cost tree which includes exactly one node from each node set. Here, we show that the GMSTP is NP-hard and that unless P = NP no polynomial-time heuristic algorithm with a finite worst-case performance ratio can exist for the GMSTP. We present various integer programming formulations for the problem and compare their linear programming relaxations. Based on the tightest formulation among the ones proposed, a dual-based solution procedure is developed and shown to be efficient from computing experiments.

A branch-and-bound algorithm for the multi-level uncapacitated facility location problem

Abstract This paper discusses the problem of locating facilities over all levels in a multi-level distribution system where commodities are shipped from origin-level facilities to destination points via a number of intermediate level facilities. The objective is to determine the optimal set of facilities to open for each distribution level, which minimizes the total distribution costs including the fixed costs associated with opening them. The problem is formulated as a mixed integer linear program with the so-called ‘tight’ or ‘disaggregated’ constraints, by which in our branch-and-bound solution method, the dual based scheme of ‘dual ascent procedure’ by Erlenkotter, and Bilde and Krarup, is successfully applied. In addition, a heuristic ‘primal descent procedure’ which improves integer solutions already obtained, and some efficient node simplification procedure are introduced. Though our approach can be applied to any multi-level case, computational experiments are conducted mostly for two-level problems such that our approach can be compared with the other approaches. Computational experience with some small scale three-level problems is also reported on.

Optimal Load Balancing on Sonet Bidirectional Rings

In this paper we consider the Ring Loading Problem, which arises in the design of SONET bidirectional rings. The issue of demand splitting divides the ring loading problem into the two kinds. One allows a demand to be split and routed in two different directions and the other does not. The former kind becomes a relaxation of the latter. We present an efficient exact solution procedure for the case with demand splitting, and a two-approximation algorithm for the case without demand splitting. Computational results are also shown to prove the efficiency of the proposed procedures.

A branch and bound algorithm for the two-level uncapacitated facility location problem with some side constraints

Abstract This paper deals with the problem of locating at minimum total costs both plants and warehouses in a two-level distribution system where commodities are delivered from plants to customers either directly or indirectly via warehouses. Some side-constraints are imposed on the problem, which represent the adjunct relationship of some warehouses to a certain plant. Proposed is an efficient branch and bound solution procedure, employing a set of new devices for lower bounds and simplifications which are obtained by exploiting the submodularity of the objective function and the special structure of the side-constraints. Computational experiments with fifteen test problems are provided.

Optimal design of a distributed network with a two-level hierarchical structure

Abstract This paper deals with the topological design of a network with a two-level hierarchical structure where the embedded backbone network is full-meshed and the local networks attached to it are of star type. The whole problem, unlike the conventional approaches partitioning it into two subproblems, is directly handled in such a general setting that both a backbone network and local access networks are to be simultaneously determined. We formulate this problem as a quadratic 0–1 programming model, and also propose an equivalent linearized version of the model. Based on the observation that the linearized model is a variant of the well established uncapacitated facility location problem, a dual-based solution procedure is developed and shown to be efficient from computing experiments which were done on a wide variety of problems with up to 50 backbone nodes and 50 user nodes.

Approximate analysis of finite fork/join queueing networks

Abstract We perform an approximate analysis on the finite-buffered acyclic fork/join queueing networks under the “blocking before service” mechanism. This study, besides being able to handle a network with complex topology and with finite buffers, is more general than the existing ones of its kind in that two performance measures, the system throughput and the average number of customers in each buffer, are taken into account. For a simple two-sibling network, we propose in detail a decomposition algorithm in which each decomposed subsystem carries over the local fork/join/tandem structure. The extension of this algorithm to a more general system is also discussed. Experimental results are provided showing that the proposed algorithm yields accurate results on the two performance measures.

A new lower bound for the frequency assignment problem

We propose a new lower bound on the number of frequencies required to meet the frequency demands in a cellular network. It extends Gamsts (1986) work by devising a procedure of frequency insertion, which makes the best of unexploited frequency spaces between the assigned frequencies. Our lower bound is claimed to have much wider and easier real-world applicability due to its relaxed prerequisite condition. Furthermore, it is shown via an illustrative example to be much tighter than its previous counterpart.

Optimal design of a two-level hierarchical network with tree-star configuration

Abstract This paper deals with the topological design problem of a hierarchical two-level network where the upper-level backbone network is of tree type and the lower-level local access networks are of star-type. As a means to widen the real-world applicability over the existing network design studies, a backbone node not opened is allowed to be included in the backbone tree for transhipment purpose. The problem is modelled as a mixed 0–1 integer programming, whose special structure is exploited for the development of a dual-based lower bounding procedure. The procedure is incorporated in the branch and bound solution method, whose effectiveness is well demonstrated by the computational experiments conducted with a variety of problems ranging up to 50 backbone nodes and 200 demand points.