Yogesh K. Agarwal

Optimal relay node placement in delay constrained wireless sensor network design

The Delay Constrained Relay Node Placement Problem (DCRNPP) frequently arises in the Wireless Sensor Network (WSN) design. In WSN, Sensor Nodes are placed across a target geographical region to detect relevant signals. These signals are communicated to a central location, known as the Base Station, for further processing. The DCRNPP aims to place the minimum number of additional Relay Nodes at a subset of Candidate Relay Node locations in such a manner that signals from various Sensor Nodes can be communicated to the Base Station within a pre-specified delay bound. In this paper, we study the structure of the projection polyhedron of the problem and develop valid inequalities in form of the node-cut inequalities. We also derive conditions under which these inequalities are facet defining for the projection polyhedron. We formulate a branch-and-cut algorithm, based upon the projection formulation, to solve DCRNPP optimally. A Lagrangian relaxation based heuristic is used to generate a good initial solution for the problem that is used as an initial incumbent solution in the branch-and-cut approach. Computational results are reported on several randomly generated instances to demonstrate the efficacy of the proposed algorithm.

Design of Capacitated Multicommodity Networks with Multiple Facilities

This paper addresses the problem of designing a multicommodity network using several facilities with different costs and capacities. The problem is addressed in a special context of designing private telecommunications networks using Fractional-T1 services. The algorithm starts from any given solution of the problem and gradually improves it by solving a series of subproblems, arriving at a local minimum. The subproblem is defined over a subset of links, called the subnetwork, by using one of the links as the base link. It is shown that the subproblem can be formulated as a multiple choice knapsack problem that is solved by dynamic programming. Computational results and lower bounds are reported on problems of up to 20 nodes and up to 3 facilities. On most problems, the algorithm produces solutions within about 5% of lower bound on the average. Although it was not possible to compute lower bounds for larger problems, heuristic solutions and running times are reported for problems of up to 99 nodes and four facilities.

Value of Information in a Capacitated Supply Chain

Abstract The aim of this study is to understand the effect of end item demand variability, production flexibility, inventory characteristics, the number of retailers, and the impact of information sharing between channel members in a capacitated supply chain. Discrete event simulation is carried out to determine the impact of the above mentioned factors in a supply chain under different information sharing strategies. The simulation allows us to capturing the dynamic and stochastic complexity of the supply chain system. A two-level supply chain with one supplier having a capacity constraint and N identical retailers experiencing stationary and stochastic demand was built using a General Purpose Simulation Software. The optimum value of decision variables for various information scenarios is determined by multiple simulation runs and the response surface methodology technique.

Fixed-Charge Transportation Problem: Facets of the Projection Polyhedron

In this paper we consider the well-known fixed-charge transportation problem. To send any flow from source si to destination tj, we incur a unit variable shipping cost of cij and a fixed cost fij. Here we study the structure of the projection polyhedron of this problem, in the space of 0-1 variables associated with fixed charges, and we develop several classes of valid inequalities and derive conditions under which they are facet defining. In some cases, if the conditions are not satisfied, we show how they can be lifted to define facets. Several heuristics for generating and adding these facets are presented. Using these results, we develop a computationally effective algorithm for solving the problem. The computational results clearly indicate the usefulness of this approach.

Solving the two-facility network design problem with 3-partition facets

The article studies the problem of designing telecommunication networks using transmission facilities of two different capacities. The point-to-point communication demands are met by installing a mix of facilities of both capacities on the edges to minimize total cost. We consider 3-partitions of the original graph which results in smaller 3-node subproblems. The extreme points of this subproblem polyhedron are characterized using a set of propositions. A new approach for computing the facets of the 3-node subproblem is introduced based on polarity theory. The facets of the subproblem are then translated back to those of the original problem using a generalized version of a previously known theorem. The approach has been tested on several randomly generated and real life networks. The computational results show that the new family of facets significantly strengthen the linear programming formulation and reduce the integrality gap. Also, there is a substantial reduction in the size of the branch-and-bound B&B tree if these facets are used. Problems as large as 37 nodes and 57 edges have been solved to optimality within a few minutes of computer time.

Optimal relay placement in Wireless Sensor networks using node cut inequalities

Optimal relay placement problem arises in wireless sensor network designs, where additional relay nodes are to be placed at a subset of given potential relay locations in order to transmit data from already existing source nodes to a base station known as root node. The relay nodes have a certain specified transmission radius and cannot transmit data beyond it. In this paper, we consider the projection of original problem onto the sub-space of relay node variables and identify a set of strong inequalities called node cut inequalities. We also propose an integer programming based approach for solving the problem using these inequalities. The computational results show that the node cut inequality based formulation provides a very tight lower bound for the problem, and can be helpful in solving the problem optimally under a branch-and-cut approach.

Fixed charge multicommodity network design using p-partition facets

We are given an undirected network G[V, E] and a set of traffic demands. To install a potential edge e ∈ E we incur a cost Fe to provide a positive capacity ae. The objective is to select edges, at minimum cost, so as to permit a feasible multicommodity flow of all traffic. We study structure of the projection polytope of this problem, in the space of binary variables associated with fixed-charges, by relating facets of a p node problem (p=2,3, or 4), defined over a multi-graph obtained by a p-partition of V, to the facets of the original problem. Inspired from the well-known “cover” inequalities of the Knapsack Problem, we develop the notion of p-partition cover inequalities. We present necessary and sufficient conditions for such inequalities to be facet defining for p = 3 and 4. A simple heuristic approach for separating and adding such violated inequalities is presented, and implemented for p values up to 10. We report optimal solutions for problems with 30 nodes, 60 edges, and fully dense demand matrices within a few minutes of cpu time for most instances. Some results for dense graph problems are also reported.

Survivable network design with shared-protection routing

In this paper we study the problem of designing a survivable telecommunication network with shared-protection routing. We develop a heuristic algorithm to solve this problem. Recent results in the area of global re-routing have been used to obtain very tight lower bounds for the problem. Our results indicate that in a majority of problem instances, the average gap between the heuristic solutions and the lower bounds is within 5%. Computational experience is reported on randomly generated problem instances with up to 35 nodes, 80 edges and 595 demand pairs and also on the instances available in SNDlib database.

Multi‐product maritime inventory routing with optional cargoes : An application to outbound automotive logistics

Purpose - The ocean transportation of automobiles is carried out by specialized Roll-on/Roll-off ships, which are designed to carry a large number of automobiles at a time. Many of these shipping companies have vertically integrated or collaborated with other logistics services providers to offer integrated maritime logistics solution to car manufacturers. The purpose of this study is to develop an optimization model to address the tactical level maritime logistics planning for such a company. Design/methodology/approach - The problem is formulated as a mixed integer linear program and we propose an iterative combined Ant colony and linear programming-based solution technique for the same. Findings - This paper can integrate the maritime transportation planning of internally managed cargoes with the inventory management at the loading and discharging ports to minimize supply-chain cost and also maximize additional revenue through optional cargoes using same fleet of ships. Research limitations/implications - The mathematical model does not consider the variability in production and consumption of products across various locations, travel times between different nodes, etc. Practical implications - The suggested mathematical model to the supply-chain planning problem and solution technique can be considered in the development of decision support system for operations planning. Originality/value - This paper extends the maritime inventory routing model by considering simultaneous planning of optional cargoes with internally managed cargoes.

Near optimal design of wavelength routed optical networks

The problem of designing a wavelength routed optical transport network without wavelength conversion at intermediate nodes is considered. A class of valid inequalities for wavelength routing and assignment is reported and is used to augment traditional network design formulations. The resulting network cost provides a lower bound on the cost of a network that permits wavelength routing. The resulting network is shown to be optimal for a majority of the problem instances tested and in those cases where it is not, a trial-and-error method is proposed that is able to find near-optimal solutions within relatively short period of time. This is achieved by developing efficient and effective heuristics that attempt to provide a feasible wavelength routing. Computational tests are reported on relatively larger problem sizes than have been reported in literature on the wavelength routing problem.