rakesh kawatra - Academia.edu (original) (raw)

Papers by rakesh kawatra

Proceedings of International Academic Conferences, 2014

We present a two-phase heuristic for designing a capacitated degree constrained min sum arboresce... more We present a two-phase heuristic for designing a capacitated degree constrained min sum arborescence. For a given directed graph G(V,E) where V={0, 1,?,n} with nonnegative costs Cij for each (i,j) ? E, our heuristic finds a minimum cost arborescence rooted at node 1 that spans the set {0, 1,?,n} with a constraint that the number of edges incident on each node i ? {1,2,?,n} is limited to a predetermined number constrained by the number of ports available on them (degree constraint). Additionally, the polling and response time constraints limit the number of nodes in the sub-trees rooted at node 1 (capacity constraint) predefined number. Lower bounds given for the integer programming formulation of the problem by our heuristic is used to estimate the quality of the solutions. Experimental results over a wide range of problem structures show that the two-phase heuristic gives verifiably good solutions to this problem.

The degree-constrained minimal spanning tree (DCMST) problem with unreliable links and node outag... more The degree-constrained minimal spanning tree (DCMST) problem with unreliable links and node outage costs consists of finding links in a network to connect a set of terminal nodes to a central node while minimizing the expected annual expenditure. The number of ports available on each terminal node limits the number of incident links (the degree constraint). Each terminal node in

problem consists of scheduling the installation of links in a communication network so as to conn... more problem consists of scheduling the installation of links in a communication network so as to connect a set of terminal nodes S = [2,3...N] to a central node (node 1) with minimal present value of costs. The cost of the network is the sum of link layout cost and node outage costs. The link capacities limit the number of terminal nodes sharing a link. Node outage cost associated with each terminal node is the economic cost incurred by the network user whenever the terminal node is disabled due to failure of a link. In the network some of the terminal nodes are active at the beginning of the planning horizon while others are activated over time. The problem is formulated as an integer-programming problem. A Lagrangian relaxation method is used to find a lower bound for the optimal objective function value. Subgradient optimization method is used to find good lower bounds. This lower bound can be used to estimate the quality of the solution given by a heuristic.

Proceedings of the 35th International Academic Conference, Barcelona, 2018

In recent years, many undergraduate programs in business have added a course on Business process ... more In recent years, many undergraduate programs in business have added a course on Business process analysis in the curriculum. In this course students learn skills to design, manage, and improve business processes. One of the tools used for designing and documenting business processes is EPC diagrams. The textbooks covering this tool/technique provide a description of the tool including its purpose and one or more EPC diagrams for sample processes. The textbooks however do not provide logic used at each step of the solution development process making it almost impossible for a student to learn the tool by simply reading the book. An instructor may create an EPC diagram in class for a sample process and while developing it may explain the logic used at each step. Even though a student may understand how to use the tool when it is explained in class, the student may forget it after some time and other than their class notes there is no repository for them to go to after class. Furthermore, it would difficult for a student to draw EPC diagram with the instructor and take notes also about the logic used. And students, who miss the class for some reason, have no place to go to find detailed information about it. We present use of screencasts in explaining how to develop an EPC diagram. This audiovisual presentation can help students learn at their own pace and since it is made available in the repository, students who miss class or are not good at taking notes or tend to have relatively short memory can play it later just before doing a related assignment or exam to refresh the concepts.

OPSEARCH, 1999

This paper studies the capacitated minimal spanning tree with unreliable links and node outage co... more This paper studies the capacitated minimal spanning tree with unreliable links and node outage costs problem. Tree topologies appear in the design of centralized communication networks. In these topologies the number of nodes in a subtree rooted at the central node is limited to a predefined number due to polling, loading, and response time restrictions. The links in a communication network are prone to failure. Whenever a link in these networks fails all the terminal nodes connected to the central node through that link are unable to communicate till the faulty link is repaired. In some networks such failures can have adverse economic effect on the network user. The economic effect on the network user due to inability of a terminal to communicate with the central node due to link failure is called node outage cost. The sum of expected yearly node outage costs for a network depends on the topology of the network. In this paper we suggest a Lagrangean based heuristic to solve the integer programming formulation of the network topology problem. The objective of the problem is to minimize the sum of link costs and node outage costs. Our computational results on a set of test data with up to 80 nodes show that compared to the previously devel

Review of Business Information Systems (RBIS), 2010

In this paper we present a new heuristic procedure to solve the degree constrained minimal spanni... more In this paper we present a new heuristic procedure to solve the degree constrained minimal spanning tree problem. This procedure uses Lagrangian relaxation of the integer programming formulation of the problem to get a lower bound for the optimal objective function value. A subgradient optimization method is used to find multipliers that give good lower bounds. A branch exchange procedure is used after each iteration of the subgradient optimization to generate a feasible solution from an infeasible Lagrangean solution. Computational results are given for problems with up to 300 nodes. The heuristic procedure presented here gives optimal solutions in most instances. For problem sets that were not solved optimally, the gap between the lower bound and the feasible solution was less than 10-2 percent.

Review of Business Information Systems (RBIS), 2013

We present an integer programming formulation of the min-sum arborescence with node outage costs ... more We present an integer programming formulation of the min-sum arborescence with node outage costs problem. The solution to the problem consists of selecting links to connect a set of terminal nodes to a root node with minimal expected annual cost, where the annual cost is the sum of annual links costs and annual outage costs. The links in the network are prone to failure and each terminal node has an associated outage cost, which is the economic cost incurred by the network user whenever that node is disabled from the central node due to failure of a link. We suggest a Lagrangian-based heuristic to get a good solution to this problem. This solution procedure also gives lower bounds to the optimal solution and is used to assess the quality of the heuristic solution. Numerical experiments taken from instances with up to 100 nodes are used to evaluate the performance of the proposed heuristic.

The Multiperiod Capacitated Minimal Spanning Tree With Node Outage Costs (MCMSTWOC) Design proble... more The Multiperiod Capacitated Minimal Spanning Tree With Node Outage Costs (MCMSTWOC) Design problem consists of scheduling the installation of links in a communication network so as to connect a set of terminal nodes S = [2,3...N] to a central node (node 1) with minimal present value of costs. The cost of the network is the sum of link layout cost

OPSEARCH, 2013

In this paper we present a mathematical formulation of the multiperiod min-sum arborescence probl... more In this paper we present a mathematical formulation of the multiperiod min-sum arborescence problem which requires scheduling the installation of directed links to connect a set of terminal nodes N = {2,3,…,n} to a central node. The selection of links and the timing of their installation should be such that the present value of expenditures including cost of installing all the links and maintaining them till the end of the planning horizon should be minimal. The set of links selected for installation should ensure that (i) each terminal node j has exactly one entering link; and (ii) for each terminal node j, a unique path exists from the central node to node j from the period when j installed till the end of the planning horizon. Some of the terminal nodes are included in the network at the beginning of the planning horizon while others are added to the network over time. We present a branch exchange heuristic embedded in the Lagrangian relaxation method to find a solution to this problem. The lower bound given by our solution method is used to estimate the quality of the solution given by the heuristic. Test results over a wide range of problem structures show that for networks with up to 140 nodes our Lagrangian-based heuristic method gives solutions that are within 5–15 % of optimality.

European Journal of Operational Research, 1994

In this paper, we present a mathematical formulation of a terminal layout problem in the design o... more In this paper, we present a mathematical formulation of a terminal layout problem in the design of a centralized communication network with unreliable links and node outage costs. The node outage cost associated with a terminal node is a cost incurred by the network user ...

European Journal of Operational Research, 2002

The multiperiod degree constrained minimal spanning tree (MDCMST) problem consists of scheduling ... more The multiperiod degree constrained minimal spanning tree (MDCMST) problem consists of scheduling the installation of links in a network so as to connect a set of terminal nodes to a central node with minimal present value of expenditures. The network design is subject to degree constraint, which limits the number of links incident on each terminal node to a prespecified number due to the number of ports available on it. Some of the terminal nodes in the network are active at the beginning of the planning horizon while others are activated over time. We formulate this problem as an integer programming problem. We suggest a Lagrangian-based heuristic to solve the integer programming formulation of the network topology problem. Lower bounds found as a byproduct of the solution procedure are used to estimate the quality of the solution given by the heuristic. Experimental results over a wide range of problem structures show that the Lagrangian-based heuristic method yields verifiably good solutions to this hard problem.

European Journal of Operational Research, 2000

The Multiperiod Capacitated Minimal Spanning Tree (MCMST) Problem consists of scheduling the inst... more The Multiperiod Capacitated Minimal Spanning Tree (MCMST) Problem consists of scheduling the installation of links in a network so as to connect a set of terminal nodes 2Y 3Y F F F Y x to a central node (node 1) with minimal present value of expenditures, where link capacities limit the number of terminal nodes sharing a link. Some of the terminal nodes are active at the beginning of the planning horizon while others are activated over time. We formulate this problem as an integer programming problem. A branch exchange heuristic procedure for solving the problem is presented. We also present a Lagrangian relaxation method to ®nd a lower bound for the optimal objective function value. This lower bound may be used to estimate the quality of the solution given by the branch exchange heuristic. Experimental results over a wide range of problem structures show that the branch exchange heuristic method yields veri®ably good solutions to this problem.

European Journal of Operational Research, 2004

Computers & Operations Research, 2007

The hop constrained min-sum arborescence with outage costs problem consists of selecting links in... more The hop constrained min-sum arborescence with outage costs problem consists of selecting links in a network so as to connect a set of terminal nodes N={2,3,……n} to a central node with minimal total link cost such that (a) each terminal node j has exactly one entering link; (b) for each terminal node j, a unique path from the central node to j exists; (c) for each terminal node j the number of links between the central node and j is limited to a predefined number h j , and (d) each terminal node has an associated outage cost, which is the economic cost incurred by the network user whenever that node is disabled due to failure of a link. We suggest a Lagrangian based heuristic to solve the integer programming formulation of this network problem.