Milind Dawande

Energy efficient schemes for wireless sensor networks with multiple mobile base stations

One of the main design issues for a sensor network is conservation of the energy available at each sensor node. We propose to deploy multiple, mobile base stations to prolong the lifetime of the sensor network. We split the lifetime of the sensor network into equal periods of time known as rounds. Base stations are relocated at the start of a round. Our method uses an integer linear program to determine new locations for the base stations and a flow-based routing protocol to ensure energy efficient routing during each round. We propose four metrics and evaluate our solution using these metrics. Based on the simulation results we show that employing multiple, mobile base stations in accordance with the solution given by our schemes would significantly increase the lifetime of the sensor network.

A Column Generation Approach for Large-Scale Aircrew Rostering Problems

This article describes a method for solving the crew rostering problem in air transportation. This problem consists of constructing personalized schedules that assign pairings, days off, and other activities to airline crew members. A generalized set partitioning model and a method using column generation have been used. This method has been adapted in a number of ways to take advantage of the nature of the problem and to accelerate solution. Numerical tests on problems from Air France have demonstrated that this method is capable of solving very large scale problems with thousands of constraints and hundreds of subproblems. The tests have also shown that these adaptations are capable of reducing solution time by a factor of about a thousand. Finally, results from this method are compared with those obtained with the method currently used at Air France.

Link scheduling in sensor networks: distributed edge coloring revisited

We consider the problem of link scheduling in a sensor network employing a TDMA MAC protocol. Our link scheduling algorithm involves two phases. In the first phase, we assign a color to each edge in the network such that no two edges incident on the same node are assigned the same color. We propose a distributed edge coloring algorithm that needs at most (/spl delta/+1) colors, where /spl delta/ is the maximum degree of the graph. To the best of our knowledge, this is the first distributed algorithm that can edge color a graph with at most (/spl delta/+1) colors. In the second phase, we map each color to a unique timeslot and attempt to identify a direction of transmission along each edge such that the hidden terminal and the exposed terminal problems are avoided. Next, considering topologies for which a feasible solution does not exist, we obtain a direction of transmission for each edge using additional timeslots, if necessary. Finally, we show that reversing the direction of transmission along every edge leads to another feasible direction of transmission. Using both the transmission assignments we obtain a TDMA MAC schedule, which enables two-way communication between every pair of neighbors. For acyclic topologies, we show that at most 2(/spl delta/+1) timeslots are required. Through simulations we show that for sparse graphs with cycles the number of timeslots assigned is close to 2(/spl delta/+1).

Sequencing and Scheduling in Robotic Cells: Recent Developments

A great deal of work has been done to analyze the problem of robot move sequencing and part scheduling in robotic flowshop cells. We examine the recent developments in this literature. A robotic flowshop cell consists of a number of processing stages served by one or more robots. Each stage has one or more machines that perform that stage’s processing. Types of robotic cells are differentiated from one another by certain characteristics, including robot type, robot travel-time, number of robots, types of parts processed, and use of parallel machines within stages. We focus on cyclic production of parts. A cycle is specified by a repeatable sequence of robot moves designed to transfer a set of parts between the machines for their processing.We start by providing a classification scheme for robotic cell scheduling problems that is based on three characteristics: machine environment, processing restrictions, and objective function, and discuss the influence of these characteristics on the methods of analysis employed. In addition to reporting recent results on classical robotic cell scheduling problems, we include results on robotic cells with advanced features such as dual gripper robots, parallel machines, and multiple robots. Next, we examine implementation issues that have been addressed in the practice-oriented literature and detail the optimal policies to use under various combinations of conditions. We conclude by describing some important open problems in the field.

On Bipartite and Multipartite Clique Problems

In this paper, we introduce the maximum edge biclique problem in bipartite graphs and the edge/node weighted multipartite clique problem in multipartite graphs. Our motivation for studying these problems came from abstractions of real manufacturing problems in the computer industry and from formal concept analysis. We show that the weighted version and four variants of the unweighted version of the biclique problem are NP-complete. For random bipartite graphs, we show that the size of the maximum balanced biclique is considerably smaller than the size of the maximum edge cardinality biclique, thus highlighting the difference between the two problems. For multipartite graphs, we consider three versions each for the edge and node weighted problems which differ in the structure of the multipartite clique (MPC) required. We show that all the edge weighted versions are NP-complete in general. We also provide a special case in which edge weighted versions are polynomially solvable.

Approximation algorithms for the multiple knapsack problem with assignment restrictions

Motivated by a real world application, we study the multiple knapsack problem with assignment restrictions (MKAR). We are given a set of items, each with a positive real weight, and a set of knapsacks, each with a positive real capacity. In addition, for each item a set of knapsacks that can hold that item is specified. In a feasible assignment of items to knapsacks, each item is assigned to at most one knapsack, assignment restrictions are satisfied, and knapsack capacities are not exceeded. We consider the objectives of maximizing assigned weight and minimizing utilized capacity.We focus on obtaining approximate solutions in polynomial computational time. We show that simple greedy approaches yield 1/3-approximation algorithms for the objective of maximizing assigned weight. We give two different 1/2-approximation algorithms: the first one solves single knapsack problems successively and the second one is based on rounding the LP relaxation solution. For the bicriteria problem of minimizing utilized capacity subject to a minimum requirement on assigned weight, we give an (1/3,2)-approximation algorithm.

On Throughput Maximization in Constant Travel-Time Robotic Cells

We consider the problem of scheduling operations in bufferless robotic cells that produce identical parts. The objective is to find a cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes the throughput rate. The robot can be moved in simple cycles that produce one unit or, in more complicated cycles, that produce multiple units. Because one-unit cycles are the easiest to understand, implement, and control, they are widely used in industry. We analyze one-unit cycles for a class of robotic cells calledconstant travel-time robotic cells. We complete a structural analysis of the class of one-unit cycles and obtain a polynomial time algorithm for finding an optimal one-unit cycle.Constant travel-time robotic cells are used in real manufacturing operations that the authors have encountered during their interactions with companies. The results and the analysis in this paper offer practitioners (i) a tool to experiment with and study the design of a proposed robotic cell during a prototyping exercise, (ii) a lower bound on the throughput of a robotic cell to help them make an informed assessment of the ultimate productivity level, and (iii) a benchmark throughput level (for comparison purposes) for robotic cells whose operations differ slightly from those discussed in this paper.

Octane: A New Heuristic for Pure 0-1 Programs

We propose a new heuristic for pure 0--1 programs, which finds feasible integer points by enumerating extended facets of the octahedron, the outer polar of the unit hypercube. We give efficient algorithms to carry out the enumeration, and we explain how our heuristic can be embedded in a branch-and-cut framework. Finally, we present computational results on a set of pure 0--1 programs taken from MIPLIB and other sources.

A Class of Hard Small 0-1 Programs

In this article, we consider a class of 0-1 programs that, although innocent looking, is a challenge for existing solution methods. Solving even small instances from this class is extremely difficult for conventional branch-and-bound or branch-and-cut algorithms. We also experimented with basis reduction algorithms and with dynamic programming without much success. The article then examines the performance of two other methods: a group relaxation for 0,1 programs, and a sorting based procedure following an idea of Wolsey. Although the results with these two methods are somewhat better than with the other four when it comes to checking feasibility, we offer this class of small 0,1 programs as a challenge to the research community.

Approximation algorithms for k-unit cyclic solutions in robotic cells

Abstract This paper considers the problem of scheduling operations in bufferless robotic cells that produce identical parts. Finding a multi-unit cyclic solution which minimizes the long-run average time to produce a part is an open problem. Most research has been focused on finding an optimal 1-unit cyclic solution. However, it is known that an optimal multi-unit cyclic solution can be better than an optimal 1-unit cyclic solution for cells with four or more machines. We present polynomial algorithms that produce multi-unit cyclic solutions whose per unit cycle times are within a constant factor of the optimum for the three most common classes of robotic cells viz., additive, constant, and Euclidean travel-time. The approximation guarantees obtained for these three classes of cells are 1.5, 1.5, and 4, respectively. As a by-product, we obtain upper bounds on the difference in the per unit cycle times between an optimal multi-unit cycle and an optimal 1-unit cycle for each of these three classes of cells.