Narayan Rangaraj

Globally Convergent Newton Methods for Nonsmooth Equations

This paper presents some globally convergent descent methods for solving systems of nonlinear equations defined by locally Lipschitzian functions. These methods resemble the well-known family of damped Newton and Gauss-Newton methods for solving systems of smooth equations; they generalize some recent Newton-like methods for solving B-differentiable equations which arise from various mathematical programs.

A performance benchmarking study of Indian Railway zones

Purpose – The paper aims to carry out a performance benchmarking study of the zones of Indian Railways (IR) to develop an alternate approach for measurement of aggregate operational performance of the railway zones and to envisage its operations in a supply chain perspective, so as to gain academic and practical insights.Design/methodology/approach – A case study research employing data envelopment analysis (DEA) methodology has been used, with the help of data obtained from the IR annual statistical statements published by the Ministry of Railways, Government of India.Findings – Within the set of inputs and outputs considered, the exercise identified the best performing railway zones over the years and the efficiency trends. Some weaknesses of the conventional DEA were addressed by including the concept of cross‐efficiencies along with self‐efficiencies, by analyzing longitudinal data spread over four years and also by comparing the efficiencies with the operating ratios. To an extent, this study has als...

Perishable inventory management and dynamic pricing using RFID technology

In price-sensitive markets, price promotions coupled with an appropriate item replenishment strategy can be effective in controlling the total costs of servicing the market. In supply chains that handle perishable products, inventory management is already a complex problem and the management of products in a dynamic-pricing environment is even more challenging. Monitoring and control of time-sensitive products can be facilitated by the application of radio frequency identification (RFID) technology, which enables non-contact, real-time data collection and efficient interfacing with the management control system in the supply chain. This paper describes an integrated framework for inventory management and pricing in a discrete time (periodic review and ordering) framework, and describes an efficient algorithm, including a new approximation, for the related optimization problem. We then propose a suitable architecture for the application of RFID technology in this context, to realize the potential benefits.

Minimization of Locally Lipschitzian Functions

This paper presents a globally convergent model algorithm for the minimization of a locally Lipschitzian function. The algorithm is built on an iteration function of two arguments, and the convergence theory is developed parallel to analogous results for the problem of solving systems of locally Lipschitzian equations. Application of the theory to a wide range of nonsmooth optimization problems is discussed.These include the minimax problem, the composite optimization problem, the implicit programming problem, and others. A recently developed nonmonotone linesearch technique is shown to be applicable in this nonsmooth context, and an extension to constrained problems is also presented.

Modelling disruptions and resolving conflicts optimally in a railway schedule

Resolving disruptions, by dispatching and rescheduling conflicting trains is an NP-complete problem. Earlier literature classify railway operations as: (i) tactical scheduling, (ii) operational scheduling, and (iii) rescheduling. We distinguish the three based on operational criticality. Existing optimisation models do not distinguish precisely between scheduling and rescheduling based on constraints modelling; the only difference is in their objective function. Our model is the first of its kind to incorporate disruptions in an MILP model and to include conflicts-resolving constraints in the model itself. The major advantage of such a formulation is that only those trains which are disrupted are rescheduled and other non-conflicting trains retain their original schedules. Our model reschedules disrupted train movements on both directions of a single track layout with an objective to minimise total delay of all trains at their destinations. Using a small sized data it is proved that all possible conflicts out of a disruption are resolved. Apart from achieving optimal resolutions, we infer through experimental verification that a non-standard dispatch ordering is a requisite for global optimality, as cogitated by other authors.

Exact approaches for static data segment allocation problem in an information network

In a large distributed database, data are geographically distributed across several separate servers (or data centers). This helps in distributing load in the access network. It also helps to serve data locally where it is required. There are various approaches based on the granularity of data for efficient data distribution in a communication network. The file allocation problem (FAP) locates files to servers, the segment allocation problem (SAP) locates database segments, and the mirror location problem (MLP) locates replicas of the entire database. The placement of such data to multiple servers can be modeled as an optimization problem. The major decisions influencing optimization involves the location of servers, allocation of content and assignment of users. In this paper, we study the segment allocation problem (SAP), which is also known as the partial mirroring problem. This approach is more tractable than the file allocation problem in realistic cases and also eliminates the overhead of (constant) update costs that is incurred in the mirror location problem. Our contribution is two-fold: Firstly, earlier works on SAP assume pre-defined segments. We build a data partitioning method using well-known facility location models. We quantify the performance of the partitioning method. We show that the method partitions the database within a reasonable limit of error. Secondly, we introduce a new model for the segment allocation problem in which the segments are completely connected to each other by high-bandwidth links and contains a cost benefit for inter-segment traffic flows. We formulate this problem as an MILP and build exact solution approaches to solve large scale problems. We demonstrate some structural properties of the problem that make it solvable, using a Benders decomposition algorithm. Computational results validate the superiority of the decomposition approach.

Mathematical models and empirical analysis of a simulated annealing approach for two variants of the static data segment allocation problem

We consider a content distribution network (CDN) in which data hubs or servers are established in multiple locations to cater to local demands. The distributions of data to these hubs along with related network design problems (such as hub location and user assignment) are the key decision problems to consider to minimize the total routing cost. A new model for allocation of segments is introduced in Sen, Krishnamoorthy, Rangaraj and Narayanan, Comput Oper 62 (2015), 282–295, in which local preferences guide the database partitioning process, and the servers are fully connected to each other. In this article, we develop a simulated annealing (SA) approach (referred to as SA-mesh) to solve this problem and compare its performance with the corresponding mixed-integer linear programming (MILP) formulation. We also formulate a much harder variant of the problem in which servers are interconnected by a tree. We develop a SA algorithm (referred to as SA-tree) for this variant, in which a local search is incorporated to find a suboptimal tree backbone. We use a customized data structure based on linked lists to represent a solution in our algorithms. This enables our algorithms to scale to much larger instances of the problem. We use optimal solutions and the benchmarks obtained by CPLEX to justify the performance of our algorithms.

Facility location models to locate data in information networks: a literature review

The usage of the Internet has grown substantially in recent times. This has resulted in high volumes of data traffic. There is a concomitant rise in bandwidth demands that could result in excessive download delays (or latency). Thus, a single-server system is no more a prudent choice for data storage. Replication of content and placing them on multiple servers is a method that is used to reduce latency. However, this solution comes at a huge cost. Moreover, replicating objects randomly does not necessarily improve system performance. It is possible to arrive at a solution to the problem of placing content so as to achieve better cost performance. Other performance measures include latency, load balancing and data availability. We refer to the problem of locating content as data location problem in information networks, or DLPIN. The choice of server locations, query routing strategy and user assignment are some of the important problems that require attention along with the location of the data/content. Resource constraints and the nature of traffic (static/dynamic) are two important parameters in the problem environment, and therefore are key distinguishing features in the models. The main contribution of this paper is a novel classification and study of DLPIN on the basis of problem features. The research in this area started with files, the smallest units of allocation. Gradually, files and programs, database segments and entire databases (or mirrors) have been studied. We design examples from these use cases to elaborate a variety of problems in a comprehensive review. Facility location models from physical logistics are extensively used to model these problems. Our paper presents a literature survey of such mathematical models for data location problems. We present a gap analysis that provides pointers to possible future research in this area. This paper also serves to document the success in the use of mathematical programming approaches for data location in information networks.

History-dependent scheduling

In this paper, we extend job scheduling models to include aspects of history-dependent scheduling, where setup times for a job are affected by the aggregate activities of all predecessors of that job. Traditional approaches to machine scheduling typically address objectives and constraints that govern the relative sequence of jobs being executed using available resources. This paper optimises the operations of multiple unrelated resources to address sequential and history-dependent job scheduling constraints along with time window restrictions. We denote this consolidated problem as the general precedence scheduling problem (GPSP). We present several applications of the GPSP and show that many problems in the literature can be represented as special cases of history-dependent scheduling. We design new ways to model this class of problems and then proceed to formulate it as an integer program. We develop specialized algorithms to solve such problems. An extensive computational analysis over a diverse family of problem data instances demonstrates the efficacy of the novel approaches and algorithms introduced in this paper. HighlightsDetailed explanation of differences between GPSP and Block-world problem has been submitted within the response document.Summary of differences between GPSP and block-world problem has been included in the paper.Justification for using only first log(n) and not all i, j, K combinations has been included in the paper.Mistakes in write-up have been corrected as pointed out by reviewers.

Approaches for solving the container stacking problem with route distance minimization and stack rearrangement considerations

We consider an optimization problem of sequencing the operations of cranes that are used for internal movement of containers in maritime ports. Some features of this problem have been studied in the literature as the stacker crane problem (SCP). However, the scope of most literature (including SCP) is restricted to minimizing the route or distance traveled by cranes and the resulting movement-related costs. In practice, cargo containers are generally stacked or piled up in multiple separate columns, heaps or stacks at ports. So, the cranes need to often rearrange or shuffle such container stacks, in order to pick up any required container. If substantial re-stacking is involved, cranes expend considerable effort in container stack rearrangement operations. The problem of minimizing the total efforts/time of the crane must therefore account for both - the stack rearrangement costs and also the movement-related (route distance) costs. The consolidated problem differs from standard route distance minimization situations if stack rearrangement activities are considered. We formally define the consolidated problem, identify its characteristic features and hence devise suitable models for it. We formulate several alternative MIP approaches to solve the problem. We compare the performance of our MIP formulations and analyze their suitability for various possible situations.