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IIM Indore

Operation Management and Quantitative Techniques

We propose and analyse finite volume Godunov type methods based on discontinuous flux for a 2×2 system of non-linear partial differential equations proposed by Hadeler and Kuttler to model the dynamics of growing sandpiles generated by a vertical source on a flat bounded rectangular table. The problem considered here is the so-called partially open table problem where sand is blocked by a wall (of infinite height) on some part of the boundary of the table. The novelty here is the corresponding modification of boundary conditions for the standing and the rolling layers and generalization of the techniques of the well-balancedness proposed in [1]. Presence of walls may lead to unbounded or discontinuous surface flow density at equilibrium resulting in solutions with singularities propagating from the extreme points of the walls. A scheme has been proposed to approximate efficiently the Hamiltonians with the coefficients which can be unbounded and discontinuous. Numerical experiments are presented to illustrate that the proposed schemes detect these singularities in the equilibrium solutions efficiently and comparisons are made with the previously studied finite difference and Semi-Lagrangian approaches by Finzi Vita et al.

World University root node

Communications in Computational Physics

Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls

“Nash’s theory of noncooperative games should now be recognized as one of the outstanding intellectual advances of the twentieth century. The formulation of Nash equilibrium has had a fundamental and pervasive impact in economics and the social sciences which is comparable to that of the discovery of the DNA double helix in the biological sciences”, says Roger Myerson, who won the Nobel Prize in Economic Sciences in 2007 and whose textbook on game theory is a classic. The celebrated journalist Erica Klarreich says of John Nash’s work: “No one cites Nash’s papers any longer because Nash equilibrium is standard vocabulary; every mathematician knows what it means. While he published only a small handful of papers, John Nash will be remembered as one of the most original and influential mathematicians of the 20th century, whose work continues to inspire new results and research directions.” Barry Mazur, Professor of Mathematics at Harvard University says: “Jane Austen wrote six novels. I think Nash’s pure mathematical contributions are on that level. Very, very few papers he wrote on different subjects, but the ones that had impact had incredible impact.” John Nash is surely one of the most brilliant minds of the twentieth century

Resonance

The creative genius: John Nash

Behavioral operation stems from the fact that the human are not rational as typically assumed in the traditional operations management theories. Behavioral operation management is the emerging and promising field in the domain of operations management. Being an emergent stream the researchers have experimental focus while dealing with behavioral operation management. This paper is an attempt to consolidate the published work on behavioral operation management experimental research methodologies and explain various options available for researchers. Also this paper proposes guidelines for selecting the appropriate experimental research methodology. Various experimental studies falling under the umbrella of behavioral operation management are vignettes, process simulation, laboratory simulation, natural experiments and mixed experimental studies. The problem at hand determines the type of experimental study. Though there are several pros and cons of using a particular design, the mixed experimental studies have found to be more acceptable to the researcher compared to other studies.

Behavioural Operations Management: Realm of Experimental Research Methodology

This paper considers the problem of a decision maker (DM), who needs to hire an agent to assess the probability of occurrence of an event that is of interest to her. To decide the agent’s reward, the DM proposes a mechanism that will give reward based on the agent’s reported subjective probability and the actual outcome of the event. The reward mechanism needs to incentivize the expert to honestly reveal his subjective probability, and the reward has to be non-negative in all cases in order to ensure agent’s participation. In such a situation, it is possible that there are some agents who lack the expertise to assess the situation, but still participate to get sure non-negative payoff. The DM wants to screen out such uninformed agents from the informed ones. This work considers two mechanisms, and analyzes the behavior of both types of agents for the two mechanisms. It shows that screening is possible along with belief elicitation in some cases.

Fulltext

Theoretical Economics Letters

Screening Agents in Belief Eliciting Mechanisms

This case presents the real-life situation of a convener who has initiated the task of implementing an online voucher sales system to collect the fees from candidates for a National Aptitude Test. The IT application was to be developed by an external vendor, but a few days before the application’s launch, the vendor’s point of contact informed the convener that development had been delayed. This placed the convenor in a difficult situation because he had already announced the launch through the national media. The options available to him were rather few. He was faced with the dilemma of whether to announce the non-availability of online voucher system to the public and face the media trial or to explore the option of pushing the external vendor further to meet the deadline. The second option required him to coordinate with the senior management of the vendor company. In any case, the timelines were tight, and he had to make the decision promptly. It would be a difficult situation for the convener, in case the application failed.

Asian Journal of Management Cases

Online Voucher Sales System for the National Aptitude Test 2013

Facility location problems reported in the literature generally assume the problem parameter values (like cost, budget, etc.) to be known with complete certainty, even if they change over time (as in multi-period versions). However, in reality, there may be some uncertainty about the exact values of these parameters. Specifically, in the context of locating primary health centers (PHCs) in developing countries, there is generally a high level of uncertainty in the availability of servers (doctors) joining the facilities in different time periods. For transparency and efficient assignment of the doctors to PHCs, it is desirable to decide the facility opening sequence (assigning doctors to unmanned PHCs) at the start of the planning horizon. We present a new formulation for a multi-period maximal covering location problem with server uncertainty. We further demonstrate the superiority of our proposed formulation over the only other formulation reported in the literature. For instances of practical size, we provide a Benders decomposition based solution method, along with several refinements. For instances that the CPLEX MIP solver could solve within a time limit of 20 hours, our proposed solution method turns out to be of the order of 150–250 times faster for the problems with complete coverage, and around 1000 times faster for gradual coverage.

European Journal of Operational Research

A new formulation and Benders decomposition for the multi-period maximal covering facility location problem with server uncertainty

For an expensive to evaluate computer simulator, even the estimate of the overall surface can be a challenging problem. In this paper, we focus on the estimation of the inverse solution, i.e., to find the set(s) of input combinations of the simulator that generates a pre-determined simulator output. Ranjan et al. [1] proposed an expected improvement criterion under a sequential design framework for the inverse problem with a scalar valued simulator. In this paper, we focus on the inverse problem for a time-series valued simulator. We have used a few simulated and two real examples for performance comparison.

Open Journal of Statistics

Inverse Problem for a Time-Series Valued Computer Simulator via Scalarization

Tumor heterogeneity is a crucial area of cancer research wherein inter- and intra-tumor differences are investigated to assess and monitor disease development and progression, especially in cancer. The proliferation of imaging and linked genomic data has enabled us to evaluate tumor heterogeneity on multiple levels. In this work, we examine magnetic resonance imaging (MRI) in patients with brain cancer to assess image-based tumor heterogeneity. Standard approaches to this problem use scalar summary measures (e.g., intensity-based histogram statistics) that do not adequately capture the complete and finer scale information in the voxel-level data. In this paper, we introduce a novel technique, DEMARCATE (DEnsity-based MAgnetic Resonance image Clustering for Assessing Tumor hEterogeneity) to explore the entire tumor heterogeneity density profiles (THDPs) obtained from the full tumor voxel space. THDPs are smoothed representations of the probability density function of the tumor images. We develop tools for analyzing such objects under the Fisher–Rao Riemannian framework that allows us to construct metrics for THDP comparisons across patients, which can be used in conjunction with standard clustering approaches. Our analyses of The Cancer Genome Atlas (TCGA) based Glioblastoma dataset reveal two significant clusters of patients with marked differences in tumor morphology, genomic characteristics and prognostic clinical outcomes. In addition, we see enrichment of image-based clusters with known molecular subtypes of glioblastoma multiforme, which further validates our representation of tumor heterogeneity and subsequent clustering techniques.

NeuroImage: Clinical

DEMARCATE: Density-based magnetic resonance image clustering for assessing tumor heterogeneity in cancer

In maritime transportation of automobiles, roll-on/roll-off (ro–ro) shipping companies operate liner shipping services across major trade routes. Large ro–ro shipping companies are well placed to offer end-to-end integrated logistics services to auto manufacturers engaged in international trade of vehicles. Therefore, we present a new mixed integer programming model for fleet deployment including inventory management at the ports along each trade route. Due to the complexity of the problem, a rolling horizon heuristic (RHH) is proposed. The RHH solves the problem by iteratively solving sub-problems with shorter planning horizon. Computational results based on real instances are presented.

Transportation Research Part E: Logistics and Transportation Review

Combined fleet deployment and inventory management in roll-on/roll-off shipping

A retailer assortment is defined as a mix of products stocked in a retail store. The identification of proper assortment has become difficult in the current consumer-centric environment. Assortment planning (AP) in a retail chain largely depends on the estimation of demand of various products under consideration. The knowledge of the true demand rates and substitution rates is important for a retailer for a variety of management decisions, such as the ideal assortment to carry, the quantum of each item to be stocked and how often to replenish the stock (Anupindi, Dada &amp; Gupta, 1998).Space elastic demand model is one of the models which have been widely used for demand estimation in retail AP literature. However, there is paucity of empirical studies in this field of research. In this article, the demand has been estimated using space elastic demand model for two product categories comprising 11 products within the category. The study illustrates the methodology for estimation of demand using space elastic demand model. The results obtained are consistent with the results obtained in few of the empirical studies done in other contexts.