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IIM Indore

Operation Management and Quantitative Techniques

In this article, we study the Poisson process of order k (PPoK) time-changed with an independent Lévy subordinator and its inverse, which we call, respectively, as TCPPoK-I and TCPPoK-II, through various distributional properties, long-range dependence and limit theorems for the PPoK and the TCPPoK-I. Further, we study the governing difference-differential equations of the TCPPoK-I for the case inverse Gaussian subordinator. Similarly, we study the distributional properties, asymptotic moments and the governing difference-differential equation of TCPPoK-II. As an application to ruin theory, we give a governing differential equation of ruin probability in insurance ruin using these processes. Finally, we present some simulated sample paths of both the processes.

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Stochastic Analysis and Applications

Time-changed Poisson processes of order k

Social storage systems are a good alternative to existing data backup systems of local, centralized, and P2P backup. Till date, researchers have mostly focussed on either building such systems by using existing underlying social networks (exogenously built) or on studying quality of service related issues. In this paper, we look at two untouched aspects of social storage systems. One aspect involves modelling social storage as an endogenous social network, where agents themselves decide with whom they want to build data backup relation, which is more intuitive than exogenous social networks. The second aspect involves studying the stability of social storage systems, which would help reduce maintenance costs and further, help build efficient as well as contented networks. We have a four fold contribution that covers the above two aspects. We, first, model the social storage system as a strategic network formation game. We define the utility of each agent in the network under two different frameworks, one where the cost to add and maintain links is considered in the utility function and the other where budget constraints are considered. In the context of social storage and social cloud computing, these utility functions are the first of its kind, and we use them to define and analyse the social storage network game. Second, we propose the concept of bilateral stability which refines the pairwise stability concept defined by Jackson and Wolinsky (J Econ Theory 71(1):44–74, 1996), by requiring mutual consent for both addition and deletion of links, as compared to mutual consent just for link addition. Mutual consent for link deletion is especially important in the social storage setting. The notion of bilateral stability subsumes the bilateral equilibrium definition of Goyal and Vega-Redondo (J Econ Theory 137(1):460–492, 2007). Third, we prove necessary and the sufficient conditions for bilateral stability of social storage networks. For symmetric social storage networks, we prove that there exists a unique neighborhood size, independent of the number of agents (for all non-trivial cases), where no pair of agents has any incentive to increase or decrease their neighborhood size. We call this neighborhood size as the stability point. Fourth, given the number of agents and other parameters, we discuss which bilaterally stable networks would evolve and also discuss which of these stable networks are efficient—that is, stable networks with maximum sum of utilities of all agents. We also discuss ways to build contented networks, where each agent achieves the maximum possible utility.

Annals of Operations Research

Stability, efficiency, and contentedness of social storage networks

We consider the problem of learning the structure of a high dimensional precision matrix under sparsity assumptions. We propose to use a shrinkage prior, called the DL-graphical prior based on the Dirichlet-Laplace prior used for the Gaussian mean problem. A posterior sampling scheme based on Gibbs sampling is also provided along with theoretical guarantees of the method by obtaining the posterior convergence rate of the precision matrix.

ARXIV.ORG

Bayesian Structure Learning in Graphical Models using Shrinkage priors

Governments across the world have been preferring public-private-partnerships (PPP) over traditional methods in the past few decades to procure public services for their citizens. Developing countries, like India has the potential to successfully deploy PPP in providing integrated emergency medical services (EMS) like that of the west. This paper provides a base for implementing PPP contractual mechanism, when the government needs to maximize it social surplus or value for money (VFM). Further, the study attempts to observe the relationship between three players in a multiple principal agent model where government and global investor act as the principals and the service providers acts as the agents. This study intends to portray the equilibrium contract set among the three players including analysing moral hazard problems, signalling aspects, incentivization and matching through the entire contract cycle.

Modelling public-private-partnerships in Indian emergency medical services applying game theory

Returns of risky assets and their time-dependent volatility are often jointly modelled by stochastic volatility models (SVMs). Over the last few decades, several SVMs have been proposed to adequately capture the features of the relationship between the return and its volatility. The earliest SVM considers a hierarchical model, with current return as a function of the current latent volatility, which is further modelled as an auto-regressive process. In an attempt to make SVM more appropriate for complex realistic market behaviour, leverage parameter was introduced, which however led to violation of martingale difference property of the risky part of return (a necessary mean-zero condition that prevents arbitrage opportunities under mild regularity conditions). Subsequently, alternative SVMs had been developed and are currently in use. In this article, we propose mean-corrections for several generalizations of SVM with leverage that capture the complex market behaviour as well as satisfy martingale difference property of returns. We also establish a few theoretical results to characterize the key desirable features of these models, and present comparison with other popular competitors. Furthermore, three real-life examples (CITI bank stock price, euro–USD rate and S&amp;P 500 index returns) have been used to demonstrate the performance of this new class of SVMs.

Applied Economics

A new class of discrete-time stochastic volatility model with correlated errors

Calibration of hydrological time-series models is a challenging task since these models give a wide spectrum of output series and calibration procedures require significant amount of time. From a statistical standpoint, this model parameter estimation problem simplifies to finding an inverse solution of a computer model that generates pre-specified time-series output (i.e., realistic output series). In this paper, we propose a modified history matching approach for calibrating the time-series rainfall-runoff models with respect to the real data collected from the state of Georgia, USA. We present the methodology and illustrate the application of the algorithm by carrying a simulation study and the two case studies. Several goodness-of-fit statistics were calculated to assess the model performance. The results showed that the proposed history matching algorithm led to a significant improvement, of 30% and 14% (in terms of root mean squared error) and 26% and 118% (in terms of peak percent threshold statistics), for the two case-studies with Matlab-Simulink and SWAT models, respectively.

Environmental and Ecological Statistics

A history matching approach for calibrating hydrological models

Measuring the consumption response to a tax regime has been a central issue in the optimal design of fiscal policy. This study leverages a large-scale natural experiment in India, the 2017 Goods-Service-Tax (GST) Reform, to quantify its impact on suppliers’ pricing strategy and consumer spending. Using scanner data on purchasing behavior of a panel of households and a triple difference design, we find a spending reduction in quantities of 0.23 percent, on average, following one percentage point increase in the GST tax. Tax elasticity is not uniform across product categories and is highest for goods in the fresh and fashion class (2.1 and 1.7, respectively). Consumers exhibit intertemporal substitution by preponing spending during the announcement period and substitute consumption across products. We also find evidence of asymmetry for tax pass-through to consumers. The tax is shifted at a lower rate in the case of tax rise, but when the tax is reduced, the elasticity of the tax exclusive price is significantly smaller than -1, resulting in a higher final price and a lower level of spending.

SSRN

Tax-Pass-through, Pricing Strategy and Consumer Spending Dynamics: The Indian GST Experience

A new method of pricing, known as pay-what-you-want (PWYW) has been successfully used in many contexts in the recent past. Success stories are in restaurants, museums, music albums, software, etc. The method where the buyer selects the price, possibly a zero price, and the seller accepts it, is a bit counter intuitive. Quite surprisingly, the PWYW pricing method has been used successfully, and some businesses have adopted it for selling their goods. We study the economic rationale behind the success of the PWYW pricing method, and analyse different situations using a simple model. Results show that the PWYW pricing method can be successful when there is a large proportion of fair-minded consumers, and a lesser proportion of free-loaders. Also, though a low marginal cost is beneficial for a PWYW method, it is not necessary. Sellers can choose to use PWYW pricing with reference prices that induce, but not bind, consumers to pay an appropriate price. Also, setting a minimum threshold price alleviates the problem of free-loaders, and the PWYW pricing method can be used profitably in the long run.

International Journal of Services and Operations Management

A pay-what-you-want pricing model for restaurants

Primary Health Centers (PHCs), which are single doctor clinics and vital to health care in rural areas of developing countries, often remain inoperative due to shortage of doctors. When doctors become available, the health administrator needs to decide that which of the inoperative PHCs should the doctor be assigned. For transparency and operational efficiency, the sequence in which the inoperative PHCs will be assigned doctors needs to be decided in advance at the start of the planning horizon. Further, the number of doctors that will become available in each period of the planning horizon is uncertain. Moreover, the health guidelines set the capacity target, i.e. the maximum population a PHC can provide service to. We introduce and study the capacitated multi period maximal covering facility location problem under server uncertainty. We provide a formulation for the problem based on the minimax regret approach. Further, we solve the problem using CPLEX MIP solver and observe that it can only solve very small instances. Hence, we provide Benders decomposition based solution methods and refinements thereof, which is 100 − 5000 times faster and could solve practical size instances in reasonable time.

IIMA Working Papers

Benders decomposition for capacitated multi-period maximal covering location problem with server uncertainty

Purpose The purpose of this paper is to model the distribution stage of the public distribution system (PDS) and optimize the inventory policy during this stage of the PDS to address some of the inefficiencies present in the system. This study models this supply chain as a multistage supply chain consisting of storage depots, issue centers, fair price shops and card holders.Design/methodology/approach A two-stage modeling approach is used to model the distribution stage in the PDS. In the first stage, the authors developed a simulation model for periodic review-based stock policy with appropriate assumptions. This helped minimize the total supply chain cost (TSCC). The TSCC consists of three cost elements, namely, ordering cost, holding cost and shortage cost. These three cost elements, in turn, depend on inventory policy parameters, such as review periods and base stock levels, at various echelons. In the second stage, a Genetic Algorithm based optimization approach was used.Findings A set of optimal policy parameters was identified. It is observed that base stock levels at issue centers are higher as compared to those in the FPS and the TSCC is less in scenario, when backorder cost is equal to the holding cost.Practical implications Present study will be useful to policy makers in improving PDS performance. This optimization of inventory policies helps actors in the PDS supply chain to choose appropriate policy parameters in the present inventory policy so as to reduce the overall distribution cost.Originality/value Unlike the previous researchers who examined the PDS from the social security perspective and tried to address specific problems to improve functioning of the PDS, this study looked at the problem as a supply chain-related problem and optimized the inventory parameters in one of the subsets of the PDS supply chain.