Puduru Viswanadha Reddy

Incentive strategies for an optimal recovery program in a closed-loop supply chain

We consider a dynamic closed-loop supply chain made up of one manufacturer and one retailer, with both players investing in a product recovery program to increase the rate of return of previously purchased products. End-of use product returns have two impacts. First, they lead to a decrease in the production cost, as manufacturing with used parts is cheaper than using virgin materials. Second, returns boost sales through replacement items.

Necessary and Sufficient Conditions for Pareto Optimality in Infinite Horizon Cooperative Differential Games

In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for infinite horizon cooperative differential games. We consider games defined by non autonomous and discounted autonomous systems. The obtained results are used to analyze the regular indefinite linear quadratic infinite horizon differential game. For the scalar case, we present an algorithm, with mild conditions on the control space, to find all the Pareto optimal solutions.

Time-consistent Shapley value for games played over event trees

In this paper, we provide a decomposition over time of Shapley value for dynamic stochastic discrete-time games, where the uncertainty is described by an event tree. We show that the suggested dynamic allocation is time consistent, that is, along the cooperative state trajectory, no player has an incentive to switch to his noncooperative strategy. This property insures that the cooperative agreement is sustainable till its maturity. The considered class of games constitutes a natural paradigm to study dynamic competition in oligopolistic markets characterized by stochastic demand.

Pareto optimality in infinite horizon linear quadratic differential games

In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal control problems with a special structure. Next, we show that if the dynamical system is controllable, certain transversality conditions hold true, and as a result all the Pareto candidates can be obtained by solving a weighted sum optimal control problem. Further, exploiting the linear structure we investigate the relationship between Pareto optimality and weighted sum minimization. Finally, for the scalar case, we present an algorithm to find all the Pareto optimal solutions assuming mild conditions on the control space.

Quality effects in different advertising models - An impulse control approach

In this paper, we integrate quality as a control variable in three classical dynamic optimal control models of advertising, namely, Nerlove–Arrow, Vidale–Wolfe and Ozga models. Quality refers to design quality, which may deteriorate over time. We assume that decisions in quality improvement can only be made at some exogenously given instants of time, and consequently we use the formalism of impulse optimal control to determine optimal advertising and quality investments. We report numerical results for the three models and discuss the impact of adding quality on the results.

Feedback Nash Equilibria in Linear-Quadratic Difference Games with Constraints

In this paper, we consider a class of noncooperative

Open-Loop Nash Equilibria in a Class of Linear-Quadratic Difference Games With Constraints

N

Fast algorithms for optimal coalition formation in federated clouds

- player finite-horizon linear-quadratic dynamic games with linear constraints. We introduce a constrained feedback information structure and provide necessary and sufficient conditions for the existence of a constrained feedback Nash equilibrium. For this class of games we show that the constrained feedback Nash equilibrium can be obtained from a feedback Nash equilibrium associated with an unconstrained multi-parametric linear-quadratic game where the parameters satisfy an equilibrium property. We show that this relation leads to a fixed-point interpretation. Further, under a few additional assumptions, we show that these fixed points can be obtained as solutions of a single large-scale linear-complementarity problem, thereby providing a method to compute the constrained feedback Nash equilibria. We illustrate our results with a numerical example.

Feedback Properties of Descriptor Systems Using Matrix Projectors and Applications to Descriptor Differential Games

We study a class of N-player finite-horizon linear-quadratic difference games with linear constraints. We introduce constrained open-loop information structure and derive necessary conditions for the existence of constrained open-loop Nash equilibria. We show that these conditions lead to a weakly coupled system of parametric two-point boundary value problem and a set of linear complementarity problems. By restricting the costate variables to be affine in the state variable, we show that these necessary conditions can be reformulated as a single large-scale linear complementarity problem. Then we provide sufficient conditions under which a solution of the linear complementarity problem constitutes a constrained open-loop Nash equilibrium.

A friendly computable characteristic function

In this paper, we formulate the optimal coalition formation in federated clouds as an integer linear programming problem under the cloud service brokerage model proposed by Mashayekhy et al. Then we propose a fast polynomial time greedy algorithm to find a near optimal coalition. The profit generated by the federation obtained using the greedy algorithm is within a negligible 0.06 percent of the optimal on an average. The greedy algorithm finds a federation 200 times faster on an average when compared with the Merge-Split algorithm. The payoff distribution within a federation is determined using exact Banzhaf index computation whereas the Merge-Split algorithm arrives at a payoff using an estimate of Banzhaf values. By computing the payoff distribution after the federation formation, we are able to achieve 66x speedup when compared with the Merge-Split algorithm.