Applications to Economics

Sethi, Suresh P.

doi:10.1007/978-3-030-91745-6_11

Cited by 17 publications

(24 citation statements)

References 71 publications

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“…The flushing operation involves controlling a dynamic system, i.e., the system that evolves over time. Hence, this work employs the use of optimal control theory, which is a branch of mathematics that finds optimal ways to control dynamic systems. , Previously, control methods have been successfully applied in the petroleum industry for enhancing working systems. Ramirez studied the application of optimal control theory for enhancing oil recovery techniques.…”

Section: Optimal Control Problems and Applicationsmentioning

confidence: 99%

Strategic Optimization of the Flushing Operations in Lubricant Manufacturing and Packaging Facilities

Jerpoth,

Hesketh,

Slater

et al. 2023

ACS Omega

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Commercial lubricant industries use a complex pipeline network for the sequential processing of thousands of unique products annually. Flushing is conducted between changeovers to ensure the integrity of each production batch. An upcoming product is used for cleaning the residues of the previous batch, resulting in the formation of a commingled/mixed oil that does not match the specifications of either of the two batches. The existing operations are based on the operator’s experience and trial and error. After a selected flush time, the samples are tested for their viscosity to determine the success of a flush. The approach results in long downtime, the generation of large commingled oil volumes, and huge economic losses. Hence, to overcome the drawback, our work introduces a solution strategy for systematically optimizing flushing operations and making more informed decisions to improve the resource-management footprint of these industries. We use the American Petroleum Institute-Technical Data Book (API-TDB) blending correlations for calculating the mixture viscosities in real-time. The blending correlations are combined with our first-principles models and validated against well-designed experimental data from the partnered lubricant facility. Next, we formulate an optimal control problem for predicting the optimum flushing times. We solve the problem using two solution techniques viz. Pontryagin’s maximum principle and discrete-time nonlinear programming. The results from both approaches are compared with well-designed experimental data, and the economic and environmental significance are discussed. The results illustrate that with the application of a discrete-time nonlinear programming solution approach, the flushing can be conducted at a customized flow rate, and the necessary flushing volume can be reduced to over 30% as compared to the trial-and-error mode of operation.

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Section: Optimal Control Problems and Applicationsmentioning

confidence: 99%

Strategic Optimization of the Flushing Operations in Lubricant Manufacturing and Packaging Facilities

Jerpoth,

Hesketh,

Slater

et al. 2023

ACS Omega

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“…Finally, we substitute both and into the manufacturer's HJB equation to derive the manufacturer's optimal advertising effort and optimal participation rate ϕ*( t ). For the technical details on applying the dynamic programming principle we refer readers to Sethi (2019).…”

Section: Solutionmentioning

confidence: 99%

Cooperative Advertising in a Dynamic Three‐Echelon Supply Chain

Kennedy

Sethi

Siu

et al. 2021

Production and Operations Management

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We propose a model to assess the value of a distributor in a dynamic stochastic cooperative advertising supply chain in which a manufacturer wholesales its product to a distributor who in turn sells it to a retailer. Moreover and importantly, the distributor also intermediates the pricing and advertising decisions between the manufacturer and the retailer. For the resulting three‐player hierarchical game formulation of the supply chain, we characterize the feedback Stackelberg equilibrium in terms of a system of coupled algebraic equations and show it to admit a unique solution. We find that the value added by the distributor to the supply chain depends critically on the nature of the demand function for the product, a result that has practical implications for the kinds of product where having a distributor is most desirable. Second, our model indicates that the presence of the distributor can enhance the margins of both the retailer and the manufacturer relative to the case of no distributor, and provide explicit conditions for this to occur. Third, we present numerical analysis that indicates that if the distributor generates sufficiently large transportation cost savings, then the three‐echelon supply chain can lead in the long run to higher market awareness, lower advertising expenditure, and higher value extracted, relative to the two‐echelon model. Finally, in addition to retailer advertising that is subsidized by the manufacturer, we also provide the manufacturer an option to do national advertising and show its viability.

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“…Other fields where these techniques can be of help are finance, production and marketing, economics of growth, etc. ; see, for instance, [30,31]. For other applications, see [5].…”

Section: A2679mentioning

confidence: 99%

Numerical Stackelberg--Nash Control for the Heat Equation

Carvalho¹,

Fernández-Cara²

2020

SIAM J. Sci. Comput.

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\bfA \bfb \bfs \bft \bfr \bfa \bfc \bft . This paper deals with a strategy to solve numerically control problems of the Stackelberg--Nash kind for heat equations with Dirichlet boundary conditions. We assume that we can act on the system through several controls, respecting an order and a hierarchy: a first control (the leader) is assumed to choose the policy; then, a Nash equilibrium pair, determined by the choice of the leader and corresponding to a noncooperative multiple-objective optimization strategy, is found (these are the followers). Our method relies on a formulation inspired by the work of Fursikov and Imanuvilov. More precisely, we minimize over the class of admissible null controls a functional that involves weighted integrals of the state and the control, with weights that blow up at the final time. The use of the weights is crucial to ensure the existence of the controls and the associated state in a reasonable space. We present several mixed formulations of the problems and, then, associated mixed finite element approximations that are easy to handle. In a final step, we exhibit some numerical experiments making use of the Freefem++ package.\bfK \bfe \bfy \bfw \bfo \bfr \bfd \bfs . controllability, Stackelberg--Nash strategies, heat equation \bfA \bfM \bfS \bfs \bfu \bfb \bfj \bfe \bfc \bft \bfc \bfl \bfa \bfs \bfs \bfi fi\bfc \bfa \bft \bfi \bfo \bfn \bfs . 34K35, 35Q93, 49J20, 90C29 \bfD \bfO \bfI .

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Applications to Economics

Cited by 17 publications

References 71 publications

Strategic Optimization of the Flushing Operations in Lubricant Manufacturing and Packaging Facilities

Strategic Optimization of the Flushing Operations in Lubricant Manufacturing and Packaging Facilities

Cooperative Advertising in a Dynamic Three‐Echelon Supply Chain

Numerical Stackelberg--Nash Control for the Heat Equation

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