<abstract xmlns="http://www.w3.org/1999/xhtml">

The parametric concept of equilibrium in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of a set of players into coalitions. Two extreme cases of such partitioning correspond to Pareto optimal and Nash equilibrium outcomes, respectively. The game is characterized by its matrix, in which each element is a subject for independent perturbations., i.e. a set of perturbing matrices is formed by a set of additive matrices, with two arbitrary Hölder norms specified independently in the outcome and criterion spaces. We undertake post-optimal analysis for the so-called stability kernel. The analytical expression for supreme levels of such perturbations is found. Numerical examples illustrate some of the pertinent cases.
</abstract>

Stability kernel in finite games with perturbed payoffs

<abstract xmlns="http://www.w3.org/1999/xhtml">

The purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic differential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic– Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002).
</abstract>

A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions

<abstract xmlns="http://www.w3.org/1999/xhtml">

We report some additional examples of explicit solutions to an inverse first-passage place problem for one-dimensional diffusions with jumps, introduced in a previous paper. If <italic>X</italic>(<italic>t</italic>) is a one-dimensional diffusion with jumps, starting from a random position <italic>η</italic> ∈ [<italic>a, b</italic>], let be <italic>τ</italic>a,b the time at which <italic>X</italic>(<italic>t</italic>) first exits the interval (<italic>a, b</italic>), and <italic>π</italic>a = <italic>P</italic> (<italic>X</italic>(<italic>τ</italic>a,b) ≤ <italic>a</italic>) the probability of exit from the left of (<italic>a, b</italic>). Given a probability <italic>q</italic> ∈ (0, 1), the problem consists in finding the density <italic>g</italic> of <italic>η</italic> (if it exists) such that <italic>π</italic>a = <italic>q</italic>; it can be seen as a problem of optimization.
</abstract>

Some examples of solutions to an inverse problem for the first-passage place of a jump-diffusion process

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of <italic>ρ-</italic>cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under <italic>ρ</italic>-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under <italic>ρ</italic>-cone arcwise connectedness assumption.
</abstract>

Set-valued minimax fractional programming problems under <italic>ρ</italic>-cone arcwise connectedness

<abstract xmlns="http://www.w3.org/1999/xhtml">

There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems, agricultural planning, information transfer, numerical analysis of stochastic processes, and resource allocation problems are just a few examples. The huge number of applications of minimax fractional programming problems inspired us to work on this topic. This paper is concerned with a nondifferentiable minimax fractional programming problem. We study a parametric dual model, corresponding to the primal problem, and derive the sufficient optimality condition for an optimal solution to the considered problem. Further, we obtain the various duality results under (<italic>p, r</italic>)-<italic>ρ</italic>-(<italic>η</italic>, <italic>θ</italic>)-invexity assumptions. Also, we identify a function lying exclusively in the class of (−1, 1)-<italic>ρ</italic>-(<italic>η</italic>, <italic>θ</italic>)-invex functions but not in the class of (1, −1)-invex functions and convex function already existing in the literature. We have given a non-trivial model of nondifferentiable minimax problem and obtained its optimal solution using optimality results derived in this paper.
</abstract>

Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (<italic>p</italic>, <italic>r</italic>)-<italic>ρ</italic>-(<italic>η</italic>, <italic>θ</italic>)-invexity

<abstract xmlns="http://www.w3.org/1999/xhtml">

This study investigates an inventory model for deteriorating products with a price and stock-dependent demand pattern where the holding cost is a non-linear function of both time and stock level. Moreover, a decreased price and a higher stock level lead to a higher rate of demand. Consequently, in this article, we present a new approach, aiming at maximization of the return on investment by maximizing the profit/cost ratio. If an inventory manager has the potential to invest in a variety of projects, but disposes of only limited resources, it is logical to strategically plan towards a better return on investment. As a result, the manager’s objective will be to develop an inventory policy with a possibly high return on investment. Therefore, a new strategy is considered in this article to optimize the profitability ratio in terms of replenishment time and selling price, which is determined as the proportion between the profit and the overall cost of the inventory scheme. This research demonstrates that optimizing the profitability ratio is equivalent to decreasing the average inventory cost of a product per unit. Also, the optimality is graphically checked and one numerical illustration is discussed to explain the result of the proposed model. Finally, sensitivity analysis of key parameters is performed to show the applicability of the proposed model. The profit/cost ratio is more sensitive to price elasticity markup or purchasing cost compared to the other parameters used. Also, for decision-makers, several helpful management insights are derived.
</abstract>

Department of Applied Sciences, Faculty of Engineering and Technology

A new approach to maximize the overall return on investment with price and stock dependent demand under the nonlinear holding cost

AHEAD OF PRINT

Volume 52 (2023): Issue 2 (June 2023)

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Volume 51 (2022): Issue 2 (June 2022)

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Volume 50 (2021): Issue 1 (March 2021) Special Issue Dedicated to the memory of Gregory E. Kersten Guest Edited by Tomasz Wachowicz, Ewa Roszkowska and Bogumił Kamiński

Control and Cybernetics

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Control and Cybernetics

Volume 51 (2022): Issue 1 (March 2022)

Stability kernel in finite games with perturbed payoffs

A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions

Some examples of solutions to an inverse problem for the first-passage place of a jump-diffusion process

Set-valued minimax fractional programming problems under ρ-cone arcwise connectedness

Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (p, r)-ρ-(η, θ)-invexity

A new approach to maximize the overall return on investment with price and stock dependent demand under the nonlinear holding cost

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