Green production and effective inventory management are increasingly recognized as essential components for promoting sustainable practices across industries, benefiting both the economy and society. This study introduces a novel inventory management framework designed to address demand disruptions and environmental impacts by implementing advanced payment policies and investments in green technology in the context of the COVID-19 pandemic. First, we develop a two-warehouse inventory system for deteriorating products, featuring a finite capacity for the owned warehouse (OW) and sufficient capacity for the rented warehouse (RW) to ensureinventory availability during both short-term and long-term lockdown scenarios. Secondly, we consider a two-parameter Weibull distribution for non-instantaneous deterioration with partial backlogging. Given the uncertainty of market demand influenced by non-linear price sensitivity, we analyze inventory classification and optimal replenishment strategy under four discrete circumstances to reflect time-varying lockdown durations and demand fluctuations.The results indicate that green technology and advanced payment systems minimize supply chain risks and decrease carbon emissions. Numerical findings indicate maximum net earnings of 631.128 and 564.428 in scenarios 1 and 2, respectively, with green investments of 5 units; however, profits diminish with increased investments. Scenario 1 is more economical than Scenario 2 because of its reduced lockdown duration, leading to decreased holding and deterioration costs.Partial backlogging is the most lucrative and sustainable Economic Order Quantity approach in the presence of shortages. These findings underscore the significance of adaptive inventory systems and sustainable practices in strengthening supply chain resilience.This study provides actionable insights for businesses looking to optimize inventory management amidst demand disruptions while promoting environmental sustainability.

In this work, the neutron star model is considered in the framework of general relativity with the polytropic equation of state p=ργ, where γ=1+1k and k is known as a polytropic index. The homotopy perturbation method is used to solve Tolman–Oppenheimer–Volkoff (TOV) equation which gives the mass of the stellar structure. The solution of Einstein’s field equations is obtained and stability, causality, and physical viability of the considered model are examined. Using the observational results of mass and radius of known stars 4U 1608-52 RX J185635-3754, SAX J1748.9-2021 and 4U 1728-34, the model parameters are estimated which led to the non-singular solutions satisfying the energy conditions.

Kim and Lee [Phys. Rev. D 63 (2001) 064014] studied charged wormholes and Morris–Thorne wormholes in the presence of scalar field using the concepts of general relativity. In this paper, we have also considered same wormholes affected with electric charge and scalar field and extended their study using the framework of [Formula: see text] gravity with [Formula: see text] gravity model, where [Formula: see text] and [Formula: see text] are constants. We have examined the possibility for minimization of the amount of exotic matter through energy conditions. Further, we have obtained the deflection angle, an important notion in gravitational lensing, by using strong field limit coefficients which may be helpful in the detection of wormholes.

Abstract This paper develops an inventory model considering a demand disruption and a linear price and time dependent demand. In this model, we analyze two possibilities and apply the FIFO dispatch policy. In the first scenario, the inventories of the owned warehouse (OW) get vacant after the lock-down relieves owing to a shorter lock-down duration, but in the second scenario, the inventories of the OW get vacant during the lock-down due to a longer lock-down duration. A two parametric Weibull distribution has been considered to mirror the real problems caused by deterioration. The study aims to minimize the total cost of a two-warehouse system during the lock-down time. Furthermore, sensitivity analysis was used to investigate the models' behavior. Taking into consideration actual conditions, this model might be useful in an emergency situation like the COVID-19 epidemic.

We explore an autonomous system analysis of dark energy models with interactions between dark energy and cold dark matter in a general systematic approach to cosmological fluids. We investigate two types of models such as local and non-local ones. In particular, a local form of interaction is directly proportional to only the energy density, while a non-local interaction is directly proportional to the energy density as well as the Hubble parameter. As a consequence, it is explicitly demonstrated that in both cases there exist the stability points in terms of cosmological parameters. This work aims at obtaining acceleration and stability using interaction models without modifying the matter or geometric component of the Universe.

We investigate the global causal structure of the end state of a spherically symmetric marginally bound Lemaitre–Tolman–Bondi (LTB) (Lemaitre 1933 Ann. Soc. Sci. Brux. A 53 51, Tolman 1934 Proc. Natl Acad. Sci. USA 20 169–76, Bondi 1947 Mon. Not. Astron. Soc. 107 410) collapsing cloud (which is well studied in general relativity) in the framework of modified gravity having the generalized Lagrangian R + α R 2 in the action. Here R is the Ricci scalar, and α ⩾ 0 is a constant. By fixing the functional form of the metric components of the LTB spacetime, using up the available degree of freedom, we realize that the matching surface of the interior and the exterior metric are different for different values of α . This change in the matching surface can alter the causal property of the first central singularity. We depict this by showing a numerical example. Additionally, for a globally naked singularity to have physical relevance, a congruence of null geodesics should escape from such singularity to be visible to an asymptotic observer for infinite time. For this to happen, the first central singularity should be a nodal point. We here give a heuristic method to show that this singularity is a nodal point by considering the above class of theory of gravity, of which general relativity is a particular case.

In this paper, we construct a thin-shell wormhole (TSW) in 4D Einstein–Gauss–Bonnet gravity (EGB) and examine the stability condition of the wormhole (WH) by using the linear and nonlinear models of the exotic fluid at the throat (a0). In addition, we have checked the validity of null, weak, and strong energy conditions for the TSWs. The energy conditions are observed to violate the linear model but it satisfies the nonlinear model. Further, 4D EGB wormhole solutions are found to exist for a particular choice of equilibrium radius as well as the equation of state parameter.

This study develops an inventory model for things that deteriorate at a rate that depends on time. The research work is about minimizing the total cost of a two-warehouse system during the lockdown period. We consider two scenarios and the LIFO policy has been used in this model. In the first scenario, the stocks of the rented warehouse (RW) become empty after the lockdown eased, and in the second scenario, the stocks of the RW become empty during the lockdown. Here, two parametric Weibull distributions for the deterioration rate and a time-dependent demand are taken into consideration. Subsequently, sensitivity analysis is examined for both scenarios by using two different examples to make the research more realistic. In an emergency like the COVID-19 epidemic, the models may be used effectively when taking into consideration the actual circumstances.

In this paper, Morris Thorne wormholes are considered in the context of [Formula: see text] gravity. A shape function is defined as [Formula: see text], where [Formula: see text] is constant. The equation of state is considered as [Formula: see text] and [Formula: see text] function is derived. The wormhole solutions are obtained and energy conditions are examined. Further, the [Formula: see text] model is found to be consistent with local gravity tests and stability of cosmological perturbations and late-time de Sitter point. Cosmological evolution is also explored using Friedman-Robertson-Walker (FRW) metric in [Formula: see text] gravity.

Horizonless compact objects with light rings are becoming more popular in recent years for numerous motives. In this paper, the conditions under which the throat of a Morris–Thorne wormhole can act as an effective photon sphere are worked out. A specific example which satisfies all the energy conditions in modified theory of gravity is considered and the formation of relativistic images is studied. We have detected photon spheres for the wormhole modeling due to the effect of strong gravitational lensing. Subsequently, we have found the expression for deflection angle in terms of the angular separation between the image and lens by determining the strong-field limit coefficients. It is found to diverge for the impact parameter corresponding to the photon sphere. We observed that the angle of Einstein ring [Formula: see text] and relativistic Einstein ring [Formula: see text] are completely distinguishable. Given the configuration of the gravitational lensing and the radii of the Einstein ring and relativistic Einstein rings, we can distinguish between a black hole and a wormhole in principle. The stability of wormholes is examined from the positivity of the shape function and satisfaction of the flare-out condition.

This work is focused on the study of charged wormholes in the following two aspects: (i) to obtain exotic matter free effective charged wormhole solutions and (ii) to determine deflection angle for gravitational lensing effect. We have defined a novel redshift function, obtained wormhole solutions using the background of [Formula: see text] theory of gravity and found the regions obeying the weak energy condition. Further, the gravitational lensing effect is analyzed by determining the deflection angle in terms of strong field limit coefficients.

Weexplore a new kind ofNLED field as a source of gravity, which can accelerate theUniverse during the inflationary era. Wepropose a new type ofNLED lagrangianwhich is characterised by two parameters: alpha (dimensionless parameter) and beta (dimensionful parameter). We investigate the classical stability and the causality aspects of this model of inflationary expansion by demanding that the speed of the soundwave c(s)(2) > 0 and 0 <= c(s) <= 1s. Corresponding to 0 <= c(s)(2) <= 12, we find 0.382(1.828) <= beta B-2 <= 0.288(1.469) for alpha=.0.1(1.0). The equation of state parameter omega = -1/3 requires beta B-2 = 0.126(0.757) corresponding to a = 0.1(1.0). We find that theUniverse is accelerating i.e. (sic) > 0 (which results in the deceleration parameter q.<.0 (i.e omega >-1/3)), provided beta B-2 >= 0.126(0.757). During inflation, the energy density rho(B) is found to bemaximum and is given by rho(max)(B) = 0.65/beta. The magnetic field necessary to trigger the inflation is found to be B similar or equal to root 0.4 rho(max)(B) = 4 x 10(51) Gauss, where rho(max)(B)(similar to rho(inf)) = 10(64) GeVB infmax () 64 4 is the energy density of the Universe during the inflationary expansion. Ourmodel also predicts the e-fold number N = 71(64) that themagnetic field at the end of inflation is about B =10(-10) (10(-4)) Gauss corresponding to z.=.0(1000) and this agrees quite well with the experimental prediction of the e- fold number. With a.=.0.3(1.0) and beta B-2 = 0.3974(0.8239), we find the scalar spectral index ns.=.0.9649, consistent with the PLANCK 2018 CMB data. Further, with alpha = 0.3(1.0), beta B-2 = 0.3974(0.8239), we predicts the tensor-to-scalar ratio r.=.0.1417(0.1449) and the tensorial spectral index nT = -0.0177(-0.0181).

This paper is focused on the study of charged wormholes which are combinations of Morris–Thorne wormhole and Reissner–Nordström spacetime. Gravitational lensing is an important tool which has been adopted to detect various objects like wormholes using the notion of deflection angle. In this work, we have evaluated deflection angle with and without using the strong field limit coefficients and compared the results. Further, exact charged wormhole solutions are obtained in [Formula: see text] gravity and the nature of the energy conditions is examined.

In this paper, we have considered the modification of general relativity and presence of extra matter part for the exploration of traversable wormhole solutions. In particular, we have considered the background of f(R, T) gravity under the effect of scalar field and electric charge, which play the role of additional matter part. The energy conditions are detected in the presence of both scalar field and electric charge and the results are compared. Further, the existence of photon spheres, due to the strong gravitational lensing, is examined and the formation of relativistic images is studied.

The present paper is intended for studying the effect of strong gravitational lensing in the context of charged wormhole. To study this effect, the conditions determining the existence of photon spheres at and outside the throat are obtained. The necessary and sufficient conditions for the existence of photon spheres at or outside the throat of the charged wormhole is derived. Furthermore, photon spheres are investigated in three cases for three different forms of redshift function. These three cases include the existence of effective photon spheres (i) at the throat, (ii) outside the throat and (iii) both at and outside the throat. Consequently, these provide the information about the formation of infinite number of concentric rings and may lead to the detection of wormhole geometries.

In the present paper, the work of Moreas et al. [P. H. R. S. Moraes, G. Ribeiro and R. A. C. Correa, A transition from a decelerated to an accelerated phase of the universe expansion from the simplest non-trivial polynomial function of T in the [Formula: see text] formalism, Astrophys. Space Sci. 361 (2016) 227–231] is extended to study the FRW model in [Formula: see text] gravity. The expressions for deceleration and Hubble parameters are determined in terms of redshift. The age of the universe is established using [Formula: see text] high-redshift type Ia supernovae data from the Supernova cosmology project and 15 low-redshift type Ia supernovae data from the Calán/Tolono Supernova survey [S. Permutter et al., Measurements of Omega and Lambda from 42 High-Redshift Supernovae, Astrophys. J. 517 (1999) 565–585]. For these redshifts, the data of observed apparent magnitude and luminosity distance are used for the comparison with the obtained theoretical values.

Natural horizonless object and its astrophysical signatures have been proposed in various aspects. In this paper, the traversable wormhole solutions are investigated for Einstein’s field equations with cosmological constant. Using redshift function Φ(r)and shape function b(r)as Φ(r)=−1r2and b(r)=r0log(r+1)log(r0+1)in the static and spherically symmetric metric of wormholes, the spherical regions are determined, where the energy conditions are satisfied for positive value of cosmological constant. Further, horizonless compact objects with light rings (or photon spheres) are becoming more popular in recent years for numerous motives. We observed that a horizonless object such as a traversable wormhole can have a photon sphere outside the throat. So, the photon spheres are detected due to the effect of strong gravitational lensing. Furthermore, the deflection angle is found to diverge for the impact parameter corresponding to the photon sphere.

The present paper is aimed at the study of traversable wormholes in f(R) gravity with a viable f(R) function defined as f(R) = R - mu R-c(R/R-c)(p), where R is scalar curvature, mu, R-c and p are constants with mu, R-c > 0 and 0 < p < 1 (Amendola et al., 2007a). The metric of wormhole is dependent on shape function b(r) and redshift function phi(r), which characterize its properties, so the shape function and redshift function play an important role in wormhole modeling. In this work, the wormhole solutions are determined for (i) phi(r) = 1/r and (ii) phi(r) = c (constant) with b(r) = r/exp(r - r(0)) (Samanta et al., 2018). Further, the regions respecting the energy conditions are investigated.

In this paper, the strong gravitational lensing is explored for traversable wormholes in [Formula: see text] theory of gravity with minimally-coupled massless scalar field. First, the effective wormhole solutions are obtained using the model [Formula: see text], where [Formula: see text] is constant, [Formula: see text] is scalar curvature and [Formula: see text] is the trace of stress-energy tensor. Furthermore, three different shape functions namely, [Formula: see text] (Ref. 36), [Formula: see text] (Refs. 35 and 37) and [Formula: see text], [Formula: see text] (Refs. 34, 35, 39, 73) are considered and studied their qualitative behavior for the construction of wormhole geometry respectively. Subsequently, gravitational lensing effect is implemented to detect the existence of photon spheres at or outside the throat of wormholes.