Green sustainable supply chain under cap and trade regulation involving Government introspection

This paper investigates Government intervention in a three-echelon supply chain comprising one manufacturer and one retailer. Government is the top level member trying to reduce environmental impacts based on the amount of carbon emission during the production process. Government controls the chain by collecting tax from the retailer which is indirectly paid by the customer and paying subsidy/imposing ne on the manufacturer. Government encourages manufacturer to reduce carbon emission by contributing some subsidy and also makes an e ort to generate Government net revenue (GNR) by imposing tax. The GNR is generated by collecting tax from the retailer on the sold product and penalty from the manufacturer at the trading price for the extra amount of emissions. The retail price is decided based on the selling price, tax and greening level. We aim to determine optimal levels of pricing, greening and amount of tax to be levied. The models for both linear and iso-elastic demand patterns are developed. The aim of this piece research is two-fold: (i) review the existent literature on the relationship between environ- mental collaboration and sustainability performance and (ii) render a tenable prototype of supply chain to illuminate the relationship between sustainability and profitability. According to the aforesaid goals this paper has carried out a detailed empirical research by using advanced structural equation modelling approaches. The research findings will be particularly important for manufacturing companies struggling to find techniques to achieve sustainability performance. Also it will aid the supply chains in developing environmental collaboration with the Govt. in order to attain the targets of GSCM.

New preference violation indices for the condition of order preservation

<p>Consistency of pairwise comparisons is one particular aspect that is studied thoroughly in the recent decades. However, since the introduction of the concept of the condition of the order preservation in 2008, there is no inconsistency measure based on the aforementioned condition. Therefore, the aim of this paper is to fill this gap and propose new preference violation indices for measuring violation of the condition of the order preservation. Further, an axiomatic system for the proposed measures is discussed, and it is shown that the proposed indices satisfy uniqueness, invariance under permutation, invariance under inversion of preferences and continuity axioms.</p> <p>&nbsp;</p>

Strong equality of Roman and perfect Roman domination in trees

A Roman dominating function (RD-function) on a graph $G = (V, E)$ is a function $f: V \longrightarrow \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$. An Roman dominating function $f$ in a graph $G$ is perfect Roman dominating function (PRD-function) if every vertex $u$ with $f(u) = 0$ is adjacent to exactly one vertex $v$ for which $f(v) = 2$. The (perfect) Roman domination number $\gamma_R(G)$ ($\gamma_{R}^{p}(G)$) is the minimum weight of an (perfect) Roman dominating function on $G$. We say that $\gamma_{R}^{p}(G)$ strongly equals $\gamma_R(G)$, denoted by $\gamma_{R}^{p}(G)\equiv \gamma_R(G)$, if every RD-function on $G$ of minimum weight is a PRD-function. In this paper we show that for a given graph $G$, it is NP-hard to decide whether $\gamma_{R}^{p}(G)= \gamma_R(G)$ and also we provide a constructive characterization of trees $T$ with $\gamma_{R}^{p}(T)\equiv \gamma_R(T)$.

A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator

Many decision-making problems can solve successfully by traditional optimization methods with a well-defined configuration. The formulation of such optimization problems depends on crisply objective functions and a specific system of constraints. Nevertheless, in reality, in any decision-making process, it is often observed that due to some doubt or hesitation, it is pretty tricky for decision-maker(s) to specify the precise/crisp value of any parameters and compelled to take opinions from different experts which leads towards a set of conflicting values regarding satisfaction level of decision-maker(s). Therefore the real decision-making problem cannot always be deterministic. Various types of uncertainties in parameters make it fuzzy. This paper presents a practical mathematical framework to reflect the reality involved in any decision-making process. The proposed method has taken advantage of the hesitant fuzzy aggregation operator and presents a particular way to emerge in a decision-making process. For this purpose, we have discussed a couple of different hesitant fuzzy aggregation operators and developed linear and hyperbolic membership functions under hesitant fuzziness, which contains the concept of hesitant degrees for different objectives. Finally, an example based on a multiobjective optimization problem is presented to illustrate the validity and applicability of our proposed models.

A joint pricing and network design model for a closed-loop supply chain under disruption (Glass Industry)

Closed-loop supply chains have attracted more attention by researchers and practitioners due to strong government regulations, environmental issues, social responsibilities and natural resource constraints over past few years. This paper presents a mixed-integer linear programming model to design a closed-loop supply chain network and optimizing pricing policies under random disruption. Reusing the returned products is applied as a resilience strategy to cope with the waste of energy and improving supply efficiency. Moreover, it is necessary to find the optimal prices for both final and returned products. Therefore, the model is formulated based on demand function and it maximizes total supply chain’s profit. Finally, its application is explored through using the real data of an industrial company in glass industry.

Incidence dimension and 2-packing number in graphs

Let G = (V,E) be a graph. A set of vertices A is an incidence generator for G if for any two distinct edges e,f ∈ E(G) there exists a vertex from A which is an endpoint of either e or f. The smallest cardinality of an incidence generator for G is called the incidence dimension and is denoted by dimI(G). A set of vertices P ⊆ V (G) is a 2-packing of G if the distance in G between any pair of distinct vertices from P is larger than two. The largest cardinality of a 2-packing of G is the packing number of G and is denoted by ρ(G). In this article, the incidence dimension is introduced and studied. The given results show a close relationship between dimI(G) and ρ(G). We rst note that the complement of any 2-packing in graph G is an incidence generator for G, and further show that either dimI(G) = ρ(G) or dimI(G) = ρ(G)−1 for any graph G. In addition, we present some bounds for dimI(G) and prove that the problem of determining the incidence dimension of a graph is NP-hard.

The implications of supplier encroachment via an online platform

E-commerce provides suppliers with the flexibility to operate an online arm via a platform in addition to their pre-existing physical stores. Although such supplier encroachment is becoming increasingly prevalent in e-commerce markets, the literature on supplier encroachment traditionally assumes that suppliers sell products to consumers directly and argues that supplier encroachment can mitigate double marginalisation problems that can secure Pareto improvements. This paper narrows this gap by investigating the implications of the supplier encroachment with an online platform under two scenarios (i.e., the platform owner forgoing or retaining its entry options). A central result obtained is that, unlike supplier-owned direct channels and in addition to the ‘win-win’ outcomes for the supplier and the traditional retailer, supplier encroachment with an online platform may also lead to ‘win-lose’ and ‘lose-lose’ outcomes. Furthermore, when the platform owner retains its entry option, such encroachment is always detrimental for the traditional retailer but beneficial for the supplier.

Decisions and coordination of retailer-led fresh produce supply chains under two-period dynamic pricing and portfolio contracts

Fresh agricultural produce is almost the staple food and necessity of people's daily diet all over the world. However, natural perishability and freshness affect the demand for fresh agricultural produce. Due to the change of freshness, the retailer has to adopt a multi-period dynamic pricing strategy to deal with unsold products. The research object of this paper is the retailer's two-echelon supply chain of fresh agricultural produce, and the aim is to achieve the optimal two-period coordination and ordering through options and wholesale contracts in the supply chain. In the case of two-period pricing, we find that the optimal wholesale order quantity increases with the decline of the price in the first period and tends to be stable with the decline of the price in the second period. In contrast, the price change in the first period has a greater impact on the retailer's optimal order quantity. The profits of both the retailer and the supplier increase significantly with the increase of the price in the first period, while the impact of the change of the price in the second period is not obvious. Meanwhile, decentralized decision-making can only be coordinated in the supply chain through the original option contract at the first-period price. In the second period, the cost-sharing contract is introduced to coordinate the supply chain, increase orders, and increase the profits of both the retailer and the supplier. These findings are of great significance for both the retailer and the supplier in the multi-period dynamic pricing of fresh produce under the option contract.

On the impact of corruption on managers' and controllers' behavior

In this paper, we study the impact of corruption in the context of a game involving a manager and a controller. We propose a model where the controller initiates the bribe demand from the manager. We identify the structure of three potential subgame perfect Nash equilibria, and show their uniqueness. Next, we analyze the influence of the corruption parameters (bribery amount, reciprocity bonus and reputation gain) and the manager's and the controller's bonuses / penalties on the equilibria. Finally, we explain how the manager and the controller may increase, decrease or maintain their performance, when the bribery amount, the reciprocity bonus or the reputation gain index increase.

Two new Hager-Zhang iterative schemes with improved parameter choices for monotone nonlinear systems and their applications in compressed sensing

Notwithstanding its efficiency and nice attributes, most research on the iterative scheme by Hager and Zhang [Pac. J. Optim. 2(1) (2006) 35-58] are focused on unconstrained minimization problems. Inspired by this and recent works by Waziri et al. [Appl. Math. Comput. 361(2019) 645-660], Sabi’u et al. [Appl. Numer. Math. 153(2020) 217-233], and Sabi’u et al. [Int. J. Comput. Meth, doi:10.1142/S0219876220500437], this paper extends the Hager-Zhang (HZ) approach to nonlinear monotone systems with convex constraint. Two new HZ-type iterative methods are developed by combining the prominent projection method by Solodov and Svaiter [Springer, pp 355-369, 1998] with HZ-type search directions, which are obtained by developing two new parameter choices for the Hager-Zhang scheme. The first choice, is obtained by minimizing the condition number of a modified HZ direction matrix, while the second choice is realized using singular value analysis and minimizing the spectral condition number of the nonsingular HZ search direction matrix. Interesting properties of the schemes include solving non-smooth functions and generating descent directions. Using standard assumptions, the methods’ global convergence are obtained and numerical experiments with recent methods in the literature, indicate that the methods proposed are promising. The schemes effectiveness are further demonstrated by their applications to sparse signal and image reconstruction problems, where they outperform some recent schemes in the literature.