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The paper attempts to discuss the impact of reference price effect on pricing decisions.

With the growth of the Internet and e-commerce, more and more customers purchase products in through online channels and choose products by comparing different prices and services, and the reference price effect has an impact on pricing decisions. To investigate the impact of consumers' reference price effect on the dual-channel supply chain, the authors establish a basic model consisting of a single dominant manufacturer and a single downstream retailer, and analyze the optional decisions under different situations and discuss the influence of reference price effect. Finally, a number case verifies the validity and rationality of the proposed model.

The results show that (1) the reference price effect has varying effects on the price, channel demand and income of manufacturers and retailers in the channel depending on the role of customers' channel preferences. (2) The manufacturer's online channel demand and profits always increase with the reference pricing effect, whereas the retailer's offline demand and profits always decline. (3) When the proportion of consumers preferring offline is higher, the manufacturer's network price and wholesale price increase with the reference price effect, while the retailer's retail price decreases with the reference price effect; when the proportion of consumers preferring offline is lower, the opposite is true, and the centralized decision results are consistent with the decentralized decision results.

This paper can clarify the impact of consumer reference price effects on the operation of dual-channel supply chains, and help inform pricing decisions of manufacturers and retailers in dual-channel supply chains.

The proposed approach can well analyze the impact of consumer reference price effect and give channel their optional decisions.

Omnichannel has become increasingly important with the development of e-commerce. In omnichannel, merchants expect customers to get the products and services at anytime, anywhere and in any way, and the same is true for customers. This drives multihoming in online platforms for both merchants and customers. Thus, once both customers and merchants are multihomed, what price and subsidy decisions should be made between platforms to compete to obtain optimal profits? The main purpose of this paper is to solve these problems and provide decision-making for two-sided platforms in omnichannel.

This study builds a dual Hotelling model to capture the utility and network effects of customers and merchants on two-sided platforms. This study introduces the exposure effect and convenience effect of multihomed customers and merchants in the model and analyzes the impact of these effects in the market with multihoming on one side. Then, this study extends the model to the market with multihoming on both sides and makes the pricing decision for two-sided platform when considering the exposure effect and convenience effect through an equilibrium solution. Finally, this study also uses numerical analysis to simulate the decision and profit of the platform.

This paper finds that the convenience effect will only increase social welfare when customers are single-homed and merchants are multihomed. In addition, when both users are multihomed, the platform will subsidize to attract merchants and customers if the convenience effect and exposure effect are relatively high. This study also finds that network effects come not only from the same platform but also from another platform in the case with multihoming on both sides. And network effects in the heterogeneous platform will be reduced by the convenience effect and exposure effect.

According to the behavioral characteristics of merchants and customers in omnichannel, this paper first adopts the dual Hotelling model to study the pricing of two-sided platforms with multihoming on both sides. This paper shows that network effects originate not only from the same platform but also from another platform and that the exposure effect and the convenience effect can exist as cross-platform network effects, which provides a new explanation for network effects in markets with multihoming on both sides. This research extends the theory of network effects and plays an important role in the development of two-sided platforms in omnichannel.

Considering two types of subsidies for producers (supplier and manufacturer) and one for consumers based on product greenness and sales quantity, this study aims to formulate optimal supply chain green innovation and subsidy strategies, and to achieve this goal with the support of information systems.

This study introduces a composite green-product supply chain where suppliers focus on green innovation for component greenness and manufacturers focus on green innovation for manufacturing process greenness. Game theory modeling is applied to investigate the differences of product greenness, supply chain members’ profit and social welfare under different government subsidy strategies.

Increasing the unit greenness subsidy coefficient can boost product greenness and supply chain members’ profits, but does not always raise social welfare. When the government exclusively offers subsidies to producers, subsidies should be allocated to suppliers when there is a significant disparity in supply chain green innovation costs. Conversely, it is more beneficial to subsidize manufacturers. Consumer subsidies have the potential to enhance both environmental and economic performance in the supply chain compared with producer-exclusive subsidies, but may not always maximize social welfare when supply chain members have low unit costs associated with green innovation.

This study examines the optimal decisions for green supply chain innovation and government subsidy strategies. Supply chain members and the government can use the information system to collect and evaluate the cost of upstream and downstream green innovation, and then develop reasonable collaborative green innovation and subsidy strategies.

The purpose of this paper is to characterize a commutative ring R with identity which is not an integral domain such that ZT(R), the total zero-divisor graph of R is connected and to determine the diameter and radius of ZT(R) whenever ZT(R) is connected. Also, the purpose is to generalize some of the known results proved by Duric et al. on the total zero-divisor graph of R.

We use the methods from commutative ring theory on primary decomposition and strong primary decomposition of ideals in commutative rings. The structure of ideals, the primary ideals, the prime ideals, the set of zero-divisors of the finite direct product of commutative rings is used in this paper. The notion of maximal Nagata prime of the zero-ideal of a commutative ring is also used in our discussion.

For a commutative ring R with identity, ZT(R) is the intersection of the zero-divisor graph of R and the total graph of R induced by the set of all non-zero zero-divisors of R. The zero-divisor graph of R and the total graph of R induced by the set of all non-zero zero-divisors of R are well studied. Hence, we determine necessary and sufficient condition so that ZT(R) agrees with the zero-divisor graph of R (respectively, agrees with the total graph induced by the set of non-zero zero-divisors of R). If Z(R) is an ideal of R, then it is noted that ZT(R) agrees with the zero-divisor graph of R. Hence, we focus on rings R such that Z(R) is not an ideal of R. We are able to characterize R such that ZT(R) is connected under the assumptions that the zero ideal of R admits a strong primary decomposition and Z(R) is not an ideal of R. With the above assumptions, we are able to determine the domination number of ZT(R).

Duric et al. characterized Artinian rings R such that ZT(R) is connected. In this paper, we extend their result to rings R such that the zero ideal of R admits a strong primary decomposition and Z(R) is not an ideal of R. As an Artinian ring is isomorphic to the direct product of a finite number of Artinian local rings, we try to characterize R such that ZT(R) is connected under the assumption that R is ta finite direct product of rings R1, R2, … Rn with Z(Ri) is an ideal of Ri for each i between 1 to n. Their result on domination number of ZT(R) is also generalized in this paper. We provide several examples to illustrate our results proved.

The implication of this paper is that the existing result of Duric et al. is applicable to large class of commutative rings thereby yielding more examples. Moreover, the results proved in this paper make us to understand the structure of commutative rings better. It also helps us to learn the interplay between the ring-theoretic properties and the graph-theoretic properties of the graph associated with it.

The results proved in this paper are original and they provide more insight into the structure of total zero-divisor graph of a commutative ring. This paper provides several examples. Not much work done in the area of total zero-divisor graph of a commutative ring. This paper is a contribution to the area of graphs and rings and may inspire other researchers to study the total zero-divisor graph in further detail.

This study aims to minimize the cost and time of blood delivery in the whole blood supply chain network (BSCN) in disaster conditions. In other words, integrating all strategic, tactical and operational decisions of three levels of blood collection, processing and distribution leads to satisfying the demand at the right time.

This paper proposes an integrated BSCN in disaster conditions to consider four categories of facilities, including temporary blood collection centers, field hospitals, main blood processing centers and medical centers, to optimize demand response time appropriately. The proposed model applies the location of all permanent and emergency facilities in three levels: blood collection, processing and distribution. Other essential decisions, including multipurpose facilities, emergency transportation, inventory and allocation, were also used in the model. The LP metric method is applied to solve the proposed bi-objective mathematical model for the BSCN.

The findings show that this model clarifies its efficiency in the total cost and blood delivery time reduction, which results in a low carbon transmission of the blood supply chain.

The researchers proposed an integrated BSCN in disaster conditions to minimize the cost and time of blood delivery. They considered multipurpose capabilities for facilities (e.g. field hospitals are responsible for the three purposes of blood collection, processing and distribution), and so locating permanent and emergency facilities at three levels of blood collection, processing and distribution, support facilities, emergency transportation and traffic on the route with pollution were used to present a new model.

A new model for two-sided platforms is presented, incorporating both the original business and an expanded (new) business. Previous studies have neglected the impact of technology R & D on the new business aspect of two-sided platforms. This study addresses this gap by examining the technology R & D effect on the new business while also considering the congestion effect on the original business. It investigates the optimal pricing and user scales for both the original and new businesses. Additionally, the profits of the original business, the new business, and the overall two-sided platform are analyzed.

Previous studies have overlooked the technology R & D effect on the new business aspect of two-sided platforms. Therefore, this study focuses on examining the technology R & D effect on the new business. Additionally, the congestion effect on the original business is considered. To determine the optimal prices for both sides of the original and new businesses, a game sequence model is introduced.

The optimal price on the service buyers (defined b side) of new business increases only with regard to technology R & D effect on b side of new business increasing. The optimal price on b side of new business is equal to half of the b-side R & D effect. The optimal profit of original business decreases with regard to the technology R & D effect of new business and cross-market network effect on the services provider (defined s side) between original business and new business increasing, respectively. To gain optimal profit of two-sided platform, the two-sided platform adopts some strategies to improve the congestion.

A new two-sided platform model is stated, in which the technology R & D effect is embraced. The expanded business scenario of two-sided platform is considered, that is, the two-sided platform has one business firstly and a new business is developed or improved of two-sided platform. To solve the prices strategy of original business and new business, a game sequence of the original business and new business is presented.

The present work focuses on the primality and the Cartesian product of graphs.

Given a graph G, a subset M of V (G) is a module of G if, for a, b ∈ M and x ∈ V (G) \ M, xa ∈ E(G) if and only if xb ∈ E(G). A graph G with at least three vertices is prime if the empty set, the single-vertex sets and V (G) are the only modules of G.

Motivated by works obtained on “the Cartesian product of graphs” and “the primality,” this paper creates a link between the two notions.

In fact, we study the primality of the Cartesian product of two connected graphs minus k vertices, where k ∈ {0, 1, 2}.

The objective of this paper is to formulate the precise meanings of grey graphs and examine some of their properties.

This article introduces innovative concepts of grey sets based on the grey number. We establish the grey graphs and examine their essential properties as isomorphisms of these graphs. Additionally, we explore the notion of a grey-complete graph and demonstrate certain properties of self-complementary grey-complete graphs.

We showcase novel facets of grey system theory through the establishment of the structures of grey graphs, and the subsequent analysis of their distinctive traits.

This article provides us with a new theoretical direction for grey system theory according to grey numbers. Thus, we present test examples that explain the routes between cities and the electrical wires between homes. Furthermore, the concept of grey graphs can be applied in several areas of engineering, computer science, neural networks, artificial intelligence, and medical diagnosis.

The proposed concepts are considered novel mathematical directions in grey system theory for the first time. Some operations of grey graphs are also explored.

One of the challenges encountered in the design of guided projectiles is their prohibitive cost. To diminish it, an appropriate avenue many researchers have explored is the use of the non-actuator method for guiding the projectile to the target. In this method, biologically inspired by the flying concept of the single-winged seed, for instance, that of maple and ash trees, the projectile undergoes a helical motion to scan the region and meet the target in the descent phase. Indeed, the projectile is a decelerator device based on the autorotation flight while it attempts to resemble the seed’s motion using two wings of different spans. There exists a wealth of studies on the stability of the decelerators (e.g. the mono-wing, samara and pararotor), but all of them have assumed the body (exclusive of the wing) to be symmetric and paid no particular attention to the scanning quality of the region. In practice, however, the non-actuator-guided projectiles are asymmetric owing to the presence of detection sensors. This paper aims to present an analytical solution for stability analysis of asymmetric decelerators and apprise the effects of design parameters to improve the scanning quality.

The approach of this study is to develop a theoretical model consisting of Euler equations and apply a set of non-dimensionalized equations to reduce the number of involved parameters. The obtained governing equations are readily applicable to other decelerator devices, such as the mono-wing, samara and pararotor.

The results show that the stability of the body can be preserved under certain conditions. Moreover, pertinent conclusions are outlined on the sensitivity of flight behavior to the variation of design parameters.

The analytical solution and sensitivity analysis presented here can efficiently reduce the design cost of the asymmetric decelerator.

The standard method to estimate a stochastic frontier (SF) model is the maximum likelihood (ML) approach with the distribution assumptions of a symmetric two-sided stochastic error v and a one-sided inefficiency random component u. When v or u has a nonstandard distribution, such as v follows a generalized t distribution or u has a χ2 distribution, the likelihood function can be complicated or untractable. This chapter introduces using indirect inference to estimate the SF models, where only least squares estimation is used. There is no need to derive the density or likelihood function, thus it is easier to handle a model with complicated distributions in practice. The author examines the finite sample performance of the proposed estimator and also compare it with the standard ML estimator as well as the maximum simulated likelihood (MSL) estimator using Monte Carlo simulations. The author found that the indirect inference estimator performs quite well in finite samples.