Complex Dynamics in a Closed-Loop Supply Chain with Risk Aversion and Fairness Concerns Under Supply Disruption

This paper is focused on a triopoly closed-loop supply chain (CLSC) game model, including triopoly oligopolies applying for circular economy development. In the CLSC model, manufacturers sell new products and re-collect waste products for maximizing their profits. This paper analyzes the game processing, the Nash equilibrium solutions, and the stability of the game model. Moreover, the influences of parameters on the system’s stability have been investigated, using the maximal Lyapunov exponent, bifurcation graph, and the stable domain. The results show that the system will be unstable when the adjustment speed of the manufacture is too high; unreasonable price strategies could easily cause system bifurcation; the critical point of system bifurcation is closely related to the collecting price.

This paper studies the effects of channel power structure and participants' risk-averse attitude on differentiated pricing policies of closed-loop supply chains. It is assumed that the manufacturer is risk-averse and the retailer is risk-neutral. The manufacturer's expected utility function and the retailer's expected profit function are obtained by mean-variance theory. Then the differentiated pricing policies and profit allocation problem are discussed under three channel power structures: manufacturer-Stackelberg (MS), retailer-Stackelberg (RS) and Vertical Nash (VN) equilibrium. The optimal wholesale prices, retail prices and production quantities of new manufactured products and remanufactured products are derived and compared under different cases. Finally numerical analysis of risk-averse degree on participants' profits is given. The study has shown that the VN mode yields the best closed-loop supply chain performances, and then is the MS mode, the worst is the RS supply chain.

This paper investigates a dual-channel supply chain with one risk-neutral manufacturer and one risk-averse retailer where there is only one perishable product with price-dependent stochastic demand. We choose Conditional Value-at-Risk criterion to measure the retailer’s risk-averse level, and assume that the manufacturer’s direct sales channel and the retailer’s traditional channel adopt a consistent pricing strategy. The model explores a Nash bargaining problem where the manufacturer and the retailer negotiate with each other on the wholesale price, the retail price and the order quantity when they have equal bargaining power. It is found that when demand uncertainty follows a uniform distribution, a Nash bargaining equilibrium exists and the retail price will decrease as the retailer becomes more risk averse. However, when the risk-averse indicator increases, the manufacturer’s profit on his direct channel will decrease, increase or first increase and then decrease, depending on the values of the related parameters. The profit shares of the manufacturer and the retailer under the Nash equilibrium model are related to the risk-averse indicator of the retailer. Furthermore, we perform three sets of numerical experiments to verify the effects of the retailer’s risk-averse indicator on decision-making and profit allocations under the different environmental parameters and gain several meaningful managerial insights.

We argue that a Nash bargaining model with behavioral factors (i.e., fairness concern and risk aversion) should be introduced to the price strategizing process in the context of a closed-loop supply chain. We consider three different pricing models: The first is when both the manufacturer and the retailer have fairness concerns; the second is when both the manufacturer and the retailer have risk aversion; and the final is when the manufacturer has risk aversion but the retailer has both risk aversion and fairness concern. Then we examine the model with game theory. The results have shown that fairness and risk aversion change the optimal pricing strategy, which affects the expected profits of retailers and manufacturers. The impacts of two (relatively irrational) behavioral factors on the wholesale and retail prices of new products, the recycle price and recycle transfer price of the waste products, are not the same. For new products, the wholesale price is most affected by behavioral factors and the sales price scores second. For waste recycling products, the transfer price is most affected by behavioral factors and the recycle price scores second. When considering fairness and risk aversion in retail, fairness concern is good for both manufacturers and retailers. This innovative pricing strategy model adds implications for sustainability in supply chain operations.

Customer and retailer rebates under risk aversion

With the rapid development of low earth-orbit (LEO) satellites, the ultra-dense LEO satellite network (UDLSN) has become a promising solution to provide Internet services for civil aviation due to its wide coverage, exceptional flexibility and high reliability. To guarantee the continuity and high-quality Internet services, satellite-aircraft handover is inevitable because of the high mobility of aircraft and satellites. However, the stringent passenger communication requirements and the considerable increase in the scale of candidate satellites pose huge challenges in satellite-aircraft handover in UDLSNs. In this paper, we investigate multiple civil aircraft handover issue including satellite handover, subchannel allocation, and power selection in the UDLSN and consider different levels of usersâ rate satisfaction, power overhead, and handover overhead as handover criteria for performance measure. The optimization problem is formulated to maximize the handover satisfaction of all civil aircraft. Particularly, the formulated handover problem is represented as a local cooperation game, where each aircraft determines the handover action and the power level by cooperating with other interference aircraft. We prove that the proposed game has at least one Nash Equilibrium (NE) solution in which no aircraft changes its handover strategy. The NE solution in the proposed game is further proven to locally or globally maximize the optimization objective and we then design the parallel handover strategy update (PHSU) algorithm to find the NE solution. Simulation results based on trajectories of real civil aircraft demonstrate that, the designed algorithm is robust, can effectively meet diverse user requirements, and reduce both handover frequency and delays.

<p style='text-indent:20px;'>This paper studies a supply chain consisting of two unreliable suppliers and a retailer, where the two suppliers' default risks are correlated. We use a mean-variance function to characterize the retailer's risk aversion. In the case of exogenous wholesale prices, we find that the retailer's risk aversion has a non-monotonic effect on its total ordering quantity. We also show that when the suppliers' default correlation increases, the retailer's total ordering quantity is non-increasing. In the case of endogenous wholesale prices, we find that the profits of the suppliers and the retailer are non-monotonic in retailer's risk aversion level or suppliers' default correlation. As risk aversion level increases, the retailer becomes less sensitive to wholesale prices. Finally, the numerical results indicate that when the suppliers' delivery rates are different, the supplier with a low delivery rate can benefit from the retailer's risk aversion under certain conditions.</p>

This paper focuses on the pricing problem of a two-stage closed-loop supply chain (CLSC) considering the cross-channel recycling and channel preference based on a single manufacturer and a single traditional retailer. The pricing decision problem raises from the manufacturer’s direct sales and the retailer’s retailing including recycling. Managers need to focus on intelligible management considering consumer channel preferences, cross-channel recovery and pricing strategies. According to game theory, centralized and decentralized CLSC decision models are used to provide an efficient solution to managers for the pricing problem. The centralized model consists of differential and uniform pricing strategy and the decentralized model consists of manufacturer-led Stackelberg, retailer-led Stackelberg and Nash equilibrium game, respectively. The impact of cross-channel recycling rate and channel preference on pricing and profitability in a two-stage CLSC system is explained elaborately in this study. The results show that cross-channel recovery rates and consumer channel preferences have a direct significant impact on pricing strategies including profit allocation decisions in CLSC. It demonstrated that different channel preferences leading to different pricing strategies and decision for manufacturers and retailers choices. Manufacturer’s pricing decreases when channel preferences are constant and cross-channel recovery rates increase. Retailer’s pricing remains stable as the cross-channel recovery rate has less affected on it. Furthermore, if the cross-channel recovery rates increase, then the manufacturers pricing decreases and retailers pricing increases. This information will be a helpful guideline for the manager to select suitable pricing strategies based on the company scenario.

This research studies the buyback contract of a supply chain system composed of a risk-neutral supplier and a risk-averse retailer. The buyback contract is divided into two cases, the credit for all unsold goods and the credit for a partial return of goods, which are theoretically analyzed and simulated numerically respectively. The results show that when the retailer is risk averse, the supply chain system is able to achieve coordination. The buyback price is an increasing function of and the buyback ratio is also an increasing function of, while the wholesale price is a decreasing function of the risk aversion.

In the framework of the newsvendor model, both single- and multi-period models are proposed to investigate the ordering strategy of a risk-averse retailer under buyback guarantee financing (BGF) and stochastic demand. In the single-period model, the classical newsvendor is extended by introducing risk aversion and capital constraints simultaneously. It is found that the optimal ordering quantity is a monotonic function in some parameters, such as increasing in the retailer's risk aversion and salvage value, while decreasing in the initial capital and wholesale price. The multi-period model is a dynamical model described by the bounded rationality decision adjustment rules. We then investigate the complex dynamics they admit, such as period-doubling bifurcation and chaotic phenomena, and have found that the dynamical models experience more complex behaviour than their static counterpart. Furthermore, in the dynamical case, we could see periodic, bifurcating or chaotic changes in ordering quantity. We also investigate the influence of BGF on ordering quantity, which may lead to a risk-averse retailer to order aggressively. Finally, some numerical simulations are given to illustrate the theoretical results and some suggestions are also provided.

In this study, we conduct a comprehensive literature review on the inventory and pricing decisions under the supply chain coordination. To be specific, we review the publications from 1997 to 2017 and divide the papers into six areas for discussion, they are: decisions under integrated supply chain, supply contract, capital-constrained, competition, risk aversion, and information asymmetry. After reviewing the literature, we identify three major future research directions. First, we propose to explore different real world industrial supply contracts and the forms of demand function. Second, limited studies consider risk aversion behaviour of the supply chain members; hence, we also propose to examine the inventory and pricing decisions under supply chain coordination with risk-averse retailer and risk-averse supplier, respectively. Finally, it is also interesting to investigate different types of information asymmetry.

Joint advertising, pricing and collection decisions in a closed-loop supply chain

Optimal inventory decisions for a risk-averse retailer when offering layaway

This article develops a game theoretic model of a supply chain with one supplier and two risk-averse retailers competing in price, service and lot size, where the Economic Order Quantity (EOQ) production-inventory policy is adopted. After studying the existence of EOQ equilibrium, we investigate how to adjust their decisions when the economic environment changes. We find that one retailer will decrease its optimal lot size, retail price and service level when it becomes more risk averse or its service investment efficiency decreases. When the supplier's capacity increases, the retailers will reduce retail price and increase service level, which in turn results in a higher lot size. The effect of the risk sensitivity of one retailer on the rival retailer's decisions depends on the relative service cost efficiency of the retailer. When the absolute risk aversion and service investment efficiency of one retailer increase, the supplier's profitability will increase due to a higher total expected demand. We further give the managerial insights for practitioners, which helps managers to make right decisions in an uncertain environment.

We consider a content sharing network of non-cooperative peers. The strategy set of each peer comprises, (i) client strategies, namely feasible request load splits to servers, and (ii) server strategies, namely scheduling disciplines on requests. First, we consider the request load splitting game for given server strategies such as First-In-First-Out or given absolute priority policies. A peer splits its request load to servers to optimize its performance objective. We consider the class of best response load splitting policies residing between the following extremes: a truly selfish, or egotistic one, where a peer optimizes its own delay, and a pseudo-selfish or altruistic one, where a peer also considers incurred delays to others. We derive conditions for Nash equilibrium points (NEPs) and discuss convergence to NEP and properties of the NEP. For both the egotistic cases, the NEP is unique. For the altruistic case, each of the multiple NEPs is an optimum, a global one for the FIFO case and a local one otherwise. Next, we include scheduling in peer strategies. With its scheduling discipline, a peer cannot directly affect its delay, but it can affect the NEP after peers play the load splitting game. The idea is that peer i should offer high priority to (and thus attract traffic from) higher-priority peers that cause large delay to i at other servers. We devise two-stage game models, where, at a first stage, a peer selects a scheduling rule in terms of a convex combination of absolute priorities, and subsequently peers play the load splitting game. In the most sophisticated rule, a peer selects a scheduling discipline that minimizes its delay at equilibrium, after peers play the load splitting game. We also suggest various heuristics for picking the scheduling discipline. Our models and results capture the dual client-server peer role and aim at quantifying the impact of selfish peer interaction on equilibria.