Narrow Results

In this research, we discuss three different approaches to generate demand forecasting and pricing decision for mix of national brand and store brand products in the era of big data. We derive the equilibrium wholesale price and retail price for the national brand products, and the equilibrium retail price for the store brand products based on demand forecast under three different information scenarios, including Noninformation Sharing ($N$), Information Sharing ($I$), and Retailer Forecasting ($R$). We comprehensively discuss how information collection, information sharing, forecast accuracy under era of big data affect firms’ prices and profits. Our numerical experiments illustrate and verify our analytical findings and provide further managerial insights and interpretations.

A firm sets up his facilities including manufacturing/remanufacturing plants and distribution/collection centers, incorporating an existing closed-loop supply chain (CLSC) network. The entering firm has to compete with the existing firms in the existing network. The entering firm behaves as the leader of a Stackelberg game while the existing firms in the existing network are followers. We assume that the entering firm can anticipate the existing firms’ reaction to his potential location decision before choosing his optimal policy. We use a CLSC network equilibrium model in which the decision makers are faced with multiple objectives to capture the existing firms’ reaction. A mathematical programming model with equilibrium constraints is developed for this competitive CLSC network design problem by taking into account the market competition existing in the decentralized CLSC network. A solution method is developed by integrating Genetic algorithm with an inexact logarithmic-quadratic proximal augmented Lagrangian method. Finally, numerical examples and the related results are studied for illustration purpose.

Due to double marginalization effect, the wholesale price contract has been proved that it cannot coordinate a decentralized supply chain (DSC) based on the framework of Stackelberg game, in which the upstream firm acts as a leader and the downstream firm acts as a follower. Nevertheless, it has shown that the partnership between the enterprises tends to be equality. Motivated by this factor, this paper studies the coordination of wholesale price contract under the perspective of equality between enterprises. First, an innovative wholesale price contract is constructed and to prove that the constructed contract can flexibly coordinate the DSC. Second, the adaptability of the constructed contract is analyzed and compared with the revenue sharing contract, which is designed under the framework of Stackelberg game. Third, numerical analysis is calculated to verify the effectiveness and operation of the model.

Although existing contributions that explore service quality guarantee problem of a logistic service supply chain (LSSC) consider fairness concern behavior of one member, little attention is paid to considering the combination of members’ fairness concern and the joint decision of pricing and service quality guarantee in LSSC. Therefore, it is necessary to research how different fairness concern affects the joint decision of pricing and service quality guarantee in an LSSC. First considering a price and quality-sensitive logistics service market, a basic model without fairness concern of a customized LSSC is established. Then, a new model with fairness concern of a decentralized LSSC is constructed based on the basic model. The optimal decision of the LSSC with fairness concern is investigated in three cases. In each case, we analyze the effect of fairness concern on the optimal decision, and the expected profits and utilities. Finally, some numerical studies are shown to verify our theoretical analyses and some managerial insights are given.

This paper addresses a network optimization interdiction problem, called the maximum capacity path interdiction problem. The problem is a hierarchical game containing two players: one evader and one interdictor. In a capacitated network, the evader wants to find a simple path from his current position to a target point with maximum capacity to send his forces along it while the interdictor decreases arc capacities under a budget constraint to interdict the advance of the evader’s forces as much as possible. This paper studies the case that each arc has a fixed cost for decreasing its capacity. An algorithm is proposed to solve the problem in strongly polynomial time. Computational experiments on two real-world datasets guarantee the efficiency and accuracy of the algorithm.

In this paper, a closed-loop supply chain consisting of a manufacturer, a retailer and a third-party remanufacturer responsible for collecting used products and remanufacturing is constructed. Considering the quality level of remanufactured products, four kinds of closed-loop supply chain alliance structure models are constructed. The optimal equilibrium decisions of these four models are compared and analyzed. The optimal decisions of the models are verified by numerical analysis. Furthermore, the impacts of the quality of remanufactured products and the decision influence of the third-party remanufacturer in the alliance on the remanufacturer’s decision are further analyzed. The results show that remanufactured products are competitive with new products, and the improvement of the remanufactured product quality will reduce the market demand of new products. The equilibrium decision of the closed-loop supply chain is affected by the alliance behavior of members in the closed-loop supply chain and the quality level of remanufactured products. The higher the decision concentration of the closed-loop supply chain is, the more favorable the supply chain is; the higher the remanufacturing quality level is, the more favorable the supply chain is, and the alliance decision of the third-party remanufacturer is affected by the quality level of remanufactured products and the decision-making influence of the third-party remanufacturer in the alliance structure. We find that the improvement of the concentration degree of closed-loop supply chain decision can benefit the supply chain by improving the remanufacturing quality level, which has direct effect on the alliance decision of the third-party remanufacturer. In most cases, the choice of the alliance is the dominant decision of the third-party remanufacturer.

Among the carbon regulation policy schemes, the cap-and-trade has received more attention because of its efficiency and flexibility. Two primary challenges with the cap-and-trade scheme are determining the correct cap and carbon trading price in the carbon market. This paper presents a bi-level model to investigate these two challenges in the cap-and-trade scheme formed between multiple supply chains and the government. At the first level, the government minimizes the cap in such a way that the costs of the supply chains do not rise too much. At the second level, the supply chains minimize their costs according to their cap and trade the dedicated allowances. An exact and a heuristic method are developed to solve the bi-level model. The computational results on a set of randomly generated instances show the effectiveness of the presented heuristic. Sensitivity analysis demonstrates that the government should choose proper amounts of caps to balance costs and environmental benefits.

This paper explores the strategic motivation for a platform to open its superior logistics service to a third-party seller with an endogenous service level. We consider a Stackelberg game between the platform and the seller who sells products to consumers who perceive the platform’s product as having a higher value than the seller’s product. We characterize the equilibrium results in two schemes regarding opening or not opening the service and present conditions for the platform to open the service and the seller to accept the service. In equilibrium, the platform’s logistics service remains at the same level before and after opening. Particularly, we demonstrate that the motivation for the platform to open the service is not simply collecting extra revenue from the service but can be understood from mitigating price competition and securing its demand and price. We find that the platform is always willing to open the logistics system because it provides the platform an additional tool to manipulate the seller’s pricing behavior and therefore improves its own profit. With a high commission rate, the platform is even willing to subsidize the seller for using the logistics service. A Pareto improvement can be realized for two firms when consumers are highly sensitive to the service level. Consumers are worse off after service opening in most cases. Our analysis offers insights into the incentives of one retailer providing high-quality service for its rival when retailers differentiate in price and service.

In this paper, we examine the retailer’s information sharing decision in an authentic supply chain with a single supplier and a single retailer under different counterfeiter encroachment situations. We propose a Stackelberg game model to analyze the optimal wholesale price of the supplier, the optimal order quantity of the retailer and the optimal production quantity of the counterfeiter. We obtain the information sharing strategies of the retailer and analyze the impact of the counterfeiter on the authentic supply chain. It is revealed that: (1) under certain conditions, the retailer will voluntarily share information with the upstream supplier and (2) the existence of the counterfeiter may increase the profit of the authentic supply chain.

The reliability of power distribution network is important. For high reliability, it is necessary for some nodes to have backup connections to other feeders in the network. The substation operator wants to expand the network such that some nodes have k redundant connection lines (i.e., k redundancy) in case the current feeder line does not work. The corporation is given this task to design the expansion planning to construct new connection lines. The substation operator will choose the minimum charged k redundant connection lines based on both of the existing network and the expansion network, which is designed by the corporation. The existing network has the cost for the redundant connection due to the operational expense. The corporation proposes the design with its own price, which may include the operational expense and the construction expense. Thus, for the corporation, how to assign the low price on the connection lines while maximizing the revenue becomes a Stackelberg minimum weight k-star game for the power distribution network expansion.

A heuristic algorithm is proposed to solve this Stackelberg minimum weight k-star game for the power distribution network expansion, using three heuristic rules for price setting in a scenario by scenario fashion. The experimental results show that the proposed algorithm always outperforms the greedy algorithm which is natural to k-star game in terms of corporation revenue. Compared to the greedy algorithm, the proposed algorithm improves up to 60.7% in the corporation revenue in the chosen minimum weight k-star, which is the minimum charged k connection lines. The average improvement is 7.5%. This effectively handles k redundancy in the power distribution network expansion while maximizing the corporation revenue.

In cognitive radio ad hoc networks, the opportunistic access of vacant wireless channel opens a new frontier for efficient spectrum utilization as in many situations, a wide range of spectrum is not even partially utilized by the license owners (primary users, PUs). While the idea seems to be lucrative for spectrum hungry users without licenses, a natural competition between potential stake holders arises, which needs to be regulated in order to efficiently utilize available resources and avoid chaos. With the introduction of unlicensed users in licensed bands, the operations and interests of PUs need to be protected, hence the spectrum owners are given an advantage and control over the multiple access policy (a leader-follower scenario). In this work, we address the problems in spectrum access and channel selection equilibrium in a leader (PU)-follower (secondary user, SU) setup. In contrast to previous game formulations that lack efficient power and pricing schemes, we present a cooperative Stackelberg potential game for cognitive players. A dynamic cost function is articulated to induce awareness in players to mitigate the effects of selfish choices in spectrum access while at the same time steer the distributed network towards achieving Nash equilibrium. The proposed scheme is mutually beneficial for all players and focuses on improving the network performance and power efficiency. We design the network potential function such that the nodes have performance based incentives to cooperate and achieve a Nash equilibrium solution for efficient channel acquisition and capacity. Simulation results show fast convergence in channel selection strategies and increase in capacity for the entire network.

The traditional centralized logistics resources allocation method can no longer adapt to the new business model of decentralized e-commerce, requiring transaction security for all parties involved in the logistics process. Utilizing blockchain and smart contract technologies to build logistics resources allocation network foundation and edge computing technology to assist the resource-constrained transport nodes in implementing complex computation, this paper proposes a distributed logistics resources allocation chain (DLRAChain) concept and designs a DLRAChain network that supports independent decision-making, fair bidding, and secure allocation of interests for all resources allocation participants. The corresponding system models are constructed according to the different roles of DLRAChain participants. Furthermore, the logistics resources requester–provider negotiation process is formulated as a two-stage Stackelberg game. To resolve the optimization problem of the game, the iterative game algorithm (IGA) and distributed logistics resources allocation algorithm (DLRAA) are proposed. Finally, the utility of warehouse and transport nodes and reward of mobile edge computing (MEC) nodes are analyzed with experimental simulation results. The results demonstrate that the proposed models adequately address the DLRA problem, and that the proposed game and corresponding algorithms efficiently achieve the optimal strategy, saving the response time of resources allocation participants.

In this paper, we consider a closed-loop supply chain (CLSC) consisting of two suppliers, one manufacturer, one risk-averse retailer and one fair-caring third-party in the presence of supply disruption. We focus on establishing a dynamic Stackelberg game model with bounded rational expectation and analyzing the game evolution process. The effects of key parameters on the Nash equilibrium solutions and their stability are investigated, as well as the complex dynamical behaviors of the CLSC system are explored by using the stability region, bifurcation graph, the largest Lyapunov exponent (LLE), strange attractors, etc. Moreover, the performance of channel members under different values of parameters is researched by utilizing the (average) expected profits or utilities index. The analysis results reveal that the excessive fast adjustment speed of the manufacturer will lead to the system losing stability and falling into chaos. Also, the retailer’s risk aversion and the third party’s fairness concerns have a destabilization effect on the Nash equilibrium point, while the possibility of supply disruption has different effects on the scope of the adjustment speed of decision variables of the manufacturer. Furthermore, in most cases, an over the top adjustment speed of the manufacturer is disadvantageous to all the channel members for more expected profits, but the third-party can achieve a better performance when the system is in periodic state. Finally, the time-delay feedback control method is proposed to eliminate the system chaos.

Aiming to clarify the leading roles of new-type agricultural business entities (abbreviated as NABEs) to small-scale farmers, integrated game models between NABEs and small-scale farmers are designed to verify the impact of scale economy and investment spillover on the equilibrium points of the game system. The influence of the investment spillover rate and the decision-making adjustment speed on the stability of the system are emphatically discussed. Numerical simulation shows that, with the increase of small-scale farmers’ decision-making adjustment speed, the system would successively show the phenomena of stability, period doubling bifurcation, chaos and discreteness. In the Cournot game, the two sides’ decision-making results such as investment intensity, selling price and eventual profits vary in the opposite direction. In the Stackelberg game of the basic mode, the two sides’ decision-making results are not evidently changed, and NABEs’ investment intensity, selling price and eventual profits are higher than those of small-scale farmers. In the order mode, system improvement can be realized by controlling the investment spillover rate. The research results indicate that with the increase of the adjustment speed of small-scale farmers’ decision-making, the repeated game decision-making aggravates the instability of the Cournot game system. This paper finds that the order pattern can make up for the scale weakness of small-scale farmers, and finally achieve a win-win situation for decision makers in the case of uncertain demands.

In this paper, we study a dual-channel closed-loop supply chain (CLSC) consisting of one manufacturer, one retailer and one third-party firm or platform (3P). The manufacturer wholesales new products through the traditional retail channel and distributes remanufactured products via 3P. We focus on establishing the dynamic Stackelberg game models for nondelayed and delayed cases, respectively. The existence and local stability of Nash equilibrium are examined as well as the complex dynamical behaviors of each model under various scenarios are investigated by numerical simulations, such as stability region, bifurcations, chaos, strange attractors, and so on. Moreover, the impacts of some key parameters on the performance of chain members are analyzed. In addition, the variable feedback control method is utilized to eliminate the system chaos. The results reveal that the high value of the consumer discount perception for remanufactured products and excessively fast price adjustment speed have a destabilization effect on the Nash equilibrium point. In addition, adopting delay decisions by manufacturer does not always make the system more stable because it can exert either positive or negative effect on the system’s stability, while an intermediate delay weight is conducive to the system have a higher chance to stay stable. Furthermore, the manufacturer’s profits will be declined significantly while the profits of retailer and 3P will be elevated to some extent when the system falls into periodic and chaotic motions, so chaos is not always necessarily detrimental to all the decision makers in the dual-channel CLSC.

This paper constructs an e-commerce supply chain (ECSC) that includes one e-commerce platform and one low-carbon manufacturer. Based on bounded rationality, the complexity of pricing, service level, and emission reduction effort decisions in an ECSC is investigated in two scenarios: horizontal Nash (HN) game and long-term platform Stackelberg (LPS) game. Finally, the effects of different adjustment speeds and critical parameters on decision variables, profits, and system stability are analyzed through various numerical simulations. The study revealed that the price adjustment parameters have a more noticeable impact on the stability and profit of ECSC in both scenarios. It is interesting that the chaos caused by the adjustment speed of the platform’s decisions leads to a decrease in the platform’s profits. However, it causes continuous fluctuations in low-carbon manufacturers’ profits. In the HN game, when the increase of critical parameters is beneficial to low-carbon manufacturers, the system’s stability will decrease. In addition, the system’s stability in the LPS game is only affected by the adjustment speed of the platform’s decisions. By comparison, we find that the adjustment of the platform’s price plays a vital role in the ECSC under different power structures. Finally, the adaptive adjustment mechanism is used to control the chaos caused by the price of the platform in the ECSC system.

This paper considers a dual-channel closed-loop supply chain (CLSC) consisting of a manufacturer who wholesales new products through the traditional retail channel and distributes remanufactured products via a direct (online) channel established by himself. Two dynamical Stackelberg game models are developed based on the assumption that the retailer is an adaptive player, and the manufacturer is a bounded rational player who may adopt a delay decision. The existence and locally asymptotic stability of the Nash equilibrium are examined. Moreover, the impacts of key parameters on the complexity characteristics of the models and the performance of chain members are studied by numerical simulation. The results reveal that the excessively fast price adjustment speeds of the manufacturer, the larger consumers’ discount perception for the remanufactured products, and the consumers’ preference for the direct channel have a strong destabilizing effect on the Nash equilibrium’s stability. Furthermore, the delay decision implemented by the manufacturer could be a stabilizing or destabilizing factor for the system. The manufacturer will tolerate a considerable profit reduction while the retailer gains more profits when the dual-channel CLSC system enters periodic cycles and chaotic motions.

As most of the supply chains in practice are decentralized, a key issue in supply chain management is to study the coordination of supply chain. The interactions among players are typically of two types, viz. vertical competition and horizontal competition. We use a game theoretic framework to analyze a two-stage supply chain. The supply chain is modeled as a Stackelberg game with a manufacturer as leader and multiple retailers as followers. We consider multiple retailers competing on quantities (Cournot competition) and study its impact on manufacturer's equilibrium decisions and profits. We show that the wholesale price contract does not achieve Nash equilibrium when retailers offer uniform pricing. On the other hand, in case of perfect price discrimination we prove the existence of unique Nash equilibrium in both deterministic and stochastic demand set-up. Under stochastic demand set-up, we consider information asymmetry between the manufacturer and retailers with respect to demand signal. Furthermore, we show the retailers' selling effort boost up the sales. As variance of sales can hurt the manufacturer's production decisions badly, we conjecture that the manufacturer can offer a retailer incentive contract which can manipulate retailers' equilibrium decision.

In this paper, we have developed a new method to solve bi-level quadratic linear fractional programming (BLQLFP) problems in which the upper-level objective function is quadratic and the lower-level objective function is linear fractional. In this method a BLQLFP problem is transformed into an equivalent single-level quadratic programming (QP) problem with linear constraints by forcing the duality gap of the lower-level problem to zero. Then by obtaining all vertices of the constraint region of the dual of the lower-level problem, which is a convex polyhedron, the single-level QP problem is converted into a series of finite number of QP problems with linear constraints which can be solved by any standard method for solving a QP. The best among the optimal solutions gives the desired optimal solution for the original bi-level programming (BLP) problem. Theoretical results have been illustrated with the help of a numerical example.

In this study we provide a more robust transboundary industrial pollution reduction strategy for global emission collaborations. We consider the dynamics of each country’s quantity of pollution as a Brownian motion with Jumps to capture the systematic jumps caused by surprise effects arising from policy uncertainties within the economy. When the output of each country’s domestic consumption good production is proportional to the level of pollution emissions, we apply optimal control theory to find the Nash noncooperative, cooperative and Stackelberg optimal emission paths. To formulate this problem we allow each country’s discounted stream of net revenues to be maximized via a Stochastic Differential Game (SDG). We then articulate the Nash noncooperative equilibria, cooperative equilibria and Stackelberg equilibria via a feedback control strategy. We show that the outcome of the game depends on the parameters of the game and the type of equilibrium one considers. Furthermore, in this continuous-time differential game paradigm model we show that the feedback Stackelberg equilibrium will not coincide with the feedback Nash noncooperative equilibrium. In this setting, if the first mover advantage of the leader (Player I) disappears then both equilibria coincide.