Non-cooperative Supply Chain Research Articles

Complex effects of cooperative behavior on authorized remanufacturing supply chain decisions under subsidies.

In this study, the dynamic effects of new product supply chain cooperation behavior on optimal government subsidies and supply chain decision-making are studied by establishing a nonlinear discrete inventory decision system; In this system, the government subsidizes authorized remanufacturers to promote remanufacturing, and cooperative behavior exists in the supply chain of new products. The research method is modeling and simulation of a supply chain system based on nonlinear system dynamics theory. The complexity analysis includes the stability analysis of the decision system, the path of the system into chaos, the change of entropy of the system and the performance in chaos system. Our findings indicate that the optimal government subsidy in the cooperative model is lower than that in the non-cooperative model. Consumer surplus is the main reason for the subsidy difference between the two models. In comparison with the cooperative supply chain, the stability of the non-cooperative supply chain is more easily affected by government subsidies. Further, the market is more likely to enter chaos due to improper adjustment of the new products' inventory with cooperative behavior in the supply chain of new products. When the system enters chaos, the new product supply chain's profit in the cooperative system is more likely to be far lower than the equilibrium profit. This study provides a theoretical reference for supply chain inventory management and government subsidy remanufacturer decision-making from the perspective of dynamic systems science.

Examining B2B channel decision-making within differential quality-level zone: a supply chain design using a non-cooperative strategic game theoretic approach (“Stackelberg Supply Chain for B2B”)

Purpose The consumers want to purchase the target products in the right place, whereas the manufacturers want to allocate their possible products to optimal distribution channels. The manufacturer must know how to handle itself in this business. The study aims to examine the B2B channel decision-making with different product qualities in a non-cooperative supply chain. Design/methodology/approach The authors develop a B2B Manufacturer-Stackelberg game as an analytical framework, combining asymmetric preference of purchase channels choice by the consumers, a continuous quality setting of the manufacturer and differential channel structure to study the manufacturer’s product strategy and channel optimisation. By horizontal comparisons across four channel structures, product variety can be classified into the differential quality-level zone through exogenous quality intervention, and the preference of manufacturers in each quality-level zone within the structures can be ranked. Findings Theoretically and practically, the hybrid-channel structure should be completely neglected when the direct channel dominates the retail channel. In contrast, dual-channel structures dominate single channels irrespective of the channel power, and channel preferences between high-quality and low-quality zones are stable, whereas the preference in medium-quality zone is unstable. In addition, the supply chain system cannot achieve global Pareto improvement without any additional coordination mechanism between the manufacturer and the retailer. Originality/value The extended results by numerical examples suggest that the bigger the area of the medium-quality zone, the more significant the product variety of the manufacturer.

A modified economic order quantity of vendor – buyer non-cooperative supply chain model for imperfect quantity and inspection error using the nash equilibrium concept

In this paper, the Economic Order Quantity (EOQ) of two-level supply-chain systems has been analyzed using the Nash Equilibrium concept. In this paper, a two-echelon supply chain consisting of a single vendor and a single buyer that both under the non-cooperative strategy. A mathematical analysis method, which according to appropriate literature, data and recent research result, is used to determine the mathematical formula of expected individual total cost both vendor and buyer, expected total cost of inventory system and also EOQ of decision variables. The non-cooperative strategy is used by the vendor and buyer to gain their optimal revenue. Thereby, game theoretical solution which is Nash equilibrium concept is used to determine the economic order quantity of this system. In this study, several assumptions are considered like the existence of the imperfect quality product in the manufacturing process and inspection error (Type I and Type II) in buyer’s place. To the best of authors’knowledge, this is the first paper that deals with a game theoretical solution, which is especially Nash equilibrium, in probabilistic supply chain under the imperfect condition and inspection error

A dynamic analysis of the investment in product innovation in a supply chain under reference price effect: competition vs cooperation

ABSTRACT This paper aims to investigate the effects of vertical competition or cooperation along a supply chain on product innovation under the reference effect. To this end, we develop game-theoretical models on the cooperative and non-cooperative supply chains and analyse the optimal decisions of the upstream manufacturer and the downstream retailer. Then, the innovation investment levels under vertical competition and under vertical cooperation are compared. We find that whether the innovation investment is higher under vertical competition depends critically on the strength of the reference effect. In particular, although a stronger reference effect lowers the product innovation investment in a cooperative supply chain, it may instead increase the investment in a non-cooperative supply chain if the retailer shares just a small proportion of the sales revenue with the manufacturer. As a result, the product innovation investment can be higher under vertical competition than under vertical cooperation in the presence of reference price effect, and even more so when the reference price effect grows stronger, the product innovation investment becomes more costly, and the demand for the product becomes more sensitive to price but less sensitive to quality.

A stochastic game theoretic framework for decentralized optimization of multi-stakeholder supply chains under uncertainty

This paper investigates the influences of uncertainty in multi-stakeholder non-cooperative supply chains, and the corresponding optimal strategies based on game theory to hedge against uncertainty in design and operations of such decentralized supply chains. We propose a novel game-theory-based stochastic model that integrates two-stage stochastic programming with a single-leader-multiple-follower Stackelberg game scheme for optimizing decentralized supply chains under uncertainty. Both the leader's and the followers’ uncertainties are considered, which directly affect their design and operational decisions regarding infrastructure development, contracts selection, price setting, production profile, transportation planning, and inventory management. The resulting model is formulated as a two-stage stochastic mixed-integer bilevel nonlinear program, which can be further reformulated into a tractable single-level stochastic mixed-integer linear program by applying KKT conditions and Glover's linearization method. An illustrative example of flight booking under uncertain flight delays and a large-scale application to shale gas supply chains are presented to demonstrate the applicability of the proposed framework.

Single versus dual-channel: A strategic analysis in perspective of retailer's profitability under three-level dual-channel supply chain

Abstract This paper explores characteristics of three different channel structures of three-echelon supply chain, namely a traditional retail channel; a manufacturer's dual-channel and a retailer's dual-channel. In the dual-channel setting, a manufacturer operates retail channel through a distributor and a retailer while either the manufacturer or the retailer operates the direct e-channel. Mathematical models for both non-cooperative and cooperative decisions are developed. Optimal pricing policies of all the proposed models are analyzed with theory. It has been showed that in three echelon supply chain, introduction of dual channel is not always profitable for the channel members compared to single retail channel. Optimal price of the product is always greater in single retail channel compared to retail prices in both the dual channels. To eliminate channel conflicts of non-cooperative supply chain, a two-way price discount mechanism is used to coordinate both the dual channels. It is analytically found that the retailer has opportunity to gain more profits in own dual-channel and in non-cooperative single retail channel instead of manufacturer dual channel. The distributor also prefers the retailer's dual-channel compared to the manufacturer's dual-channel. All analytical results are illustrated numerically.

Economic and Environmental Life Cycle Optimization of Noncooperative Supply Chains and Product Systems: Modeling Framework, Mixed-Integer Bilevel Fractional Programming Algorithm, and Shale Gas Application

In this work, we propose a general modeling framework for the economic and environmental life cycle optimization of supply chains and product systems with noncooperative stakeholders. This framework is based on the functional-unit-based life cycle optimization approach and the leader–follower Stackelberg game structure to capture the decentralized feature and noncooperative relationships between multiple stakeholders across the product life cycle. The leader enjoys the priority of decision-making to optimize both its own economic performance and the life cycle environmental performance of the supply chain or product system. After the observation of leader’s decisions, the follower takes actions correspondingly to optimize its own economic performance. The resulting problem is formulated as a mixed-integer bilevel fractional program to account for conflicting objectives and interactions among different stakeholders. Design and operational decisions for both leader and follower are taken into consideration,...

Modeling logistics service providers in a non-cooperative supply chain

This paper presents a mathematical model for the design of a non-cooperative supply chain where transportation activities are provided by logistics companies. We consider a four-layer network comprised of manufacturers, retailers, customers, and logistics service providers (LSPs). In this problem, manufacturers, retailers, and LSPs do not collaborate or engage in any type of bargaining strategy among one other. Instead, they compete to supply products to customers at demand markets, while each agent seeks to maximize his own profit. LSPs compete among themselves to provide logistics (transportation/warehousing) services to manufacturers. It is considered that manufacturers, LSPs, and retailers collaborate to maximize services. Normally this problem cannot be modeled as an optimization problem, so we use a variational inequality approach to formulate it. To the best of our knowledge, this important problem, which helps evaluate options and make decisions when logistics activities are provided by LSPs, has not been modeled in the literature and this constitutes our main contribution. The model determines the optimal level of production for each manufacturer, the flow of products between manufacturers and retailers, the flow of products to be handled by each logistics service provider and the flow of products between retailers and demand markets in a non-cooperative environment. Numerous experiments are presented and adapted from test examples that are available in the literature, while results and important findings are discussed.

Game-theoretic modeling and optimization of multi-echelon supply chain design and operation under Stackelberg game and market equilibrium

We propose a bilevel mixed-integer nonlinear programming (MINLP) model for the optimal design and planning of non-cooperative supply chains from the manufacturer's perspective. Interactions among the supply chain participants are captured through a single-leader–multiple-follower Stackelberg game under the generalized Nash equilibrium assumption. Given a three-echelon superstructure, the lead manufacturer in the middle echelon first optimizes its design and operational decisions, including facility location, sizing, and technology selection, material input/output and price setting. The following suppliers and customers in the upstream and downstream then optimize their transactions with the manufacturer to maximize their individual profits. By replacing the lower level linear programs with their KKT conditions, we transform the bilevel MINLP into a single-level nonconvex MINLP, which is further globally optimized using an improved branch-and-refine algorithm. We also present two case studies, including a county-level biofuel supply chain in Illinois, to illustrate the application of the proposed modeling and solution methods.

Research on Pareto Improvement of Two-Stage Supply Chain Based on Return and Penalty Policy

This paper does research on order quantity and profits of members in cooperative and non-cooperative supply chains. First, the supply and demand model of members of non-cooperative supply chains is established, and optimization research on order quantity and price variables in this model has been carried out. Then the cooperation model in returnable cooperative supply chain is built by introducing return and penalty variables, and optimization strategy has been provided. Finally the analog simulation of both models is conducted. It turns out that larger order quantity and better maximum total profits can be achieved in cooperative supply chains compared with that in non-cooperative ones when prices are same. Cooperative model can accomplish Pareto improvement.

Competitive pricing decisions in a two-echelon supply chain with horizontal and vertical competition

Abstract This study investigates the pricing decisions in a non-cooperative supply chain that consists of two retailers and one common supplier. The retailers order from the common supplier and compete in the same market. We analyze six power structures that characterize exclusively horizontal competition between the retailers and vertical competition between the supplier and the retailers, leading to different sequences of moves among the chain members. We derive the analytical forms of the equilibrium quantities under each power structure and explore the effect of retail substitutability on the equilibrium quantities among all power structures. We further investigate the performances of the game models as compared with the integrated model.

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Managing a Noncooperative Supply Chain with Limited Capacity

We consider a two-stage serial supply chain with capacity limits, where each installation is operated by managers attempting to minimize their own costs. A multiple-period model is necessitated by the multiple stages, capacity limits, stochastic demand, and the explicit consideration of inventories. With appropriate salvage value functions, a Markov equilibrium policy is found. Intuitive profit dominance allows for existence of a unique equilibrium solution, which is shown to be a modified echelon base-stock policy. This equilibrium policy structure is sustained in the infinite horizon. A numerical study compares the behavior of the decentralized system with the first-best integrated capacitated system. The performance of this decentralized system relative to the integrated system across other parameters can be very good over a broad range of values. This implies that an acceptable system performance may be attained without the imposition of a contract or other coordinating mechanism, which themselves may encounter difficulties in implementation in the form of negotiation, execution, or enforcement of these agreements. We find instances where tighter capacities may actually enhance channel efficiency. We also examine the effect of capacity utilization on the system suboptimality.

An optimal dicisional model in two-echelon supply chain

This paper studies inventory and pricing policies in a non-cooperative supply chain with one supplier and several retailers who are involved in producing, delivering and selling a single product. We consider inventory policies in an information-asymmetric vendor managed inventory. The study brings up a scenario where a supplier produces the product at thewholesale price to multiple retailers. The retailers also distribute the product in dispersed and independent markets at retail selling prices. The demand rate for each market is a non-decreasing concave function of the marketing expenditures of both local retailers and the manufacturer, but a non-increasing and convex function of the retail selling prices. The primary purpose is to determine wholesale price, marketing expenditure for supplier and retailers, replenishment cycles for the product, and backorder quantity to maximize the total profit for both groups of supplier and retailers. The scenario is modeled as a Stackelberg game where the manufacturer is the leader and the retailers are the followers.

An Analysis of the Co-operative Supply Chain's EPQ Model under Trade Credit

An EPQ model for the co-operative supply chain under the conditions of permissible delay in payments is developed in this work, in order to compare the co-operative supply chain with noncooperative supply chain; we also propose another EPQ model for the non-cooperative supply chain under the same conditions. In addition, we provide an efficient algorithm to obtain the optimal solution, and the results of numerical examples indicate that the cooperative supply chain will contribute to improving its EPQ and profit