Supply chain networks with global outsourcing and quick-response production under demand and cost uncertainty

This paper develops a modeling and computational framework for supply chain networks with global outsourcing and quick-response production under demand and cost uncertainty. Our model considers multiple off-shore suppliers, multiple manufacturers, and multiple demand markets. Using variational inequality theory, we formulate the governing equilibrium conditions of the competing decision-makers (the manufacturers) who are faced with two-stage stochastic programming problems but who also have to cooperate with the other decision-makers (the off-shore suppliers). Our theoretical and analytical results shed light on the value of outsourcing from novel real option perspectives. Moreover, our simulation studies reveal important managerial insights regarding how demand and cost uncertainty affects the profits, the risks, as well as the global outsourcing and quick-production decisions of supply chain firms under competition.     

Modeling and analysis of the multiperiod effects of social relationship on supply chain networks

In this paper, we analyze the effects of levels of social relationship on a multiperiod supply chain network with multiple decision-makers (suppliers, manufacturers, and retailers) associated at different tiers. The model incorporates the individual attitudes towards disruption and opportunism risks and allows us to investigate the interplay of the heterogeneous decision-makers and to compute the resultant network equilibrium pattern of production, transactions, prices, and levels of social relationship over the multiperiod planning horizon. In our analysis, we focus on the following questions: (1) how do the evolving relationships affect the profitability and risks of supply chain firms as well as the prices and demands of the product in the market? (2) how do the relationships with the upstream supply chain firms affect the relationships with the downstream firms, and how these relationships influence the profitability and risks of the supply chain firms? (3) how do the supply disruption risks interact with the opportunism risks through supply chain relationships, and how these risks influence the profitability of the firms? The results show that high levels of relationship can lead to lower supply chain overall cost, lower risk, lower prices, higher product transaction and therefore higher profit.     

Supply chain networks,wages, and labor productivity: insights from Lagrange. analysis and computations

The COVID-19 pandemic has dramatically demonstrated the importance of labor to supply chain network activities from production to distribution with shortfalls in labor availability, for numerous reasons, resulting in product shortages and the reduction of profits of firms. Even as progress has been made through vaccinations, issues associated with labor are still arising. Increasing wages is a strategy to enhance labor productivity and, also to ameliorate, in part, labor shortages, but has not, until this work, been explored in a full supply chain network context. Specifically, in this paper, a game theory supply chain network model is constructed of firms competing in producing a substitutable, but differentiated, product, and seeking to determine their equilibrium product path flows, as well as hourly wages to pay their workers, under fixed labor amounts associated with links, and wage-responsive productivity factors. The theoretical and computational approach utilizes the theory of variational inequalities. We first introduce a model without wage bounds on links and then extend it to include wage bounds. Lagrange analysis is conducted for the latter model, which yields interesting insights, as well as an alternative variational inequality formulation. A series of numerical examples reveals that firms can gain in terms of profits by being willing to pay higher wages, resulting in benefits also for their workers, as well as consumers, who enjoy lower demand market prices for the products. However, sensitivity analysis should be conducted to determine the range of such wage bounds. Ultimately, we observed, that the profits may decrease and then stabilize. This work adds to the literature on the integration of concepts from economics and operations research for supply chain networks and also has policy implications.

     

Bullwhip effect in a supply chain model with multiple delivery delays

We develop a model of differential equations for a supply chain with delivery time delays between every adjacent firms. Based on the supply chain model, we provide a new perspective of the bullwhip effect and show that the bullwhip effect is intrinsic in supply chains in the sense that the equilibrium state of each firm in the supply chain is a cumulative forward product of the ratios of order fulfillment and placement between adjacent firms toward the end customer demand. We also show that it is the multiple time delays instead of the constant end consumer demand that determine the stability of the equilibrium states. However, the consumer demand has impacts on the stability of the equilibrium states of the supply chain when the end retailer’s inventory decisions are linearly related to the end consumer demand.     

The effect of supplier capacity on the supply chain profit

In this paper, we study the role of capacity on the efficiency of a two-tier supply chain with two suppliers (leaders, first tier) and one retailer (follower, second tier). The suppliers compete via pricing (Bertrand competition) and, as one would expect in practice, are faced with production capacity. We consider a model with differentiated substitutable products where the suppliers are symmetric differing only by their production capacity. We characterize the prices, production amounts and profits in three cases: (1) the suppliers compete in a decentralized Nash equilibrium game, (2) the suppliers “cooperate” to optimize the total suppliers’ profit, and (3) the two tiers of the supply chain are centrally coordinated. We show that in a decentralized setting, the supplier with a lower capacity may benefit from restricting her capacity even when additional capacity is available at no cost. We also show that the loss of total profit due to decentralization cannot exceed 25 % of the centralized chain profits. Nevertheless, the loss of total profit is not a monotonic function of the “degree of asymmetry” of the suppliers’ capacities. Furthermore, we provide an upper bound on the supplier profit loss at equilibrium (compared with the cooperation setting) that depends on the “market power” of the suppliers as well as their market size. We show that there is less supplier profit loss as the asymmetry (in terms of their capacities) increases between the two suppliers. The worst case arises when the two suppliers are completely symmetric.     

A supply chain network economic model with time-based competition

This paper presents an integrated model for time-cost competition between supply chains with heterogeneous customers. The firms in our model can offer various time options for their production/service to time-sensitive customers. This gives rise of a new concept of time-based supply chain, which we call T-chain, to be the basic element in the competition and extends the inter supply chain competition to a new dimension of time. Assuming the customers are heterogeneous in time-cost bi-criteria decision making, we integrate the discrete choice theory into supply chain network competition and formulate the equilibrium conditions as a multinomial logit based variational inequality problem. Numerical examples are presented for model illustration and managerial insights such as profit maximization for a firm who participates in this supply chain network.     

An analysis of the structural complexity of supply chain networks

Each enterprise in a supply chain network needs quantitative indicators to analyze and manage its interactions with different business partners in the network. Supply chains exhibit the characteristics of complex systems. In a supply chain network, a large number of firms cooperate simultaneously with many suppliers and customers, and interact through a variety of information and material flows to achieve a balance between supply and demand. However, the complexity of a supply chain is not a simple linear structure where a small change often results in a chain reaction. When supply chain complexity increases, monitoring and managing the interaction between different elements of the chain becomes more difficult. An entropy model based on information theory provides an appropriate means of quantifying the complexity of a supply chain system by delivering information required to describe the state of the system. The entropy measure links uncertainty and complexity so that, as a system grows in uncertainty, it becomes more complex and more information is required to describe and monitor it. In this paper, we propose an entropy-based measure for analyzing the structural complexity in relation to the structure and system uncertainty. The method provides guidelines for estimating the complexity throughout the supply chain structure.     

Supply chain network equilibrium with strategic financial hedging using futures

In this paper, we develop a network equilibrium model for supply chain networks with strategic financial hedging. We consider multiple competing firms that purchase multiple materials and parts to manufacture their products. The supply chain firms’ procurement activities are exposed to commodity price risk and exchange rate risk. The firms can use futures contracts to hedge the risks. Our research studies the equilibrium of the entire network where each firm optimizes its own operation and hedging decisions. We use variational inequality theory to formulate the equilibrium model, and provide qualitative properties. We provide analytical results for a special case with duopolistic competition, and use simulations to study an oligopolistic case. The analytical and simulation studies reveals interesting managerial insights.     

Coordination of cooperative cost-reduction efforts in a supply chain partnership

We study cooperative cost reduction in a decentralized supply chain with a single manufacturer and multiple suppliers. The manufacturer assembles components that are procured from the suppliers to produce a final product. Both the manufacturer and the suppliers invest in reducing the unit production costs of the components. We see that neither of the two well-known conventional contracts, the wholesale price contract and the cost-plus pricing contract, generally coordinates the supply chain, i.e., under both of these types of contract, the individual optimal cost-reduction efforts of players deviate from the centralized system-optimal solution. However, this result is not surprising because these contracts encourage either only the manufacturer or only the suppliers alone to invest in cost reduction.     

Formulation and analysis of horizontal mergers among oligopolistic firms with insights into the merger paradox: a supply chain network perspective

In this paper, we consider oligopolistic firms with supply chain networks who are involved in the production, storage, and distribution of a homogeneous product to demand markets and explore what has become known in the literature as the “merger paradox.” We present the oligopolistic supply chain network equilibrium model associated with the competing firms before the horizontal mergers and also develop the supply chain network optimization model post the complete merger. In addition, we develop the model in which only a subset of the firms in the industry merge. The governing concept of the competing firms is that of Cournot–Nash equilibrium. We utilize finite-dimensional variational inequality theory for the formulation, analysis, and solution of both the pre and the post-merger supply chain network problems. We provide numerical examples for which we compute the total costs, the total revenues, as well as the profits obtained for the firms pre and post the mergers for a variety of distinct oligopoly problems. The generality of the network models and the flexibility of the computational approach, which yields closed form expressions for the product flows at each iteration, allows us to obtain deeper insights into the merger paradox.     

Impact of product pricing and timing of investment decisions on supply chain co-opetition

In supply chain co-opetition, firms simultaneously compete and co-operate in order to maximize their profits. We consider the nature of co-opetition between two firms: The product supplier invests in the technology to improve quality, and the purchasing firm (buyer) invests in selling effort to develop the market for the product before uncertainty in demand is resolved. We consider three different decision making structures and discuss the optimal configuration from each firm’s perspective. In case 1, the supplier invests in product quality and sets the wholesale price for the product. The buyer then exerts selling effort to develop the market and following demand potential realization, sets the resale price. In case 2, the supplier invests in product quality followed by the buyer’s investment in selling effort. Then, after demand potential is observed, the supplier sets the wholesale price and the buyer sets the resale price. Finally, in case 3, both firms simultaneously invest in product quality and selling effort, respectively. Subsequently, observing the demand potential, the supplier sets the wholesale price and the buyer sets the resale price. We compare all configuration options from both the perspective of the supplier and the buyer, and show that the level of investment by the firms depends on the nature of competition between them and the level of uncertainty in demand. Our analysis reveals that although configuration 1 results in the highest profits for the integrated channel, there is no clear dominating preference on system configuration from the perspective of both parties. The incentives of the co-opetition partners and the investment levels are mainly governed by the cost structure and the level of uncertainty in demand. We examine and discuss the relation between system parameters and the incentives in desiging the supply contract structure.     

基于风险管理的动态供应链超网络均衡模型

基于风险管理的动态供应链超网络均衡模型的研究有助于供应链超网络节点厂商在动态环境下优化其风险管理,降低风险损失,提升供应链网络在风险管理下的竞争优势。本文以三层供应链超网络为研究对象,采用风险发生概率和损失函数表达供应链超网络中节点厂商中断风险的特征,构建了基于风险管理的动态供应链超网络均衡模型。模型中包括三种类型的节点,产品生产商、零售商和需求市场,生产商考虑风险损失的情况下,基于动态变化的风险、需求和成本追求个体期望效益最优化。接着,通过进化变分不等式来表达动态供应链超网络风险管理下的均衡解,并采用投影动态系统求解进化变分不等式,通过数值算例验证方法的可靠性和合理性,通过投影动态系统解释某一个厂商趋近均衡解的过程。通过单一厂商趋近均衡解的过程,阐述其他厂商相应的最优决策。     

Supply chain network sustainability under competition and frequencies of activities from production to distribution

In this paper, we develop a competitive supply chain network model with multiple firms, each of which produces a differentiated product by brand and weights the emissions that it generates through its supply chain network activities in an individual way. The supply chain network activities of production, transport and distribution, and storage have associated with them distinct capacities and the firms seek to determine their optimal product flows and frequencies of operation so that their utilities are maximized where the utilities consist of profits and weighted emissions. Multiple production, storage, and transport mode options are allowed. The governing equilibrium concept is that of Cournot–Nash equilibrium. We provide both path and link flow variational inequality formulations of the equilibrium conditions and then propose an algorithm, which, at each iteration, yields closed form expressions for the underlying variables. Numerical examples illustrate the generality of the model and the information provided to managerial decision-makers and policy-makers. This paper adds to the growing literature on sustainable supply chains through the development of a computable general competitive supply chain network game theory model, which brings a greater realism to the evaluation of profit and emission trade-offs through the incorporation of frequencies.     

Distributed supply chain management using ant colony optimization

Successful supply chain management requires a cooperative integration between all the partners in the network. At the operational level, the partners individual behavior should be optimal and therefore their activities have to be planned using sophisticated optimization tools. However, these tools should take into account the planning of the remaining partners, through the exchange of information, in order to allow some kind of cooperation between the elements of the chain. This paper introduces a new supply chain management technique, based on modeling a generic supply chain with suppliers, logistics and distributers, as a distributed optimization problem. The different operational activities are solved by the optimization meta-heuristic called ant colony optimization, which allows the exchange of information between different optimization problems by means of a pheromone matrix. The simulation results show that the new methodology is more efficient than a simple decentralized methodology for different instances of a supply chain.     

Redesigning product lines in a period of economic crisis: a hybrid simulated annealing algorithm with crossover

Bandit products have captured significant market shares in China and have started to expand throughout the world. A striking feature of supply chains for bandit products is decentralization, where the upstream firm determines the product quality and the downstream firms compete on prices. We study the competition between a centralized mainstream firm and a decentralized bandit supply chain. We demonstrate that the structural difference between the mainstream firm and the bandit supply chain reduces competition intensity and the quality difference between their products. Surprisingly, the inherent inefficiency in a bandit supply chain, combined with the force of competition, actually leads to both higher product quality and higher price. Furthermore, due to the free-riding effect, the bandit supply chain may even offer higher quality products than the mainstream firm. The mainstream firm’s profit as a function of the free-riding effect is U-shaped, so that free-riding by the bandit supply chain may eventually benefit the mainstream firm. Finally, decentralization benefits the bandit supply chain when the competition is on product features.     

Pricing and equity in cross-regional green supply chains

This paper addresses the problem of the firms operating on cross-border or inter-regional platforms that are subject to the enforcement of each local government's carbon emissions regulatory policy, thus causing an imbalance in the sharing of the burden of the greening of the total supply chain. We introduce the concept of equity as the incentive mechanism to coordinate this green supply chain which is a function of the carbon emission permits and the revenue generated by the firms. Due to the complexity and imbalance in the original incentive mechanism to this problem, we provide a new equivalent supply chain network equilibrium model under elastic demand based on user equilibrium theory. We state the user equilibrium conditions and provide the equivalent formulation. We show the trade-offs under various carbon emissions regulatory policies. A product with higher price elasticity and carbon emission intensity not only hampers the firm from gaining a higher revenue, but it also reduces the equity of the system under an invariant emission regulatory policy.     

The impact of decision timing on the suppliers’ interactions: simultaneous moves <Emphasis Type="Italic">versus</Emphasis> sequential moves

The last few decades have witnessed a huge growth of outsourcing in industry where the downstream firm assigns its production tasks to different upstream suppliers. This makes the supply chain structure more complicated and gives rise to some relevant operational questions. This paper focuses on a supply chain structure that consists of one assembler and two suppliers, and both suppliers’ production yields are stochastic. The assembler delegates the quantity decisions to the suppliers, and the two suppliers choose their production quantities either simultaneously or sequentially. We compare the suppliers’ equilibrium production strategies under these two scenarios. Our results show that the decision sequence can exert significant influences on the firm’s and channel’s equilibrium payoffs. At any given wholesale price, both suppliers produce more components under sequential moves than under simultaneous moves, and this results in higher payoffs for the suppliers, the assembler and the entire supply chain. The supplier’s profit increases if he can make the decision later under sequential moves. From the channel’s perspective, it is more beneficial for the supplier with a higher production cost to make the decision first. The assembler is able to extract more surplus by endogenously setting the wholesale price. However, this may make the suppliers worse off under sequential moves than under simultaneous moves.     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

A dynamic inventory model with supplier selection in a serial supply chain structure

Considering the inherent connection between supplier selection and inventory management in supply chain networks, this article presents a multi-period inventory lot-sizing model for a single product in a serial supply chain, where raw materials are purchased from multiple suppliers at the first stage and external demand occurs at the last stage. The demand is known and may change from period to period. The stages of this production–distribution serial structure correspond to inventory locations. The first two stages stand for storage areas for raw materials and finished products in a manufacturing facility, and the remaining stages symbolize distribution centers or warehouses that take the product closer to customers. The problem is modeled as a time-expanded transshipment network, which is defined by the nodes and arcs that can be reached by feasible material flows. A mixed integer nonlinear programming model is developed to determine an optimal inventory policy that coordinates the transfer of materials between consecutive stages of the supply chain from period to period while properly placing purchasing orders to selected suppliers and satisfying customer demand on time. The proposed model minimizes the total variable cost, including purchasing, production, inventory, and transportation costs. The model can be linearized for certain types of cost structures. In addition, two continuous and concave approximations of the transportation cost function are provided to simplify the model and reduce its computational time.     

Equilibrium analysis of supply chain structures under power imbalance

This paper investigates the implications of channel power on supply chain stability in a setting where multiple suppliers sell substitutable products through a common retailer. Such supply chains have been traditionally analyzed as one- or two-stage Stackelberg non-cooperative games with all suppliers sharing balanced (equal) decision-making power. In this paper, we relax this assumption and formulate game-theoretic models to examine scenarios where one supplier can act as the Stackelberg leader. Consequently, we analyze new supply chain structures and introduce the notion of structure dominance, a novel approach to analyze the performance of supply chains that has practical implications. Thus, a decision maker can employ the concepts of structure dominance to determine whether there exist supply chain scenarios that are more stable than others, i.e., less prone to power reconfigurations, at both agent and group level. We find that power imbalance causes significant declines in supply chain profits, and the more balanced the agents are the higher their profits when demand is linear, regardless of product competition. It develops that neither the Manufacturer Stackelberg nor the Retailer Stackelberg supply chains are stable structures in our generalized setting, but that structures where power is equally split between agents provide for best stability and performance.