Managing Disruptions in Decentralized Supply Chains with Endogenous Supply Process Reliability

Supply disruptions are all too common in supply chains. To mitigate delivery risk, buyers may either source from multiple suppliers or offer incentives to their preferred supplier to improve its process reliability. These incentives can be either direct (investment subsidy) or indirect (inflated order quantity). In this study, we present a series of models to highlight buyers’ and suppliers’ optimal parameter choices. Our base‐case model has deterministic buyer demand and two possibilities for the supplier yield outcomes: all‐or‐nothing supply or partial disruption. For the all‐or‐nothing model, we show that the buyer prefers to only use the subsidy option, which obviates the need to inflate order quantity. However, in the partial disruption model, both incentives—subsidy and order inflation—may be used at the same time. Although single sourcing provides greater indirect incentive to the selected supplier because that avoids order splitting, we show that the buyer may prefer the diversification strategy under certain circumstances. We also quantify the amount by which the wholesale price needs to be discounted (if at all) to ensure that dual sourcing strategy dominates sole sourcing. Finally, we extend the model to the case of stochastic demand. Structural properties of ordering/subsidy decisions are derived for the all‐or‐nothing model, and in contrast to the deterministic demand case, we establish that the buyer may increase use of subsidy and order quantity at the same time.     

Supplier competition and its impact on firm׳s sourcing strategy

Most research on firms׳ sourcing strategies assumes that wholesale prices and reliability of suppliers are exogenous. It is of our interest to study suppliers׳ competition on both wholesale price and reliability and firms׳ corresponding optimal sourcing strategy under complete information. In particular, we study a problem in which a firm procures a single product from two suppliers, taking into account suppliers׳ price and reliability differences. This motivates the suppliers to compete on these two factors. We investigate the equilibria of this supplier game and the firm׳s corresponding sourcing decisions. Our study shows that suppliers׳ reliability often plays a more important role than wholesale price in supplier competition and that maintaining high reliability and a high wholesale price is the ideal strategy for suppliers if multiple options exist. The conventional wisdom implies that low supply reliability and high demand uncertainty motivate dual-sourcing. We notice that when the suppliers׳ shared market/transportation network is often disrupted and demand uncertainty is high, suppliers׳ competition on both price and reliability may render the sole-sourcing strategy to be optimal in some cases that depend on the format of suppliers׳ cost functions. Moreover, numerical study shows that when the cost or vulnerability (to market disruptions) of one supplier increases, its profit and that of the firm may not necessarily decrease under supplier competition.     

供应中断情况下基于备份供应商的应急决策分析

在供应商-制造商二级供应链中,制造商作为领导者,采用一个战略供应商和一个备份供应商。有两种期权执行模式,一种是需求未知情况下提前向备份供应商订货的推式订货模式,另一种是获知需求后再向备份供应商订货的推式与拉式相结合的订货模式。证明了所建模型均为凸规划,并利用Karush-Kuhn-Tucker条件求得备份供应商的能力预定量、战略供应商订货量以及最优利润的表达式,得出了是否采用备份供应商的临界值。研究结果表明：推式模式下战略供应商的订货量较大,推拉结合模式下备份供应商的能力预定量较大,推拉结合模式下制造商的利润较大;随着战略供应商可靠性系数的增大,推式模式下首先放弃备份供应商的使用;当战略供应商的采购成本、备份供应商的期权执行成本和缺货成本较大,且残值以及可靠性系数较小时,推拉结合模式相对于完全推式的效果更加明显。     

Role of Random Capacity Risk and the Retailer in Decentralized Supply Chains with Competing Suppliers

This research considers a supply chain under the following conditions: (i) two heterogeneous suppliers are in competition, (ii) supply capacity is random and pricing is endogenous, (iii) consumer demand, with and without an intermediate retailer, is price dependent. Specifically, we examine how uncertainty in supply capacity affects optimal ordering and pricing decisions, supplier and retailer profits, and the incentives to reduce such uncertainty. When two suppliers sell through a monopolistic retailer, supply uncertainty not only affects the retailer's diversification strategy for replenishment, but also changes the suppliers’ wholesale price competition and the incentive for reducing capacity uncertainty. In this dual‐sourcing model, we show that the benefit of reducing capacity uncertainty depends on the cost heterogeneity between the suppliers. In addition, we show that a supplier does not necessarily benefit from capacity variability reduction. We contrast this incentive misalignment with findings from the single‐supplier case and a supplier‐duopoly case where both suppliers sell directly to market without the monopolistic retailer. In the latter single‐supplier and duopoly cases, we prove that the unreliable supplier always benefits from reducing capacity variability. These results highlight the role of the retailer's diversification strategy in distorting a supplier's incentive for reducing capacity uncertainty under supplier price competition.     

Managing Supply Disruptions when Sourcing from Reliable and Unreliable Suppliers

We study a manufacturer's optimal multiple‐sourcing strategies when some but not all suppliers face risks of complete supply disruptions. Using an approximate model, we show that the optimal unreliable orders are ranked by a simple and intuitive criterion, and are invariant of minor market size changes. Furthermore, when ordering from one reliable and one unreliable supplier, we show that the total order quantity and its allocation between the two suppliers are independent decisions. We then test and confirm the robustness of the insights without the approximation, as well as when we relax various assumptions.     

供应商产出随机与供应中断下的双源采购决策

研究在需求与供应不确定条件下,一个制造商向两个存在产出随机和供应中断可能性的供应商采购零部件时的最优决策问题。论文分别针对两种情况：（1）只考虑供应商产出随机,（2）同时考虑供应商产出随机与供应中断可能性,建立了两种情况下制造商与两个供应商之间的博弈模型,证明了在两种情况下,制造商均存在最优订货量、供应商存在最优生产量使自身利润最优。研究发现,供应商产出稳定性的改善（即产出随机性降低）不仅可以使自身获得更大的利润,也使制造商获得更大的利润。供应商最优生产量随着自身产出随机性降低先增后减。同时,供应商供应中断可能性的降低会为自身带来更大的收益,也为制造商带来更大的收益。     

存在信息更新时的双源采购和后备生产结合策略研究

在现实的采购运作中,双源采购和后备生产是两种最常见的风险应对策略。本文在考虑信息更新的情况下,探讨了一个两阶段动态采购决策模型：第一阶段,制造商向存在供应风险的一个或两个主供应商订货;第二阶段,制造商根据主供应商风险信息的更新,决定是否向供应可靠但价格较高的后备供应商订货。本文得到了两阶段的最优采购策略,分析发现,当固定采购成本较低时：若潜在市场需求较小,双源采购将排斥后备生产;若潜在市场需求较大,双源采购和后备生产共存;若潜在市场需求适中,后备生产可能排斥双源采购,两者也可能共存。特别地,在潜在市场需求适中时,可靠性改进概率的增大或后备供应商生产成本的降低,将使后备生产趋于排斥双源采购;反之,可靠性改进概率的减小、固定采购成本的降低或后备生产成本的增加,将使两者趋于共存。     

Price and Service Competition in an Outsourced Supply Chain

We consider a buyer who outsources the manufacturing of a product to multiple symmetric make‐to‐stock suppliers who compete on price and service (fill rate). The buyer allocates demand to the suppliers using a score function with an exponential form, which specifies the relative importance of price vs. service, in order to minimize his costs, while the suppliers choose their prices and fill rates to maximize their profits. For the case of dual‐sourcing, we characterize the optimal parameter of the exponential score function, considering the impact of the buyer's decisions on the suppliers, and considering how the suppliers compete against each other to earn a portion of the buyer's demand. We prove the existence of a unique equilibrium and characterize the equilibrium behavior of the system. We then consider a general number of suppliers and show that the equilibrium prices and fill rates, and the buyer's cost, are increasing in the number of suppliers. We compare these results to a model of single‐sourcing, in which the buyer is the Stackelberg leader and extracts all profits from the supplier. We find that the buyer always prefers single‐sourcing to multisourcing. Finally, we study a centralized system and use the results to develop a coordinating contract for the decentralized system.     

Flexible Backup Supply and the Management of Lead‐Time Uncertainty

We consider replenishment decisions for a constant rate demand environment from a supplier with uncertain lead times. We study the potential use of a flexible backup supplier as an emergency response to accurate lead‐time information arriving at (or close after) the beginning of the demand interval and well after an original order with the stochastic lead‐time supplier has been placed. The emergency response decisions involve whether to order and how much from the flexible backup supplier, with the objective of minimizing the cost of meeting demand. We derive the optimal emergency‐response policy and clearly outline its implications on the optimized safety lead time of the original order placement and on the cost of meeting demand. We examine the impact on the use of the flexible backup supplier of factors like the arrival time of accurate lead‐time information and the response lead time of the backup supplier. We further study the potential benefits of the use of the flexible backup supplier in a dual role: as one of the two suppliers in a redundant supply system assigned to originally meet the demand and as an emergency response to later‐arriving lead‐time information. Our numerical studies illustrate the benefits from the use of the flexible backup supplier as an emergency response, but for reasonable purchase premiums and short lead times of flexible backup supply options, their use in a dual (regular and emergency response) role often leads to improved performance over safety lead‐time single and uncertain lead‐time supplier‐replenishment strategies. The benefits of the backup supply options are accentuated the higher the lead‐time uncertainty of the stochastic lead‐time supplier is.     

Supply Diversification with Responsive Pricing

We study sourcing and pricing decisions of a firm with correlated suppliers and a price‐dependent demand. With two suppliers, the insight—cost is the order qualifier while reliability is the order winner—derived in the literature for the case of exogenously determined price and independent suppliers, continues to hold when the suppliers' capacities are correlated. Moreover, a firm orders only from one supplier if the effective purchase cost from him, which includes the imputed cost of his unreliability, is lower than the wholesale price charged by his rival. Otherwise, the firm orders from both. Furthermore, the firm's diversification decision does not depend on the correlation between the two suppliers' random capacities. However, its order quantities do depend on the capacity correlation, and, if the firm's objective function is unimodal, the total order quantity decreases as the capacity correlation increases in the sense of the supermodular order. With more than two suppliers, the insight no longer holds. That is, when ordering from two or more suppliers, one is the lowest‐cost supplier and the others are not selected on the basis of their costs. We conclude the paper by developing a solution algorithm for the firm's optimal diversification problem.     

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.     

Dual Sourcing Under Random Supply Capacities: The Role of the Slow Supplier

Sourcing from multiple suppliers with different characteristics is common in practice for various reasons. This paper studies a dynamic procurement planning problem in which the firm can replenish inventory from a fast and a slow supplier, both with uncertain capacities. The optimal policy is characterized by two reorder points, one for each supplier. Whenever the pre‐order inventory level is below the reorder point, a replenishment order is issued to the corresponding supplier. Interestingly, the reorder point for the slow supplier can be higher than that of the fast even if the former has a higher cost, lower reliability, and smaller capacity than the latter, suggesting the possibility of ordering exclusively from an inferior slow supplier in the short term. Moreover, the firm may allocate a larger portion of the long‐term total order quantity to the slow supplier than to the fast, even if the former does not possess any cost or reliability advantage over the latter. Such phenomena, different from the observations made in previous studies, happen when the demand is uncertain and the supply is limited or unreliable. Our observations highlight the importance of incorporating both demand uncertainty and supplier characteristics (i.e., cost, lead time, capacity and uncertainty) in a unified framework when formulating supplier selection and order allocation strategies.     

考虑随机市场需求的双渠道供应链风险补偿策略研究——从质量与价格竞争视角

在由两个供应商和单个零售商构成的二级双渠道供应链系统中，分析了随机市场需求以及供应商之间同时存在价格与质量竞争的情形下的双渠道供应链协调问题。在供应链集中决策、无风险补偿及有风险补偿三种情境下，构建了基于质量和价格的风险补偿模型并求得纳什均衡解。研究结果表明：存在可行的需求风险补偿策略使得供应链达到协调水平，并且需求风险补偿策略对零售商更加有利；在需求风险补偿策略下，需求风险补偿价格与其对应批发价格正相关，与其产品质量水平负相关；价格竞争程度对零售商订货量具有负向影响作用，对供应链总利润影响作用随着竞争程度增加而减弱，质量竞争程度对零售商订货量和供应商产品质量水平具有正向影响作用，对供应链总利润影响呈倒U型关系；需求风险补偿策略能够激励零售商的订货行为，强化价格竞争程度和质量竞争程度对供应商订货量和供应链总利润的影响；在供应链系统中双渠道营销模式下的供应链总利润要优于单渠道营销模式下的供应链总利润。本文结论不仅详细剖析了风险补偿策略对双渠道供应链协调的影响关系，也理清了价格与质量竞争对各方行为策略的影响机理。     

An integrated supplier selection and inventory problem with multi-sourcing and lateral transshipments

In this research, we consider the supplier selection problem of a firm offering a single product via multiple warehouses. The warehouses face stationary, stochastic demand and replenish their inventory via multiple suppliers, to be determined from a set of candidates, with varying price, capacity, quality, and disruption characteristics. Additionally, the warehouses may simultaneously replenish their inventory from other warehouses proactively. With these characteristics, the problem is a multi-sourcing, supplier selection, and inventory problem with lateral transshipments. Even though the benefits of multi-sourcing and lateral transshipments have been presented in the literature individually to mitigate risks associated with uncertain demand and disrupted supply, the intertwined sourcing and inventory decisions under these settings have not been investigated from a quantitative perspective. We develop a decomposition based heuristic algorithm, powered with simulation. While the decomposition based heuristic determines a solution with supplier selection and inventory decisions, the simulation model evaluates the objective function value corresponding to each generated solution. Experimental results show, contrary to the existing literature, inferior decisions may result when considering the selection of suppliers solely on unit and/or contractual costs. We also evaluate the impact of multi-sourcing with rare but long disruptions compared to frequent but short ones.     

Pricing and ordering decisions in a supply chain with downward substitution and imperfect process yield

We consider a manufacturer sourcing from two suppliers of asymmetric component quality and producing a quality-differentiated product, namely a low- and high-quality version, with each having deterministic demand. The manufacturer adopts the existing process to produce low-quality products with components from the supplier with low component quality, and develops a new process to produce high-quality products with components from the supplier with high component quality. The new process has imperfect yield, and products that do not meet the specifications for high-quality products can substitute for low-quality products produced with the existing process. We investigate the suppliers’ price decisions and the manufacturer’s ordering and production decisions in a game-theoretical model under dual sourcing. Our analyses reveal that increasing product differentiation or higher yield of high-quality products do not necessarily translate to a higher profit for the manufacturer. In light of the manufacturer’s sourcing strategies, we show that sourcing from a single supplier with high- and low-quality components yields a lower profit than sourcing from one supplier with high component quality and the other with low component quality. Finally, we investigate the manufacturer’s decision-making with endogenous yield rate of high-quality products. Our analyses demonstrate that the manufacturer benefits from setting the yield rate of high-quality products ahead of the suppliers’ price decisions.     

Optimal Inventory Control with Dual‐Sourcing,Heterogeneous Ordering Costs and Order Size Constraints

We consider a dual‐sourcing inventory system, where procuring from one supplier involves a high variable cost but negligible fixed cost whereas procuring from the other supplier involves a low variable cost but high fixed cost, as well as an order size constraint. We show that the problem can be reduced to an equivalent single‐sourcing problem. However, the corresponding ordering cost is neither concave nor convex. Using the notion of quasi‐convexity, we partially characterize the structure of the optimal policy and show that it can be specified by multiple thresholds which determine when to order from each supplier and how much. In contrast to previous research, which does not consider order size constraints, we show that it is optimal to simultaneously source from both suppliers when the beginning inventory level is sufficiently low. We also show that the decision to source from the low‐cost supplier is not monotonic in the inventory level. Our results require that the variable costs satisfy a certain condition which guarantees quasi‐convexity. However, extensive numerical results suggest that our policy is almost always optimal when the condition is not satisfied. We also show how the results can be extended to systems with multiple capacitated suppliers.     

Joint supplier selection and scheduling of customer orders under disruption risks: Single vs. dual sourcing

This paper presents a stochastic mixed integer programming approach to integrated supplier selection and customer order scheduling in the presence of supply chain disruption risks, for a single or dual sourcing strategy. The suppliers are assumed to be located in two different geographical regions: in the producer's region (domestic suppliers) and outside the producer's region (foreign suppliers). The supplies are subject to independent random local disruptions that are uniquely associated with a particular supplier and to random semi-global (regional) disruptions that may result in disruption of all suppliers in the same geographical region simultaneously. The domestic suppliers are relatively reliable but more expensive, while the foreign suppliers offer competitive prices, however material flows from these suppliers are more exposed to unexpected disruptions. Given a set of customer orders for products, the decision maker needs to decide which single supplier or which two different suppliers, one from each region, to select for purchasing parts required to complete the customer orders and how to schedule the orders over the planning horizon, to mitigate the impact of disruption risks. The problem objective is either to minimize total cost or to maximize customer service level. The obtained combinatorial stochastic optimization problem will be formulated as a mixed integer program with conditional value-at-risk as a risk measure. The risk-neutral and risk-averse solutions that optimize, respectively average and worst-case performance of a supply chain are compared for a single and dual sourcing strategy and for the two different objective functions. Numerical examples and computational results are presented and some managerial insights on the choice between the two sourcing strategies are reported.     

产能不确定供应商的风险厌恶行为对供应链的影响

针对具有产能不确定性的风险厌恶供应商和风险中性零售商组成的供应链系统,本文采用经典的风险指标Value-at-risk(VaR)衡量供应商的风险厌恶程度,并将其作为供应商的优化约束条件之一。在斯坦伯格顺序博弈的模型框架下,零售商做定价和订货量决策,供应商做批发价决策。本文求得供应商批发价在VaR约束下的理论上下界,研究了风险厌恶程度对最优批发价的影响。与风险中性环境下的结果相比,在设立合理目标利润的前提下,高风险厌恶程度可能使得供应商提高批发价,低风险厌恶程度则对供应商批发价无影响。当目标利润设立很高时,供应商为了逐利将会降低批发价诱导零售商提高订货量。     

Risk Mitigation Benefit from Backup Suppliers in the Presence of the Horizontal Fairness Concern

The backup supply strategy is demonstrated as an effective approach to mitigating supply risk. We study a supply chain in which a leader manufacturer designs a contract to a potential backup supplier to mitigate the yield uncertainty of the primary supplier. In this context, the backup supplier may compare with the primary supplier and have horizontal fairness concerns. We model the contract design problem using a Stackelberg game and characterize the optimal decisions for the manufacturer and backup supplier, in both fairness and off‐fairness settings. The theoretical results show that the leader manufacturer must sacrifice his own payoff to balance the payoffs of both suppliers. As a result, using a self‐interested backup supplier is the dominating strategy, whereas using a fair‐minded backup supplier is only suggested when the reliability of the primary supplier is low and the fairness concern of the backup supplier is not strong. Additionally, the backup supplier only benefits from fairness concerns when the level is not exceeding a threshold value. With regard to high fairness levels beyond this threshold, fairness concern has negative effects on the monetary payoff and even might lead to loss of the business. By conducting laboratory experiments, we provide evidence of the horizontal fairness concern from the backup supplier. Further, we show that if the primary supplier also has horizontal fairness concerns, the leader manufacturer can conditionally benefit from a promoted yield reliability due to an extra effort from the primary supplier.     

Mitigating Supply Uncertainty: The Interplay Between Diversification and Pricing

We consider a firm's sourcing problem from one reliable supplier and one unreliable supplier in two price‐setting scenarios. In the committed pricing scenario, the firm makes the pricing decision before the supply uncertainty is resolved. In the responsive pricing scenario, the firm's pricing decision is made after the supply uncertainty is resolved. For the committed pricing scenario, we develop a condition on supply uncertainty that guarantees the unimodality of the firm's objective function. By comparing the firm's optimal diversification decisions in the two pricing scenarios, we examine the interplay of supply diversification strategy and responsive pricing strategy in mitigating supply uncertainty. While both strategies are effective in mitigating supply uncertainty, we show that they are not necessarily substitutes. The relationship between these two strategies depends on two adverse effects caused by supply uncertainty: the lost‐revenue effect and the lost‐goodwill effect. More specifically, when the lost‐revenue effect dominates the lost‐goodwill effect, these two strategies are complements; otherwise, they are substitutes. Furthermore, we examine the impact of market size, price sensitivity, supplier reliability, and failure rebate on the interplay between these two strategies, and discuss the implications of our results. Finally, we extend our analysis to the case of two unreliable suppliers and show that the insights regarding the interplay between diversification and pricing continue to hold.