Selection of supply portfolio under disruption risks

This paper deals with the optimal selection of supply portfolio in a make-to-order environment in the presence of supply chain disruption risks. Given a set of customer orders for products, the decision maker needs to decide from which supplier to purchase custom parts required for each customer order to minimize total cost and mitigate the impact of disruption risks. The selection of suppliers and allocation of orders is based on price and quality of purchased parts and reliability of delivery. The two types of disruption scenarios are considered: scenarios with independent local disruptions of each supplier and scenarios with local and global disruptions that may result in all suppliers disruption simultaneously. The problem is formulated as a single- or bi-objective mixed integer program and a value-at-risk and conditional value-at-risk approach is applied to control the risk of supply disruptions. The proposed portfolio approach is capable of optimizing the supply portfolio by calculating value-at-risk of cost per part and minimizing expected worst-case cost per part simultaneously. Numerical examples are presented and some computational results are reported.     

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。     

On the fair optimization of cost and customer service level in a supply chain under disruption risks

This paper presents a new decision-making problem of a fair optimization with respect to the two equally important conflicting objective functions: cost and customer service level, in the presence of supply chain disruption risks. Given a set of customer orders for products, the decision maker needs to select suppliers of parts required to complete the orders, allocate the demand for parts among the selected suppliers, and schedule the orders over the planning horizon, to equitably optimize expected cost and expected customer service level. The supplies of parts are subject to independent random local and regional disruptions. The fair decision-making aims at achieving the normalized expected cost and customer service level values as much close to each other as possible. The obtained combinatorial stochastic optimization problem is formulated as a stochastic mixed integer program with the ordered weighted averaging aggregation of the two conflicting objective functions. Numerical examples and computational results, in particular comparison with the weighted-sum aggregation of the two objective functions are presented and some managerial insights are reported. The findings indicate that for the minimum cost objective the cheapest supplier is usually selected, and for the maximum service level objective a subset of most reliable and most expensive suppliers is usually chosen, whereas the equitably efficient supply portfolio usually combines the most reliable and the cheapest suppliers. While the minimum cost objective function leads to the largest expected unfulfilled demand and the expected production schedule for the maximum service level follows the customer demand with the smallest expected unfulfilled demand, the equitably efficient solution ensures a reasonable value of expected unfulfilled demand.     

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.     

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.     

Selection of resilient supply portfolio under disruption risks

This paper deals with the optimal selection and protection of part suppliers and order quantity allocation in a supply chain with disruption risks. The protection decisions include the selection of suppliers to be protected against disruptions and the allocation of emergency inventory of parts to be pre-positioned at the protected suppliers. The decision maker needs to decide which supplier to select for parts delivery and how to allocate orders quantity among the selected suppliers, and which of the selected suppliers to protect against disruptions and how to allocate emergency inventory among the protected suppliers. The problem objective is to achieve a minimum cost of suppliers protection, emergency inventory pre-positioning, parts ordering, purchasing, transportation and shortage and to mitigate the impact of disruption risks by minimizing the potential worst-case cost. As a result a resilient supply portfolio is identified with protected suppliers capable of supplying parts in the face of disruption events. A mixed integer programming approach is proposed to determine risk-neutral, risk-averse or mean-risk supply portfolios, with conditional value-at-risk applied to control the risk of worst-case cost. Numerical examples are presented and some computational results are reported.     

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.     

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.     

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。     

The optimal number of suppliers considering the costs of individual supplier failures

This paper utilizes the decision tree approach to determine the optimal number of suppliers in the presence of supplier failure risks. Previous proposed models have considered only two states of nature: all suppliers fail to deliver and not all suppliers fail to deliver. In practice, however, there is clearly a partial loss associated with the failure of any individual supplier. We present models that allow a more realistic decision-making process by taking into consideration the independent risks of individual supplier failures when the probability of failure for each of the suppliers is equal as well as the case where the probability of failure from each of the suppliers is not equal. We also consider various levels of supplier failure probability and possible procurement or operating cost savings gained from using less reliable suppliers. The results indicate that when suppliers are highly reliable, sole sourcing is the lowest cost approach under all experimental conditions. However, as the suppliers become less reliable, additional suppliers may be required to obtain the lowest cost. Finally, it was shown that only in the extreme conditions of unreliable suppliers, high loss to operational cost per supplier, and low ability to mitigate the failure from a partial set of suppliers, having a large number of suppliers is an effective strategy.     

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。     

Sourcing Decisions with Stochastic Supplier Reliability and Stochastic Demand

Supplier sourcing strategies are a crucial factor driving supply chain success. In this paper, we investigate the implications of uncertain supplier reliability on a firm's sourcing decisions in an environment with stochastic demand. In particular, we characterize specific conditions under which a firm should choose a single versus multiple supplier sourcing strategy. In an environment with both uncertain demand and supply, we characterize the total order quantity, the number of suppliers selected for order placement, and the allocation of the total order quantity among these selected suppliers. For deeper managerial insight, we also examine the sensitivity of the optimal sourcing decisions to interactions between uncertainties in product demand and supply reliability. We show that sourcing from a single supplier is an optimal strategy for environments characterized by high levels of demand uncertainty or high salvage values. A numerical analysis based on data obtained from an office products retailer further reinforces our analytical results. In addition, we also find that when minimal order quantities are imposed, there are situations where it is not optimal to place an order with the lowest cost supplier.     

Integrated supply,production and distribution scheduling under disruption risks

This paper presents a bi-objective stochastic mixed integer programming approach for a joint selection of suppliers and scheduling of production and distribution in a multi-echelon supply chain subject to local and regional disruption risks. Two conflicting problem objectives are minimization of cost and maximization of service level. The three shipping methods are considered for distribution of products: batch shipping with a single shipment of different customer orders, batch shipping with multiple shipments of different customer orders and individual shipping of each customer order immediately after its completion. The stochastic combinatorial optimization problem is formulated as a time-indexed mixed integer program with the weighted-sum aggregation of the two objective functions. The supply portfolio is determined by binary selection and fractional allocation variables while time-indexed assignment variables determine the production and distribution schedules. The problem formulation incorporates supply–production, production–distribution and supply–distribution coordinating constraints to efficiently coordinate supply, production and distribution schedules. Numerical examples modelled after an electronics supply chain and computational results are presented and some managerial insights are reported. The findings indicate that for all shipping methods, the service-oriented supply portfolio is more diversified than the cost-oriented portfolio and the more cost-oriented decision-making, the more delayed the expected supply, production and distribution schedules.     

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.     

A Multi‐Supplier Sourcing Problem with a Preference Ordering of Suppliers

We study a sourcing problem faced by a firm that seeks to procure a product or a component from a pool of alternative suppliers. The firm has a preference ordering of the suppliers based on factors such as their past performance, quality, service, geographical location, and financial strength, which are commonly included in a supplier scorecard system. Thus, the firm first uses available inventory from supplier 1, if any, then supplier 2, if any, and so on. The suppliers differ in costs and prices. The buyer firm seeks to determine which suppliers to purchase from and in what quantities to maximize its total expected profit subject to the preference ordering constraint. We present the optimal solution to this problem, and show that it has a portfolio structure. It consists of a sub‐set of suppliers that are ordered by their underage and overage costs. This portfolio achieves a substantial profit gain compared to sourcing from a unique supplier. We present an efficient algorithm to compute the optimal solution. Our model applies to component sourcing problems in manufacturing, merchandizing problems in retailing, and capacity reservation problems in services.     

Keep Your Friends Close? Supply Chain Design and Disruption Risk

In this article, we evaluate the relationship between supply chain design decisions and supply chain disruption risk. We explore two supply chain design strategies: (i) the dispersion of supply chain partners to reduce supply chain disruption risk versus (ii) the co‐location of supply chain partners to reduce supply chain disruption risk. In addition, we assess supply chain disruption risk from three perspectives: the inbound material flow from the supplier (supply side), the internal production processes (internal), and the outbound material flow to the customer (customer side) as a disruption can occur at any of these locations. We measure disruption risk in terms of stoppages in flows, reductions in flow, close calls (disruptions that were prevented at the last minute), disruption duration (time until normal operation flow was restored), and the spread of disruptions all the way through the supply chain. We use seemingly unrelated regression (SUR) to analyze our data, finding that lead times, especially supply side lead times, are significantly associated with higher levels of supply chain disruption risk. We find co‐location with suppliers appears to have beneficial effects to the reduction of disruption duration, and, overall supply side factors have a higher impact when it comes to supply chain disruption risk than comparable customer side factors.     

Single or dual sourcing: decision-making in the presence of supply chain disruption risks

The focus of this paper is placed on evaluating the impacts of supply disruption risks on the choice between the famous single and dual sourcing methods in a two-stage supply chain with a non-stationary and price-sensitive demand. The expected profit functions of the two sourcing modes in the presence of supply chain disruption risks are first obtained, and then compared so that the critical values of the key factors affecting the final choice are identified. Finally, the sensitivity of the buyer's expected profit to various input factors is examined through numerical examples, which provide guidelines for how to use each sourcing method.     

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.     

面临汇率和供应风险的双渠道采购决策研究

多渠道采购是制造商降低采购风险的有效手段之一。本文考虑一个制造商向两个供应商进行联合采购的最优决策问题。其中本土(国内)供应商价格稳定,但供应不可靠;母国(国外)供应商供应可靠,但实际价格受汇率波动影响。本文研究了制造商在风险厌恶情形下的最优联合采购决策,并与风险中性情形进行了比较。研究表明,风险中性制造商只会向一个供应商采购;而风险厌恶制造商的采购决策会受到供应可靠性、汇率的波动以及两者相关关系的影响。具体来说,当产品合格率和汇率相对独立时,风险厌恶的制造商倾向于单渠道采购;当合格率和汇率相关时则可能选择双渠道采购以分散风险。数值实验表明,双渠道采购可以有效降低制造商的损失风险。     

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.