Strategic cooperation with a backup supplier for the mitigation of supply disruptions

We study optimal sourcing decisions for a firm with a dedicated supplier and a backup supplier. The dedicated supplier charges a lower wholesale price but faces a potential disruption risk. The backup supplier is assumed to be perfectly reliable but charges a higher wholesale price. The primary question we address is how the firm should cooperate with the backup supplier to hedge against the disruption risk. We consider three common cooperation options: advance purchase, reservation and contingency purchase. Our basic results show that the firm should choose advance purchase strategy if the disruption probability is high, while contingency purchase strategy benefits the firm more if the disruption probability is low. Under an intermediate disruption probability, the firm should choose reservation strategy only if the reservation fee is sufficiently low. Then, we explore the optimal backup strategy under partial disruption risk. The results show that the advance purchase and the reservation strategy should be adopted more widely when the dedicated supplier guarantees a relatively high yield rate after disruption.     

Flexible strategies under supply disruption: the interplay between contingent sourcing and responsive pricing

Due to possible supply disruptions because of a low-cost unreliable supplier, a firm may use a high-cost reliable supplier as an additional regular supplier (dual sourcing) or an emergency backup supplier with an extra emergency cost (contingent sourcing). We consider the firm's sourcing problem when the pricing decision is made before any supply uncertainty is resolved (committed pricing) or after the supply state is realised (responsive pricing). By comparing the relative value of responsive pricing in contingent sourcing to that in dual sourcing, we study the relationship between contingent sourcing and responsive pricing in mitigating supply disruption risks. We show that the emergency cost and potential lost sales caused by disruption probability jointly impact the interplay of these two strategies. More specifically, when the emergency cost is low and the potential lost sales are lower under contingent sourcing than that under dual sourcing, contingent sourcing and responsive pricing are substitutes; otherwise, they are complements. Furthermore, we examine how disrupted capacity, i.e. the quantity that the unreliable supplier can deliver when disrupted, impacts the interplay, and find that the probability of the substitution relationship becomes higher when the disrupted capacity increases. We also find that under committed pricing, contingent sourcing is not optimal for any value of disruption probability when the emergency cost is high, a phenomenon that does not exist under responsive pricing.     

The optimal technology licensing strategy under supply disruption

We study the problem of whether and how a patent-holding firm (supplier S1) should license its technology patent to a potential rival (supplier S2). If the license is given, the two suppliers both produce a critical component for their downstream manufacturer simultaneously (sequentially) when the manufacturer adopts a dual (contingent) sourcing mode. However, both suppliers face risks of complete supply disruptions. In the study, we examine how the supply risk affects S1's technology licensing willingness and under which conditions royalty or fixed-fee licensing is its optimal strategy. The results show that when the manufacturer adopts contingent sourcing, S1 is always willing to license its technology to S2 and fixed-fee licensing is the optimal strategy. However, when dual sourcing is adopted, either royalty and fixed-fee licensing could be S1's optimal licensing strategy, depending on the reliability degree of the suppliers’ productions. Our findings extend the conclusion from previous researchers about royalty and fixed-fee licensing in a Cournot duopoly model.     

Dual-channel supply chain pricing decisions with a risk-averse retailer

This paper investigates a dual-channel supply chain with one risk-neutral manufacturer and one risk-averse retailer where there is only one perishable product with price-dependent stochastic demand. We choose Conditional Value-at-Risk criterion to measure the retailer’s risk-averse level, and assume that the manufacturer’s direct sales channel and the retailer’s traditional channel adopt a consistent pricing strategy. The model explores a Nash bargaining problem where the manufacturer and the retailer negotiate with each other on the wholesale price, the retail price and the order quantity when they have equal bargaining power. It is found that when demand uncertainty follows a uniform distribution, a Nash bargaining equilibrium exists and the retail price will decrease as the retailer becomes more risk averse. However, when the risk-averse indicator increases, the manufacturer’s profit on his direct channel will decrease, increase or first increase and then decrease, depending on the values of the related parameters. The profit shares of the manufacturer and the retailer under the Nash equilibrium model are related to the risk-averse indicator of the retailer. Furthermore, we perform three sets of numerical experiments to verify the effects of the retailer’s risk-averse indicator on decision-making and profit allocations under the different environmental parameters and gain several meaningful managerial insights.     

Procurement decisions and information sharing under multi-tier disruption risk in a supply chain

We consider a manufacturer's procurement decision in a three-tier supply chain (SC) under disruption risk. The manufacturer sources components from a single first-tier supplier (FT). The FT, in turn, sources raw materials from a single second-tier supplier (ST). Suppliers in both tiers are unreliable, i.e. prone to disruption risk. Increasing SC visibility through information sharing is a potential disruption management strategy for the manufacturer. While the manufacturer can obtain disruption risk information for the FT, disruption risk information for the ST is not easily accessible to the manufacturer except through the FT, who may not be willing to share ST information. We study different mechanisms under which the manufacturer can obtain ST information, and its impact on manufacturer's and FT's decisions and potential profits. We show that information sharing makes the manufacturer's procurement decisions more conservative, i.e. carrying more inventories, but the FT's procurement decision is contingent on the ST's reliability; more proactive (conservative) when ST is unreliable (reliable), i.e. carrying less (more) inventories. We demonstrate that there are two ways to induce the FT to share its information, and numerically show that their effectiveness is contingent on multiple factors, including FT and ST reliabilities and information sharing costs.     

Mitigating supply disruption with a backup supplier under uncertain demand: competition vs. cooperation

In case of supply disruption following major disasters, many supply chains tend to break down due to stock-outs and take a long time to recover. However, by keeping emergency sources of supply, some supply chains continue to function smoothly even after a major disaster. In this work, using a game-theoretic-framework, we consider a two-suppliers-one-retailer supply chain with price-dependent stochastic demand in which suppliers are prone to disruption. To investigate the impact of supply disruption we consider two models: SC model, in which the retailer does not maintain any emergency sources of supply against any supply disruption, and SCB model, in which the retailer maintains a backup supplier to mitigate the impact of supply disruption. We mainly focus on the pricing strategies of the suppliers and the mitigating strategies of the retailer under supply and demand uncertainty. We address two coordinating mechanisms to enhance supply chain performance. Our results indicate that in the presence of supply disruption, even with lower probabilities, the retailer would always prefer to take the advantage of a backup supplier and the optimal reserve quantity increases with disruption probabilities. We further investigate the scenario in which the suppliers would always prefer to cooperate with each other.     

A portfolio approach to supply chain disruption management

A new, computationally efficient portfolio approach to supplier selection in the presence of supply chain disruption risks is proposed, where the selection of supply portfolios for parts is combined with production scheduling of finished products. Unlike most of reported research on the supply chain risk management which focuses on the risk mitigation decisions taken prior to a disruption, the proposed portfolio approach combines decisions made before, during and after the disruption. The two decision-making approaches are considered: an integrated approach with the perfect information about the future disruption scenarios, and a hierarchical approach with no such information available. In the integrated approach, which accounts for all potential disruption scenarios, the primary supply portfolio that will hedge against all scenarios is determined along with the recovery supply portfolio and production schedule for each scenario. In the hierarchical approach, first the primary supply portfolio is determined, and then, when a primary supplier is hit by a disruption, the recovery supply portfolio is selected. For the integrated and the hierarchical decision-making, mixed integer programming models are developed with the two risk-neutral conflicting objectives that account for both time and cost of recovery: minimising expected cost or maximising expected service level. The findings indicate that for both objectives, the integrated decision-making selects a more diversified primary supply portfolio than the hierarchical approach and when all primary suppliers are shutdown by disruption, a single sourcing recovery portfolio is usually selected.     

On the risk-averse optimization of service level in a supply chain under disruption risks

The worst-case optimization of service level in the presence of supply chain disruption risks is considered for the two different service levels measures: the expected worst-case demand fulfillment rate and the expected worst-case order fulfillment rate. The optimization problem is formulated as a joint selection of suppliers and stochastic scheduling of customer orders under random disruptions of supplies. The suppliers are located in different geographic regions and the supplies are subject to random local and regional disruptions. The obtained combinatorial stochastic optimization problem is formulated as a mixed integer program with conditional service-at-risk as a worst-case service level measure. The risk-averse solutions that optimize the worst-case performance of a supply chain are compared for the two service level measures. In addition, to demonstrate the impact on the cost in the process of optimizing the worst-case service level, a joint optimization of expected cost and conditional service-at-risk using a weighted-sum approach is considered and illustrated with numerical examples. The findings indicate that the worst-case order fulfillment rate shows a higher service performance than the worst-case demand fulfillment rate. Maximization of the expected worst-case fraction of fulfilled customer orders better mitigates the impact of disruption risks. The supply portfolio is more diversified and the expected worst-case fraction of fulfilled orders is greater for most confidence levels. Finally, the results clearly show that worst-case service level is in opposition to cost.     

Evaluation mechanism for structural robustness of supply chain considering disruption propagation

This paper aims to develop a novel evaluation mechanism for assessing the structural robustness of a supply chain considering disruption propagation. Disruption propagation means that the impact of risks propagates to the whole supply chain along the connected structure. Based on the propagation model, a structural robustness evaluation mechanism is devised by integrating two quantitative metrics, average path length and in degree-out degree. To validate the proposed mechanism, the result of the quantitative assessment of the structural robustness on random networks is compared with the probability of network disruption due to the random risk. From the results of the statistical verifications and sensitivity analysis, it can be said that the proposed mechanism is better at explaining the robustness of a supply chain. In other words, all components of a network, such as nodes and arcs, and their relationships should be considered altogether, in order to more accurately measure the robustness. It may be possible to apply the proposed mechanism to the very first step of designing the supply chain. Especially, in the case of it being hard to redesign a supply chain structure after practically launching and operating the designed network, the proposed mechanism may be utilised to verify whether the planned supply chain is robust to risks or not.     

Two-period vs. multi-period model for supply chain disruption management

A novel two-period modelling approach is developed for supply chain disruption mitigation and recovery and compared with a multi-period approach. For the two-period model, planning horizon is divided into two aggregate periods: before disruption and after disruption. The corresponding mitigation and recovery decisions are: (1) primary supply and demand portfolios and production before a disruption, and (2) recovery supply, transshipment and demand portfolios and production after the disruption. In the multi-period model, a multi-period planning horizon is applied to account for a detailed timing of supplies and production. The primary and recovery portfolios are determined simultaneously and for both approaches the integrated decision-making, stochastic mixed integer programming models are developed. While the simplified two-period setting may overestimate (for best-case capacity constraints) or underestimate (for worst-case capacity constraints) the available production capacity, it can be easily applied in practice for a fast, rough-cut evaluation of disruption mitigation and recovery policy. The findings indicate that for both two- and multi-period setting, the developed multi-portfolio approach leads to computationally efficient mixed integer programming models with an embedded network flow structure resulting in a very strong linear programming relaxation.     

Budget allocation in coping with supply chain disruption risks

Disruption management, as an important research topic, has attracted scholars’ broad attention in recent years due to the increasing exposure of disruption risks in supply chains. To date, researches in this field often focus on either prevention or mitigation measures and the budget allocation problem is paid relatively little attention. This paper therefore proposes an approach to determine the optimal budget allocation based on prevention measures in combination with mitigation measures. First, considering different disruption situations, the bow-tie is applied to developing the disruption management frameworks that integrate risk prevention and risk mitigation. Second, the corresponding optimization models are formulated to determine the optimal budget allocation plans. In order to validate the proposed approach, we compare the computation results with those obtained from the prevention approach and the mitigation approach. Also, random experiments are conducted to analyse the impacts of randomly generated disruption and response scenarios. Finally, a real-life case is provided to testify the usefulness and merits of our proposed approach. The results show that the proposed approach can help decision-makers reduce more loss caused by the disruption risks.     

Random yield and coordination mechanisms of a supply chain with emergency backup sourcing

This paper considers a supply chain in which a buyer purchases finished items from a contracting supplier to satisfy a stochastic market demand, where the supplier’s production is subject to random yield. We assume that the buyer can make up the shortage by sourcing from an emergency backup supplier. We develop two Stackelberg game models, i.e. buyer-Stackelberg (BS) model and supplier-Stackelberg (SS) model, and find that the decentralised BS model results in a higher stocking factor of supplier’s input than the decentralised SS model. Compared with BS model, the buyer in SS model performs more explicit order plan, and we find that only when the actual yield of the supplier is insufficient, the buyer would use emergency backup sourcing to make up the shortage. When the manufacturing operation of the supplier is in the good state, the buyer only orders a certain amount and has some leftover. When the actual yield of the supplier is moderate, the buyer uses up every item produced from the supplier regardless of the yield rate. Comparing both channel structures, SS operation is a more effective way of controlling both inventory cost and backup sourcing cost, and it can be beneficial for each player as well as for the whole channel. Finally, we develop the coordination mechanism for each channel to investigate the issues of risk handling and risk sharing for uncertain demand and uncertain yield.     

Incorporating risk aversion and fairness considerations into procurement and distribution decisions in a supply chain

This paper considers a three-tier supply chain in which a manufacturer uses raw materials sourced from multiple suppliers to produce an item and sells it through multiple distributors. We develop an integrated optimisation model to study supply chain procurement and distribution decisions incorporating the manufacturer’s aversion to risk and the distributors’ concern for fairness in a climate of uncertain supply and demand. Resilient strategies, such as alternative sourcing and transshipment, are also considered when optimising the supply chain cost and service level. To solve the problem, a Monte Carlo simulation-based multi-objective stochastic programming model is built. It uses the CVaR (Conditional Value-at-Risk) and unfairness aversion utility function to reflect the decision maker’s risk aversion and the customer’s concern for fairness, respectively. A Normalised Normal Constraint based algorithm is adopted to obtain the Pareto Frontier. In addition, the numerical analysis provides some valuable insights for supply chain managers.     

Using game theory for analysing pricing models in closed-loop supply chain from short- and long-term perspectives

Closed-loop supply chain (CLSC) management is an environmental approach to supply chain management that aims to prevent hazardous material from entering the nature by means of creating a reverse flow. This paper studies the short- and long-term behaviour of agents in implementing the appropriate collecting strategy in a two-echelon CLSC. In short-term, based on the Stackelberg game, several novel pricing models for different collecting strategies are proposed and compared. Then, the optimal policies of the pricing decisions are determined for each model. The long-term behaviour of companies in implementing collecting process is examined by evolutionary game theory and the most stable strategy is selected. Furthermore, a numerical example is presented to compare the different collecting structures. Finally, a managerial insight is provided to indicate the effect of key parameters such as remanufacturing rate, marketing elasticity and government subsidies on selecting the appropriate strategy.     

Responding to supplier temporary price discounts in a supply chain through ordering and pricing decisions

This paper considers a one-retailer and one-supplier supply chain and addresses the question of how a retailer should use its ordering and pricing decisions to respond to its supplier’s temporary price discounts. The paper considers a hybrid environment – somewhere between deterministic and stochastic modelling approaches – that is, the retailer does not know when the next promotion from its supplier will occur but, once the promotion is announced, all its details are deterministic and often there is some time remaining before the promotion actually starts. We include in the objective function penalties on deviations from the original plan and explore the properties of the retailer’s ordering and pricing decisions under fixed and flexible set-up scenarios. We show that, when the set-up epochs are fixed, the retailer’s order quantities are monotonic and non-decreasing in situations where retail prices can be either fixed or flexible. When the set-up epochs are flexible, the ordering cycle is identical. Finally, we use some numerical examples to illustrate the proposed approach.     

Equilibrium markup pricing strategies for the dominant retailers under supply chain to chain competition

Markup pricing policies have been widely employed in the retailing industry. Under such policies, a retailer requires a retail margin over the wholesale price charged by the supplier to guarantee her profitability. This paper investigates and compares the performance of two commonly used markup pricing policies, namely, fixed-dollar markup and percentage markup, for the dominant retailers facing chain-to-chain competition. Our results demonstrate that the equilibrium pricing strategy for the dominant retailers seeking to maximise their respective profits is [PP]-strategy (i.e. both retailers select the percentage markup pricing policy), no matter what the demand curve and the level of chain-to-chain competition are. Unfortunately, this equilibrium will get in the prisoner’s dilemma since the percentage markup pricing strategy might yield lower profits for the retailers and suppliers compared to its fixed-dollar counterpart when the level of chain-to-chain competition is high enough under the linear demand, which is contrast to the literature. If the criteria for the dominant retailers to select which markup pricing policy to offer is the whole channel’s profit obtained under the decentralised decision-making scenario instead of themselves, [PP]-strategy is the dominant strategy and the unique Nash equilibrium of the pricing policy choice game regardless of the competitive intensity under the iso-elastic demand. This result holds true for the linear demand only when the level of chain-to-chain competition is below certain threshold; otherwise, both [FF] (i.e. both retailers select the fixed-dollar markup pricing policy) and [PP] can be the equilibrium pricing strategy.     

Enhanced joint pricing and lotsizing problem in a two-echelon supply chain with logit demand function

In retail supply chains, ordering and pricing policies for the retailer and shipment plan for the supplier are the most important decisions. These policies are often conducted either individually or sequentially with poor overall performance for the whole supply chain resulting to extra inventory and other deficiencies. In this paper, an integrated marketing-inventory model in a two-echelon supply chain model is developed involving discount promotion, customer behaviour more realistically and operations aspects to determine optimal ordering, shipping and pricing quantities simultaneously. An efficient analytical solution procedure and a Particle Swarm Optimisation solution algorithm are also developed. Finally, a number of numerical tests are conducted to approve the interesting theoretical results of the analytical approach.     

Optimal reservation pricing strategy for a fashion supply chain with forecast update and asymmetric cost information

We address the reservation pricing problem for a two-echelon fashion supply chain in which the downstream manufacturer with private information on its operations cost (low or high type) reserves the capacity for a critical component from the upstream supplier before placing the final order. We consider the case when the demand forecast is partially updated. We find that a novel menu of reservation contracts containing the unit reservation fee with reservation quantity and final order could induce the manufacturer to reveal its operations cost information truthfully. We also show that the supplier should require less capacity reservation and charge a lower unit reservation fee if it has asymmetric information about the manufacturer’s operations cost. Finally, we analyse the effects of forecast update, and our results indicate that: (i) the supplier benefits from forecast update because the optimal reservation pricing strategy is designed to reveal the true information and meanwhile induce a higher capacity reservation; and (ii) a greater amount of forecast update decreases the supply chain deficit and increases the supplier’s agency cost.     

A pricing/ordering model for a dyadic supply chain with buyback guarantee financing and fairness concerns

The paper investigates pricing/ordering issues in a dyadic supply chain, in which a core supplier sells products through a budget-constrained retailer. The retailer faces stochastic demand and is fairness-concerned as well. If needed, the retailer can get financing support from bank by means of buyback guarantee financing (BGF) mode, which is often used in China. By introducing Nash bargaining solution as the fairness reference point, we formulate the retailer’s fairness-concerned utility function and develop a two-echelon pricing/ordering game model. We then study the combined impacts of fairness concerns and BGF on two members’ equilibrium strategies and supply chain performance. We also discuss the corresponding issues under no budget constraint, no financing service and bank financing. Our results show that: (1) two members’ equilibrium strategies are significantly influenced by the retailer’s fairness-concerned behaviour and initial budget; (2) as compared to no budget constraint, BGF can bring the whole supply chain more performance, which means that BGF can yield value-added; (3) When the retailer takes the risk of uncertain market solely, the retailer’s fairness concerns are beneficial for supply chain to improve the performance.     

Optimisation of online retailer pricing and carrier capacity expansion during low-price promotions with coordination of a decentralised supply chain

In recent years, many online retailers in China set low prices on 11 November, which stimulates huge delivery demand and results in many problems although carriers make an effort to increase their delivery capacities temporarily. To circumvent this difficulty, we consider a supply chain consisting of an online retailer, who can set price to influence the demand, and a capacitated carrier, whose capacity can be expanded at a high cost. We derive the optimal decisions in the centralised and decentralised decision systems, and compare the performances of the two systems. We find that the optimal decisions, and which system has lower price, larger capacity increment, and more late delivered goods depends on the model parameters (the market scale, the late delivery costs, the capacity expansion cost, the delivery fee, and the demand uncertainty). Specially, we show that, contrary to the traditional channel, the online retailer in the decentralised system may set lower price and the carrier has less incentive to expand capacity in the decentralised system in some situations, which underlines the need for coordination. In addition, we propose coordination contracts to improve the overall performance of the supply chain under deterministic and random demands.