Risk and quality control in a supply chain: competitive and collaborative approaches

This paper provides a quantitative and comparative economic and risk approach to strategic quality control in a supply chain, consisting of one supplier and one producer, using a random payoff game. Such a game is first solved in a risk-neutral framework by assuming that both parties are competing with each other. We show in this case that there may be an interior solution to the inspection game. A similar analysis under a collaborative framework is shown to be trivial and not practical, with a solution to the inspection game being an ‘all or nothing’ solution to one or both the parties involved. For these reasons, the sampling random payoff game is transformed into a Neyman–Pearson risk constraints game, where the parties minimize the expected costs subject to a set of Neyman–Pearson risk (type I and type II) constraints. In this case, the number of potential equilibria can be large. A number of such solutions are developed and a practical (convex) approach is suggested by providing an interior (partial sampling) solution for the collaborative case. Numerical examples are developed to demonstrate the procedure used. Thus, unlike theoretical approaches to the solution of strategic quality control random payoff games, the approach we construct is both practical and consistent with the statistical risk Neyman–Pearson approach.     

The Effect of Acceptance Sampling and Risk Aversion on the Quality Delivered by Suppliers

Firms often use acceptance sampling to monitor the quality of the raw materials and components delivered by suppliers. In this paper, we use numerical methods to examine how a risk averse supplier reacts to the acceptance sampling plan used by a customer. We assume that the supplier produces and delivers a quality level that maximizes the supplier's expected utility. We examine the sensitivity of the optimal delivered quality to changes in the price, to changes in the supplier's level of risk aversion, and to changes in the parameters of the customer's sampling plan. We conclude that risk averse suppliers deliver higher quality, that higher capability suppliers do not necessarily deliver higher quality, and that the optimal quality is sensitive to the lot size. We also conclude that since the risk of rejection motivates suppliers to improve quality, customers have an economic justification for using acceptance sampling even when there is no statistical justification.     

An a posteriori decision support methodology for solving the multi-criteria supplier selection problem

This research presents a novel, state-of-the-art methodology for solving a multi-criteria supplier selection problem considering risk and sustainability. It combines multi-objective optimization with the analytic network process to take into account sustainability requirements of a supplier portfolio configuration. To integrate ‘risk’ into the supplier selection problem, we develop a multi-objective optimization model based on the investment portfolio theory introduced by Markowitz. The proposed model is a non-standard portfolio selection problem with four objectives: (1) minimizing the purchasing costs, (2) selecting the supplier portfolio with the highest logistics service, (3) minimizing the supply risk, and (4) ordering as much as possible from those suppliers with outstanding sustainability performance. The optimization model, which has three linear and one quadratic objective function, is solved by an algorithm that analytically computes a set of efficient solutions and provides graphical decision support through a visualization of the complete and exactly-computed Pareto front (a posteriori approach). The possibility of computing all Pareto-optimal supplier portfolios is beneficial for decision makers as they can compare all optimal solutions at once, identify the trade-offs between the criteria, and study how the different objectives of supplier portfolio configuration may be balanced to finally choose the composition that satisfies the purchasing company's strategy best. The approach has been applied to a real-world supplier portfolio configuration case to demonstrate its applicability and to analyze how the consideration of sustainability requirements may affect the traditional supplier selection and purchasing goals in a real-life setting.     

反S型权重风险偏好对一类两级供应链的影响

大量实证研究表明,人们在不确定条件下,总是倾向于高估小概率事件并低估大概率事件,呈现反型权重风险偏好的特点。本文针对一类常见的由单供应商和单零售商组成的两级供应链,其中供应商有随机产出风险,分别考察了供应商与零售商的风险态度对其决策的影响。通过构建斯坦伯格博弈模型分析了供需双方的最优订购量和最优计划生产量。结果表明,供需双方或一方有反型风险态度时,保证供需双方均有激励动机签订契约的前提下,分散决策供应链的效率可达到集中决策的效果,也即供应链有可能达到协调。     

Mitigating supply risk: an approach with quantity flexibility procurement

This paper considers a buyer that procures from its major supplier whose production is subject to random yield risk. To mitigate supply risk, the buyer can procure from another reliable supplier who provides quantity flexibility (QF) contract. Under both deterministic and stochastic demand, we study the buyer’s optimal procurement decisions. We analyze the structural properties of optimal solutions and identify the conditions under which the quantity flexibility procurement policy should be used. We also examine the effect of supply risk, flexibility, wholesale price and demand risk on the procurement decisions. We find that the higher supply risk and demand risk reduce the buyer’s profit but have different impact on the buyer’s order policy. For the QF supplier, it may not obtain more orders by providing larger flexibility to the buyer, on the contrary, doing this may benefit the risky supplier. For the QF supplier or risky supplier, given its competitor’s wholesale price, it can increase its order share by lower wholesale price.     

Using spatial games to model dynamic evolutionary systems

Modelling the dynamics of evolutionary competing species on a physical grid is a challenging modelling problem. This paper presents a novel modelling approach for synthesizing evolutionary dynamics of competing species using a spatial game perspective. This modelling approach describes the movement of players (‘species’ in our context) across a lattice. The model is based on a payoff function which controls the move likelihood and direction of the players (‘predators’ and ‘preys’). Using simulated results, the paper provides a comparison between the spatial game model and an existing predator-prey dynamic model. Finally, a case study is performed to illustrate the application of this formalism and validate the model.     

Optimal ordering policies in inventory systems with random demand and random deal offerings

In this paper, we determine the optimal order policies for a firm facing random demand and random deal offerings. In a periodic review setting, a firm may first place an order at the regular price. Later in the period, if a price promotion is offered by the supplier (with a certain probability), the firm may decide to place another order. We consider two models in the paper. In the first model, the firm does not share the cost savings (due to the promotion offered by the supplier) with its own customers, i.e. its demand distribution remains fixed. In the second model, the cost savings are shared with the final customers. As a result, the demand distribution shifts to the right. For both the models, in a dynamic finite-horizon problem, the order policy structure is divided into three regions and is as follows. If the initial inventory level for the firm exceeds a certain threshold level, it is optimal not to order anything. If it is in the medium range, it is optimal to wait for the promotion and order only if it is offered. The order quantity when the promotion is offered has an ‘order up to’ policy structure. Finally, if the inventory level is below another threshold, it is optimal to place an order at the regular price, and to place a second order if the promotion is offered. The low initial inventory level makes it risky to just wait for the promotion to be offered. The sum of the order quantities in this case has an ‘order up to’ structure. Finally, we model the supplier's problem as a Stackelberg game and discuss the motivation for the supplier to offer a promotion for the case of uniform demand distribution for the firm. In the first model (when the firm does not share the cost savings with its customers), we show that it is rarely optimal for the supplier to offer a promotion. In the second model, the supplier may offer a promotion depending on the price elasticity of the product.     

A variables sampling plan based on Cpmk for product acceptance determination

Process capability indices are useful management tools, particularly in the manufacturing industry, which provide common quantitative measures on manufacturing capability and production quality. Most supplier certification manuals include a discussion of process capability analysis and describe the recommended procedure for computing a process capability index. Acceptance sampling plans have been one of the most practical tools used in classical quality control applications. It provides both vendors and buyers to reserve their own rights by compromising on a rule to judge a batch of products. Both sides may set their own safeguard line to protect their benefits. Two kinds of risks are balanced using a well-designed sampling plan. In this paper, we introduce a new variables sampling plan based on process capability index C_pmk to deal with product sentencing (acceptance determination). The proposed new sampling plan is developed based on the exact sampling distribution hence the decisions made are more accurate and reliable. For practical purpose, tables for the required sample sizes and the corresponding critical acceptance values for various producer’s risk, the consumer’s risk and the capability requirements acceptance quality level (AQL), and the lot tolerance percent defective (LTPD) are provided. A case study is also presented to illustrate how the proposed procedure can be constructed and applied to the real applications.     

供应链协作创新模式比较与协调

从供应链中居于核心地位的供应商出发,基于下游制造商对上游创新的影响,在需求对价格敏感情况下考虑了供应商、制造商、第三方研发机构协作创新的博弈过程,对供应链创新协作的三种模式进行了建模分析。研究结果发现在创新能力相当的情况下,无论从创新力度、各方期望利润,还是从满足需求量等来看,供应商与供应链上关系紧密的下游协作创新的模式不仅可以降低自己创新的投资和创新风险,而且提高了整个供应链创新力度和水平,又可以在收益上双赢,其优于不进行协作创新和委托第三方研发机构的协作创新模式。最后进一步提出了供应链协调策略。     

Defending and improving the ‘slotting fee’: how it can benefit all the stakeholders dealing with a newsvendor product with price and effort-dependent demand

‘Slotting fee’ (hereafter ‘SF’) is an upfront fee a ‘supplier’ is required to pay a retailer in order to have his product sold on the retailer's shelves. It is becoming increasingly common, but also widely reviled. This paper considers a newsvendor product whose expected demand is dependent on retail price and sales effort. The question we pose is: given that the Stackelberg-dominant retailer has to choose a pricing contract with which she transacts with the supplier, how would the supply-chain stakeholders fare when the retailer implements SF instead of another practical pricing contract? We show that, contradicting its negative public image, SF empowers the dominant retailer to specify contract terms that will benefit all the stakeholder-groups. That is, the supplier's and the retailer's profits are higher, the production workers are asked to produce more, and the consumers pay a lower retail price. We also propose a new ‘composite’ contract format that incorporates both the SF and ‘buyback’ features. This composite format empowers the retailer to provide even greater benefits to the supply-chain's stakeholders.

     

基于电商平台的混合销售渠道对供应链决策的影响研究

考虑到电商平台对消费者强大的吸引力,本文建立了由供应商和平台商构成的基于电商平台混合销售的供应链模型。混合销售渠道包含直销和分销,其中平台商拥有电商平台,供应商通过电商平台进行直销,平台商分享一定的收益;而分销是指平台商从供应商处批发产品进行销售。分别建立了集中式和分散式决策模型,研究发现:随着消费者对分销渠道接受程度的提高,两种情形下直销渠道的零售价不变,分销渠道的零售价提高;分散式情形下的批发价、供应商和平台商的利润均提高;随着供应商分享收益比例的提高,两种渠道的零售价都降低,但批发价提高,供应商的利润提高,而平台商的利润下降,但供应链的总利润提高;研究得到了保证博弈双方都能从直销渠道中获利的收益分享比例范围。     

政府补贴下供应链合作减排的微分博弈

借助微分博弈理论,研究政府补贴下由一个供应商和一个制造商组成的供应链长期合作减排的动态协调问题。在产品需求受减排量的影响下,构建了集中式和分散式微分博弈模型,并设计了成本分担契约协调供应链。结合算例对参数进行灵敏度分析,研究发现:政府补贴对企业减排起到有效的激励作用并且有助于供应链实现协调;成本分担契约的引入可提高供应商和制造商的减排努力水平、产品减排量及需求量,并实现了供应链协调;随着供应商、制造商减排成本系数以及减排量自衰减率的增大,引入契约后产品减排量呈下降趋势;相反,随着产品减排量对减排努力水平的敏感性以及消费者低碳意识的增强,产品减排量呈上升趋势。     

Multi-period price promotions in a single-supplier, multi-retailer supply chain under asymmetric demand information

This paper considers a two-stage supply chain in which a supplier serves a set of stores in a retail chain. We consider a two-stage Stackelberg game in which the supplier must set price discounts for each period of a finite planning horizon under uncertainty in retail-store demand. As a mechanism to stimulate sales, the supplier offers periodic off-invoice price discounts to the retail chain. Based on the price discounts offered by the supplier, and after store demand uncertainty is resolved, the retail chain determines individual store order quantities in each period. Because the supplier offers store-specific prices, the retailer may ship inventory between stores, a practice known as diverting. We demonstrate that, despite the resulting bullwhip effect and associated costs, a carefully designed price promotion scheme can improve the supplier’s profit when compared to the case of everyday low pricing (EDLP). We model this problem as a stochastic bilevel optimization problem with a bilinear objective at each level and with linear constraints. We provide an exact solution method based on a Reformulation-Linearization Technique (RLT). In addition, we compare our solution approach with a widely used heuristic and another exact solution method developed by Al-Khayyal (Eur. J. Oper. Res. 60(3):306–314, 1992) in order to benchmark its quality.     

Linear Transformation of Products: Games and Economies

In this paper, we introduce situations involving the linear transformation of products (LTP). LTP situations are production situations where each producer has a single linear transformation technique. First, we approach LTP situations from a (cooperative) game theoretical point of view. We show that the corresponding LTP games are totally balanced. By extending an LTP situation to one where a producer may have more than one linear transformation technique, we derive a new characterization of (nonnegative) totally balanced games: each totally balanced game with nonnegative values is a game corresponding to such an extended LTP situation. The second approach to LTP situations is based on a more economic point of view. We relate (standard) LTP situations to economies in two ways and we prove that the economies are standard exchange economies (with production). Relations between the equilibria of these economies and the cores of cooperative LTP games are investigated.     

Two-stage non-cooperative games with risk-averse players

This paper formally introduces and studies a non-cooperative multi-agent game under uncertainty. The well-known Nash equilibrium is employed as the solution concept of the game. While there are several formulations of a stochastic Nash equilibrium problem, we focus mainly on a two-stage setting of the game wherein each agent is risk-averse and solves a rival-parameterized stochastic program with quadratic recourse. In such a game, each agent takes deterministic actions in the first stage and recourse decisions in the second stage after the uncertainty is realized. Each agent’s overall objective consists of a deterministic first-stage component plus a second-stage mean-risk component defined by a coherent risk measure describing the agent’s risk aversion. We direct our analysis towards a broad class of quantile-based risk measures and linear-quadratic recourse functions. For this class of non-cooperative games under uncertainty, the agents’ objective functions can be shown to be convex in their own decision variables, provided that the deterministic component of these functions have the same convexity property. Nevertheless, due to the non-differentiability of the recourse functions, the agents’ objective functions are at best directionally differentiable. Such non-differentiability creates multiple challenges for the analysis and solution of the game, two principal ones being: (1) a stochastic multi-valued variational inequality is needed to characterize a Nash equilibrium, provided that the players’ optimization problems are convex; (2) one needs to be careful in the design of algorithms that require differentiability of the objectives. Moreover, the resulting (multi-valued) variational formulation cannot be expected to be of the monotone type in general. The main contributions of this paper are as follows: (a) Prior to addressing the main problem of the paper, we summarize several approaches that have existed in the literature to deal with uncertainty in a non-cooperative game. (b) We introduce a unified formulation of the two-stage SNEP with risk-averse players and convex quadratic recourse functions and highlight the technical challenges in dealing with this game. (c) To handle the lack of smoothness, we propose smoothing schemes and regularization that lead to differentiable approximations. (d) To deal with non-monotonicity, we impose a generalized diagonal dominance condition on the players’ smoothed objective functions that facilitates the application and ensures the convergence of an iterative best-response scheme. (e) To handle the expectation operator, we rely on known methods in stochastic programming that include sampling and approximation. (f) We provide convergence results for various versions of the best-response scheme, particularly for the case of private recourse functions. Overall, this paper lays the foundation for future research into the class of SNEPs that provides a constructive paradigm for modeling and solving competitive decision making problems with risk-averse players facing uncertainty; this paradigm is very much at an infancy stage of research and requires extensive treatment in order to meet its broad applications in many engineering and economics domains.     

The design of a Tort law to control accidents

In this paper we analyse a two-stage game involving the government and n agents who engage in a single activity (driving). The government establishes the legal policy setting and the agents proceed to play a non-cooperative game of incomplete information with a risk of accident in which their behavioral strategy is their level of care. We examine the Nash-equilibrium conditions for single-activity accidents between heterogeneous agents, ‘good’ drivers or ‘bad’ drivers allowing a variable damage function and a liability rule defined on the cube. The relative desirability for society of alternative equilibria and the conditions under which they can obtain are discussed. The constraints which circumscribe the ability of the government to induce an equilibrium involving careful driving are demonstrated. It transpires that when the proportion of good drivers increases, it becomes more difficult to sustain a careful equilibrium whereas an equilibrium of reckless behavior becomes easier to sustain. Various extensions of the models are also presented.     

Determination of the optimal trade credit policy: a supplier-Stackelberg model

This paper considers a two-echelon supply chain, where one supplier sells through a retailer a product with a stable market demand. We focus on how the supplier induces the retailer through trade credit to order more to reduce his/her own inventory-related cost. Under a ‘supplier-Stackelberg’ setting, we provide the supplier with the method of determining two trade credit scenarios: unconditional and conditional trade credit. We show that the unconditional trade credit scenario is always beneficial to the retailer but harmful to the supplier in most situations, while the conditional trade credit scenario is always beneficial to both parties. In addition, we specify the conditions under which the provision of unconditional trade credit is beneficial to the supplier. The three insights obtained in this paper are the following: (i) When the retailer’s per-unit opportunity cost is less than his/her per-unit opportunity gain, unconditional trade credit can induce the retailer to order less instead of more. (ii) If the supplier offers the retailer unconditional trade credit, the length of trade credit offered will have an upper bound. (iii) A well-designed conditional trade credit policy can realize a win-win outcome but also enables the supplier to occupy all the savings in the channel's cost incurred by trade credit, but any unconditional trade credit policy does not.     

Consumers risk and quality control in a collaborative supply chain

The purpose of this paper is to provide a strategic collaborative approach to risk and quality control in a cooperative supply chain by using a Neyman–Pearson quantile risk framework for the statistical control of risks. The paper is focused on the statistical quality control of a supplier and a producer, applying the traditional Neyman–Pearson theory to the control of quality in a supply chain environment. In our framework, the risks assumed by the parties in the supply chain depend on the organizational structure, the motivations and the power relationships that exist between members of the supply chain.     

A capacity reservation game for suppliers with multiple blocks of capacity

This paper studies a supplier competition model in which a buyer reserves capacity from a number of suppliers that each have multiple blocks of capacity (e.g., production or power plants). The suppliers each submit a bid that specifies a reservation price and an execution price for every block, and the buyer determines what blocks to reserve. This game involves both external competition between suppliers and internal competition between blocks from each supplier. We characterize the properties of pure-strategy Nash equilibria for the game. Such equilibria may not always exist, and we provide the conditions under which they do.     

Question selection responding to information on customers from heterogeneous populations to select offers that maximize expected profit

The advent of Internet broking pages allows customers to ‘apply’ to a number of different companies at one time, leading to multiple offers made to a customer. The saturated condition of the personal financial products has led to falling ‘take’ rates. Financial institutions are trying to increase the ‘take’ rates of their personal financial products. Applicants for credit will have to provide information for risk assessment, which can be used to assess the probability of a customer accepting an offer. Interactive channels such as the Internet and telephone allow questions that are asked to depend on previous answers. The questions selected need to provide information to assess the probability of acceptance of a particular variant of financial product. In this paper, we investigate a model to predict the best offer to extend next to a customer based on the response for the questions, as well as the question selection itself.