Trading reliability targets within a supply chain using Shapley's value

The development of complex systems involves a multi-tier supply chain, with each organisation allocated a reliability target for their sub-system or component part apportioned from system requirements. Agreements about targets are made early in the system lifecycle when considerable uncertainty exists about the design detail and potential failure modes. Hence resources required to achieve reliability are unpredictable. Some types of contracts provide incentives for organisations to negotiate targets so that system reliability requirements are met, but at minimum cost to the supply chain. This paper proposes a mechanism for deriving a fair price for trading reliability targets between suppliers using information gained about potential failure modes through development and the costs of activities required to generate such information. The approach is based upon Shapley's value and is illustrated through examples for a particular reliability growth model, and associated empirical cost model, developed for problems motivated by the aerospace industry. The paper aims to demonstrate the feasibility of the method and discuss how it could be extended to other reliability allocation models

Cooperation and profit allocation in distribution chains

We study the coordination of actions and the allocation of profit in distribution chains under decentralized control. We consider distribution chains in which a single supplier supplies goods for replenishment of stocks of several retailers who, in turn, sell these goods to their own separate markets. The goal of the supplier and the retailers is to maximize their individual profits. Since the optimal joint profit under centralized control is larger than the sum of the individual optimal profits under decentralized control, cooperation among firms by means of coordination of actions may improve individual profits. The effects of cooperation are studied by means of cooperative games. For each distribution chain we define a corresponding cooperative game and study its properties. Among others we show that such games are balanced. Based on the nice core structure a stable solution concept for these games is proposed and its properties are interpreted in terms of the underlying distribution chain. \u

A Stackelberg game theoretic model for optimizing product family architecting with supply chain consideration

Planning of an optimal product family architecture (PFA) plays a critical role in defining an organization's product platforms for product variant configuration while leveraging commonality and variety. The focus of PFA planning has been traditionally limited to the product design stage, yet with limited consideration of the downstream supply chain-related issues. Decisions of supply chain configuration have a profound impact on not only the end cost of product family fulfillment, but also how to design the architecture of module configuration within a product family. It is imperative for product family architecting to be optimized in conjunction with supply chain configuration decisions. This paper formulates joint optimization of PFA planning and supply chain configuration as a Stackelberg game. A nonlinear, mixed integer bilevel programming model is developed to deal with the leader–follower game decisions between product family architecting and supply chain configuration. The PFA decision making is represented as an upper-level optimization problem for optimal selection of the base modules and compound modules. A lower-level optimization problem copes with supply chain decisions in accordance with the upper-level decisions of product variant configuration. Consistent with the bilevel optimization model, a nested genetic algorithm is developed to derive near optimal solutions for PFA and the corresponding supply chain network. A case study of joint PFA and supply chain decisions for power transformers is reported to demonstrate the feasibility and potential of the proposed Stackelberg game theoretic joint optimization of PFA and supply chain decisions

A distributed coordination mechanism for supply networks with asymmetric information

The paper analyses the problem of coordination in supply networks of multiple retailers and a single supplier, where partners have asymmetric, private information of demand and costs. After stating generic requirements like distributedness, truthfulness, efficiency and budget balance, we use the apparatus of mechanism design to devise a coordination mechanism that guarantees the above properties in the network. The resulting protocol is a novel realisation of the widely used Vendor Managed Inventory (VMI) where the responsibility of planning is at the supplier. We prove that together with the required generic properties a fair sharing of risks and benefits cannot be guaranteed. We illustrate the general mechanism with a detailed discussion of a specialised version, assuming that inventory planning is done according to the newsvendor model, and explore the operation of this protocol through computational experiments

Strategic Inventories in a Supply Chain with Vertical Control and Downstream Cournot Competition

Strategic Inventory (SI) has been an area of increased interest in theoretical supply chain literature recently. Most of the work so far however, has only considered a supply chain without downstream competition between retailers. Competition is ubiquitous in most market situations, hence, interactions between SI and retailer competition merits study as a first step in bringing the conversations and insights from this stream of literature to the real world. We present here a two-period and a three-period model of one manufacturer supplying an identical product to two retailers who form a Cournot duopoly. We also study a Commitment contract, where the manufacturer commits to all the selling seasons’ wholesale prices at the beginning of the 1st period. Commitment contracts have been shown previously to eliminate SI carriage over two selling seasons in the absence of retailer competition. We aim to deduce if this type of contract has the same effect in the presence of downstream competition. We determine closed-form Nash Equilibrium decision variable values for each of these models using game-theoretic modeling, a price-dependent linear demand function, and backward induction. We find that, the introduction of downstream Cournot duopoly competition leads to lower profits for both the manufacturer and retailer. This holds, whether the number of selling season is two or three. Consumer Surplus is also uniformly lower under retailer competition, compared to a downstream monopoly supply chain. When we try to deduce the effect of SI carriage under Cournot duopoly competition, by comparing an SC with Cournot duopoly competition and SI allowed between periods, to a similar SC with a Cournot duopoly downstream and a static, repeating, one-shot game in each period, with no SI carried – we find again that manufacturer and retailer profits are both lower when SI carriage is allowed. This holds whether the number of selling seasons is two or three. Consumer Surplus is also lower uniformly over both two and three selling seasons. Under a Commitment contract, over two selling seasons, the manufacturer ends up with an advantage, making a higher profit with downstream retailer competition, than compared to supplying to a monopoly downstream under the same contract. The retailers, while competing as a Cournot duopoly, are not able to use the relative advantage that comes from a Commitment contract to make a higher profit, as they are, when the downstream is a single retailer monopoly. The consumer also is disadvantaged by the introduction of downstream Cournot competition under a Commitment contract. When we compare a manufacturer supplying to a Cournot duopoly downstream of retailers, with, and without a Commitment contract (dynamic ordering), we see that the manufacturer and consumer benefit under a Commitment contract, making higher profits, but the retailer is at a disadvantage. It would be an interesting extension of this work to generalize the results from two and three selling seasons, presented here, to the “n” period case. It would also be benefi-cial to run empirical studies in real-world supply chains to validate if and to what extent the insights developed by this kind of game-theoretic modeling hold in a real-world supply chain setting. Development of contracts that are more effective than a Commitment con-tract in coordinating this supply chain would be another possible area for further research