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.     

On the core of routing games

A repairman makes a round-trip along a set of customers. He starts in his home location, visits each customer exactly once, and returns home. The cost of his trip has to be shared by the customers. A cooperative cost game, calledrouting game, is associated with this allocation problem, and anO(n ²) algorithm is given which computes a core element of a routing game if the core is non-empty. The non-emptiness of the core depends on the tour which is traversed by the repairman. Several procedures are given to construct tours which guarantee the non-emptiness of the core.     

On stability of collaborative supplier selection

This note discusses the possibility of fair gain sharing in cooperative situations where players optimally partition themselves across a number of alternative channels. An example is group purchasing among a set of buyers facing with a range of suppliers. We introduce channel selection games as a new class of cooperative games and give a representation of their cores. With two channels (suppliers), the game has a non-empty core if the gain functions across every individual channel is supermodular.     

A note on the 5-person traveling salesman game

LetN=1,2,...,n be a set of customers andG=(N {0},E) an undirected connected graph with non-negative edge lengths. 0 is the home location of a salesman who visits the customers inN. Each subset can invite the salesman to visit its members only. The costc(S) of coalitionS is the length of a shortest tour that starts in 0, visits each customer inS at least once and returns to 0. The cooperative cost game defined in this way is called a (symmetric) traveling salesman game (TSG).The core of a TSG can be empty when ¦N¦ 6 and it was proved that it always has a non-empty core when ¦N¦ 4. In this note we shall prove that a TSG always has a non-empty core when ¦N¦=5.     

Congestion network problems and related games

This paper analyzes network problems with congestion effects from a cooperative game theoretic perspective. It is shown that for network problems with convex congestion costs, the corresponding games have a non-empty core. If congestion costs are concave, then the corresponding game has not necessarily core elements, but it is derived that, contrary to the convex congestion situation, there always exist optimal tree networks. Extensions of these results to a class of relaxed network problems and associated games are derived.     

On balanced games with infinitely many players: Revisiting Schmeidler's result

We consider transferable utility cooperative games with infinitely many players and the core understood in the space of bounded additive set functions. We show that, if a game is bounded below, then its core is non-empty if and only if the game is balanced. This finding generalizes Schmeidler (1967) “On Balanced Games with Infinitely Many Players”, where the game is assumed to be non-negative. We also generalize Schmeidler's (1967) result to the case of restricted cooperation too.     

The effect of supplier capacity on the supply chain profit

In this paper, we study the role of capacity on the efficiency of a two-tier supply chain with two suppliers (leaders, first tier) and one retailer (follower, second tier). The suppliers compete via pricing (Bertrand competition) and, as one would expect in practice, are faced with production capacity. We consider a model with differentiated substitutable products where the suppliers are symmetric differing only by their production capacity. We characterize the prices, production amounts and profits in three cases: (1) the suppliers compete in a decentralized Nash equilibrium game, (2) the suppliers “cooperate” to optimize the total suppliers’ profit, and (3) the two tiers of the supply chain are centrally coordinated. We show that in a decentralized setting, the supplier with a lower capacity may benefit from restricting her capacity even when additional capacity is available at no cost. We also show that the loss of total profit due to decentralization cannot exceed 25 % of the centralized chain profits. Nevertheless, the loss of total profit is not a monotonic function of the “degree of asymmetry” of the suppliers’ capacities. Furthermore, we provide an upper bound on the supplier profit loss at equilibrium (compared with the cooperation setting) that depends on the “market power” of the suppliers as well as their market size. We show that there is less supplier profit loss as the asymmetry (in terms of their capacities) increases between the two suppliers. The worst case arises when the two suppliers are completely symmetric.     

存在破产成本时保理授信下供应商赊销策略研究

在存在破产成本的前提下,构建了保理商确定授信额度的量化模型,并研究了供应商如何在保理授信下确定赊销量的问题。研究结果表明,保理商的授信以保理费率不低于临界值为前提。当保理费率高于一定水平时,授信额度较高,供应商将在额度内进行赊销交易。否则,供应商将超出授信额度进行赊销交易,并且此时,若固定破产成本高于阈值,供应商最优赊销量存在上限,保理对供应链的作用主要体现在其风险分担功能上;若固定破产成本低于阈值,供应商最优赊销量存在下限,保理对供应链的作用主要体现在其融资功能上。     

On computational complexity of membership test in flow games and linear production games

Let Γ≡(N,v) be a cooperative game with the player set N and characteristic function v: 2^N→R. An imputation of the game is in the core if no subset of players could gain advantage by splitting from the grand coalition of all players. It is well known that, for the flow game (and equivalently, for the linear production game), the core is always non-empty and a solution in the core can be found in polynomial time. In this paper, we show that, given an imputation x, it is NP-complete to decide x is not a member of the core, for the flow game. And because of the specific reduction we constructed, the result also holds for the linear production game. Received: October 2000/Final version: March 2002     

基于投资投入的销售商对供应商激励研究

降低成本的投资是为了改善单位成本的效率. 它保证了单位成本在以后的每个生产过程中均处于较低的水平. 然而,投资的套牢和补偿问题的存在往往会降低供应链投资的积极性. 为解决这个问题,采用Stackelberg博弈的分析思路,分别研究投资能够被观察时和投资不能够被观察时的激励契约,得到如下结论：若销售商进行生产投资,则投资是不足的;若供应商进行生产投资,供应商对生产投资的水平甚至有可能高于链最优的投资水平.     

Supply chain scheduling with receiving deadlines and non-linear penalty

We study the operations scheduling problem with delivery deadlines in a three-stage supply chain process consisting of (1) heterogeneous suppliers, (2) capacitated processing centres (PCs), and (3) a network of business customers. The suppliers make and ship semi-finished products to the PCs where products are finalized and packaged before they are shipped to customers. Each business customer has an order quantity to fulfil and a specified delivery date, and the customer network has a required service level so that if the total quantity delivered to the network falls below a given targeted fill rate, a non-linear penalty will apply. Since the PCs are capacitated and both shipping and production operations are non-instantaneous, not all the customer orders may be fulfilled on time. The optimization problem is therefore to select a subset of customers whose orders can be fulfilled on time and a subset of suppliers to ensure the supplies to minimize the total cost, which includes processing cost, shipping cost, cost of unfilled orders (if any), and a non-linear penalty if the target service level is not met. The general version of this problem is difficult because of its combinatorial nature. In this paper, we solve a special case of this problem when the number of PCs equals one, and develop a dynamic programming-based algorithm that identifies the optimal subset of customer orders to be fulfilled under each given utilization level of the PC capacity. We then construct a cost function of a recursive form, and prove that the resulting search algorithm always converges to the optimal solution within pseudo-polynomial time. Two numerical examples are presented to test the computational performance of the proposed algorithm.     

基于合作博弈的组装供应链转移定价策略

研究了由n个供应互补的原料产品的上游供应商和一个组装生产最终产品的下游组装商组成的集团公司内部的转移价格问题。其中下游组装商面临的是一个价格敏感型的需求。每个上游供应商可以独立决策其销售价格,并决定是否以谈判的价格出售原料产品给下游组装商。供应链系统内的所有供应商和组装商都可以自由决定彼此之间是否进行合作。结果表明,在大联盟结构下,供应链的利润是最高的。为了分配大联盟结构下供应链系统总的利润,本文构造了特征函数具有超模性质的合作博弈,并利用Shapley值分配方法给出了整个供应链系统内部的转移价格。     

Stock Control with Two Suppliers and Normal Lead Times

This paper helps practitioners to compute the mean and variance of the lead time demand distribution when two suppliers are used simultaneously to replenish stock of a single item. The lead times of each supplier are assumed to be normally distributed and two replenishment orders are placed, one with each supplier, at the same time. The results indicate that the reorder level required to give a specific probability of no stock-out during replenishment is lower when using two suppliers simultaneously. Tables have also been prepared to help practitioners determine the minimum sizes of replenishment orders when two suppliers are used and replenishment orders are placed at the same time.     

Suppliers’ competition and manufacturer’s product mix: the role of ingredient brand

This paper proposes a pricing game among a manufacturer and two competing suppliers. One of the suppliers establishes an ingredient brand, which can enhance the valuations of the end products. The equilibrium is derived to investigate the impact of the ingredient brand awareness and the production costs on the suppliers’ pricing competition, the manufacturer’s product mix and retail price(s), and profits. The result shows that the manufacturer may provide unique product or differentiated products, depending on the effectiveness of ingredient branding strategy. We distinguish two different monopolistic scenarios in supplier market and provide the condition for each supplier to survive. We find that the ingredient branding strategy mitigates the pricing competition between suppliers and benefits the manufacturer in a low production cost industry.     

造船企业与供应商产品质量演化博弈分析

船舶作为大型复杂系统产品,其上游供应商所提供的零部件质量会对最终产品的质量产生重要影响。在考虑造船企业和供应商质量策略和收益的基础上,本文构建了双方的演化博弈模型,对其策略的稳定性开展分析;进一步地,引入了造船企业的动态惩罚措施研究如何对双方的策略产生影响。研究结果表明:(1)造船企业对配套供应商采取产品质量提升措施的奖励和惩罚力度、供应商采取相应措施的收益与成本会直接影响博弈的相关结果;(2)造船企业和配套供应商在三种条件下存在各自的演化稳定策略,同时在一定条件下系统的演化过程呈现周期性质的特征;(3)当造船企业采取动态惩罚措施时,此博弈模型存在稳定的Nash均衡点。研究结果可以为造船企业督促供应商改善供货质量提供决策支持。     

基于博弈视角的中小型供应商联盟决策研究

在绿色供应链管理背景下,中小型供应商在供应链中处于相对弱势的地位,往往在强势的供应链核心企业面前失去定价权;此外,由于其在经济和技术上的双重困难,中小型供应商的生产活动所造成的环境污染日益严重。供应链联盟作为一种新型的企业合作模式,是解决中小型供应商发展问题的有效途径。本文试图构建绿色供应链下的中小型供应商战略联盟博弈模型,并从博弈角度探讨中小型供应商联盟的必要性、可行性以及联盟的最优决策策略,以期探索中小型供应商依托供应链联盟而形成的发展模式。研究结果显示,中小型供应商联盟有利于整体供应链的绿色发展,提升中小型供应商在供应链中的地位。本研究结论能够为绿色供应链中的各方企业提供决策建议。     

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.     

Analysis of a Continuous Review Stock-control Model with Multiple Suppliers

This paper analyses the use of multiple suppliers to replenish one stock item. The replenishment order is split into several portions, one for each supplier, and orders for these portions are placed simultaneously with the respective suppliers. Approximate expressions are derived for the mean and variance of the effective lead time, which is the minimum of the individual lead times of each supplier. These results give effective lead-time-demand mean and variance that are smaller than those of the individual suppliers. The results can be used to lower the operating cost of the stocking policy.     

基于双层博弈模型的民用航空产业链研究

本文针对民用航空市场中的大飞机制造商及航空发动机制造商建立双层博弈模型。在上层模型中,大飞机制造商以市场利润为目标决定其产量及对各发动机供应商的采购量;在下层模型中,航空发动机供应商通过求解一个优化问题决定其自身产量。在求解过程中,将下层优化问题转化为KKT条件,并作为上层优化问题的约束条件,使用分布式迭代算法(Distributed iterative algorithm),进行编程求解。本文通过求解波音-空客双寡头格局下的市场均衡对模型的有效性进行验证,并进一步分析国产大飞机C919量产后市场均衡的变化。