价值创造结构、K-重划分与联盟稳定性变化研究

与传统以“价值增加”为核心的边际分析不同,强调价值创造“结构”本身的特性.认为联盟结构的特征函数集合描述了价值创造的力量结构和联盟是否稳定的内在属性.研究表明,价值创造的特征函数结构同联盟核存在的最小价值创造的值之间存在线性变换关系,联盟的最大的k-重划分值等于联盟核存在的最小值.在联盟稳定性变化的临界状态下,其划分点作为了联盟结构的“合并”和“分解”点,不能出现在交集为空的互补性集合之间,各子联盟集合满足价值创造非互补性和线性可加性.     

Stability and Preference Alignment in Matching and Coalition Formation

We study matching and coalition formation environments allowing complementarities and peer effects. Agents have preferences over coalitions, and these preferences vary with an underlying, and commonly known, state of nature. Assuming that there is substantial variability of preferences across states of nature, we show that there exists a core stable coalition structure in every state if and only if agents' preferences are pairwise‐aligned in every state. This implies that there is a stable coalition structure if agents' preferences are generated by Nash bargaining over coalitional outputs. We further show that all stability‐inducing rules for sharing outputs can be represented by a profile of agents' bargaining functions and that agents match assortatively with respect to these bargaining functions. This framework allows us to show how complementarities and peer effects overturn well known comparative statics of many‐to‐one matching.     

The Farsighted Stable Set

Harsanyi (1974) criticized the von Neumann–Morgenstern (vNM) stable set for its presumption that coalitions are myopic about their prospects. He proposed a new dominance relation incorporating farsightedness, but retained another feature of the stable set: that a coalition S can impose any imputation as long as its restriction to S is feasible for it. This implicitly gives an objecting coalition complete power to arrange the payoffs of players elsewhere, which is clearly unsatisfactory. While this assumption is largely innocuous for myopic dominance, it is of crucial significance for its farsighted counterpart. Our modification of the Harsanyi set respects “coalitional sovereignty.” The resulting farsighted stable set is very different from both the Harsanyi and the vNM sets. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single‐payoff allocation. This condition roughly establishes an equivalence between core allocations and the union of allocations over all single‐payoff farsighted stable sets. We then conduct a comprehensive analysis of the existence and structure of farsighted stable sets in simple games. This last exercise throws light on both single‐payoff and multi‐payoff stable sets, and suggests that they do not coexist.     

产品组合竞争下远视互补品供应商联盟的稳定结构

考虑由4个远视供应商与1个零售商所组成的两层供应链系统,基于最大一致集的概念,探讨部分供应商可替代时互补品联合销售联盟的远视稳定结构。研究发现:当供应商的成本相差较小时,如果两类产品组合的零售竞争强度较小,则远视供应商会偏好各自独立销售给下游零售商;如果两类产品组合的零售竞争强度较大,则远视供应商会偏好形成一个由3个供应商联合销售的大联盟。当供应商的成本相差较大时,远视供应商会偏好形成联合销售的大联盟,或者偏好各自独立销售给下游零售商。但是,两个供应商形成的联合销售联盟不是远视稳定的。     

Collaborative job scheduling in the wine bottling process

This paper proposes a horizontal collaborative approach for the wine bottling scheduling problem. The opportunities for collaboration in this problem are due to the fact that many local wine producers are usually located around the same region and that bottling is a standard process. Collaboration among wineries is modeled as a cooperative game, whose characteristic function is derived from a mixed integer linear programming model. Real world instances of the problem are, however, unlikely to be solved to optimality due to its complex combinatorial structure and large dimension. This motivates the introduction of an approximated version of the original game, where the characteristic function is computed through a heuristic procedure. Unlike the exact game, the approximated game may violate the subadditivity property. Therefore, it turns relevant not only to find a stable cost allocation but also to find a coalition structure for selecting the best partition of the set of firms. We propose a maximum entropy methodology which can address these two problems simultaneously. Numerical experiments illustrate how this approach applies, and reveal that collaboration can have important positive effects in wine bottling scheduling decreasing delay by 33.4 to 56.9% when improvement heuristic solutions are used. In contrast to the exact game in which the grand coalition is always the best outcome, in the approximated game companies may be better forming smaller coalitions. We also devise a simple procedure to repair the characteristic function of the approximated game so that it recovers the subadditivity property.     

The Development of Green Infrastructure Policy in the North West Region of the UK 2005–2010

ABSTRACT

This article examines the development of green infrastructure policy-making in the North West region of the UK 2005–2010, through the articulation of three phases. Drawing on a conceptualisation of discourse coalitions, it is argued that this instance of the green infrastructure policy-making process became a way of bringing together various stakeholders around a shared goal. The activities that took place and how green infrastructure was conceptualized ensured that a range of policy interests was represented, and consequently, a stable discourse coalition was formed around economic priorities.     

Storage constrained vendor managed inventory models with unequal shipment frequencies

We consider a supply chain where a vendor manages its multiple retailers' stocks under a vendor managed inventory (VMI) contract that specifies upper stock limits at the retailers' premises and overstock costs for exceeding those limits. We formulate a mixed integer nonlinear program that minimizes total supply chain costs and allows unequal shipment frequencies to the retailers. We develop an algorithm to solve its relaxed version which provides a lower bound cost solution. We propose a cost efficient heuristic procedure to generate delivery schedules to the retailers. We conduct a sensitivity analysis to provide insights on the performance of the proposed heuristic. Results show that our heuristic finds optimal or near optimal solutions, and it proposes substantial savings compared to the total supply-chain cost in the cases where there is no VMI and where there is VMI but with equal shipment frequencies to retailers.     

The Impact of Forecast Errors on Early Order Commitment in a Supply Chain*

Supply chain partnership involves mutual commitments among participating firms. One example is early order commitment, wherein a retailer commits to purchase a fixed‐order quantity and delivery time from a supplier before the real need takes place. This paper explores the value of practicing early order commitment in the supply chain. We investigate the complex interactions between early order commitment and forecast errors by simulating a supply chain with one capacitated supplier and multiple retailers under demand uncertainty. We found that practicing early order commitment can generate significant savings in the supply chain, but the benefits are only valid within a range of order commitment periods. Different components of forecast errors have different cost implications to the supplier and the retailers. The presence of trend in the demand increases the total supply chain cost, but makes early order commitment more appealing. The more retailers sharing the same supplier, the more valuable for the supply chain to practice early order commitment. Except in cases where little capacity cushion is available, our findings are relatively consistent in the environments where cost structure, number of retailers, capacity utilization, and capacity policy are varied.     

The value of VMI beyond information sharing in a single supplier multiple retailers supply chain under a non-stationary (Rn,Sn) policy

This study aims to determine the value of vendor-managed inventory (VMI) over independent decision making with information sharing (IS) under non-stationary stochastic demand with service-level constraints. For this purpose, we utilize mixed-integer linear programming formulations to quantify the benefits that can be accrued by a supplier, multiple retailers and the system as a whole by switching from IS to VMI. More specifically, we investigate the incremental value that VMI provides beyond IS in terms of expected cost savings, inventory reductions, and decrease in shipment sizes from the supplier to the retailers by conducting a large number of computational experiments. Results reveal that the decision transfer component of VMI improves these performance measures significantly when the supplier׳s setup cost is low and order issuing efficiency is high. The benefits offered by VMI are negligible under the problem settings where the supplier׳s order issuing efficiency is low and the production setup serves solely a single replenishment under IS.     

Duality Approaches to Economic Lot‐Sizing Games

Sharing common production, resources, and services to reduce cost are important for not for profit operations due to limited and mission‐oriented budget and effective cost allocation mechanisms are essential for encouraging effective collaborations. In this study, we illustrate how rigorous methodologies can be developed to derive effective cost allocations to facilitate sustainable collaborations in not for profit operations by modeling the cost allocation problem arising from an economic lot‐sizing (ELS) setting as a cooperative game. Specifically, we consider the economic lot‐sizing (ELS) game with general concave ordering cost. In this cooperative game, multiple retailers form a coalition by placing joint orders to a single supplier in order to reduce ordering cost. When both the inventory holding cost and backlogging cost are linear functions, it can be shown that the core of this game is non‐empty. The main contribution of this study is to show that a core allocation can be computed in polynomial time under the assumption that all retailers have the same cost parameters. Our approach is based on linear programming (LP) duality. More specifically, we study an integer programming formulation for the ELS problem and show that its LP relaxation admits zero integrality gap, which makes it possible to analyze the ELS game by using LP duality. We show that there exists an optimal dual solution that defines an allocation in the core. An interesting feature of our approach is that it is not necessarily true that every optimal dual solution defines a core allocation. This is in contrast to the duality approach for other known cooperative games in the literature.     

Cooperative sales promotion with a point-sharing policy: Advantages and limitations

Consumption-point programs have been commonly implemented in retail industries in efforts to promote sales and improve customer loyalty. In Korea, many retailers from different industries use a point-sharing policy to augment the conventional consumption-point program of each retailer. In a multi-retailer coalition under such a cooperative sales promotion policy, by purchasing from one coalition retailer, customers earn points that they can redeem points at other retailers in the coalition. On one hand, the introduction of this policy gives customers great flexibility for redeeming earned points, which can increase the demand at all retailers who promote the policy. On the other hand, the additional product costs associated with the points created by one retailer may spill over and be partly borne by other retailers, possibly distorting the coalition members’ equilibrium decisions under decentralized control. Under the general assumptions about the demand functions, we developed a model consisting of two retailers with fixed retail prices and addressed the retailers’ equilibrium decisions under a pure point-sharing policy. The findings suggest that the policy resulted in a cost spillover phenomenon. Then, we revealed that a pure point-sharing policy may fail to maximize the total profit of the coalition. Moreover, we showed that a pure point-sharing policy does not dominate the individual point scheme, which may explain the reason that point sharing is useful but not ubiquitously used in the real world. Our numerical examples also illustrate the way a pure point-sharing policy influences retailers’ profits when retail prices are decision variables. To improve the overall profit under the point-sharing policy further, we propose a target rebate contract to coordinate a pair of retailers. This contract can maximize the total profit and arbitrarily split the profit between retailers.     

Shipping Fees or Shipping Free? A Tale of Two Price Partitioning Strategies in Online Retailing

In this article, we study the price partitioning decisions of online retailers regarding shipping and handling (S&H) fees. Specifically, we analyze two partitioning formats used by retailers in this context. In the first scenario, retailers present customers with a price that is partitioned into a product price and a separate S&H surcharge (the PS strategy); in the second, customers are offered free shipping through a non‐partitioned format where the product price already includes the shipping cost (the ZS strategy). We first develop a stylized game‐theoretic model that captures the competitive dynamics between (and within) these two formats. Analysis of the model provides insights into how both firm and product level characteristics drive a retailer's strategic choice regarding which partitioning format to adopt and, hence, determines the equilibrium market structure in terms of proportion of ZS and PS retailers. Subsequently, we conduct empirical analyses, based on product and S&H prices data for two different product categories (digital cameras and printers) collected from online retailers, to validate all the results of our theoretical model. We establish that PS retailers charge lower product prices than ZS ones, but the total price (product + S&H) charged is higher for the first group. The S&H charge for PS retailers can be significant—it is, on average, 5.4% (printers) and 3.0% (digital cameras) for our two product categories. Furthermore, retailers which are popular and/or face risky cost environment are more likely to opt for the ZS strategy, while retailers whose portfolio mostly includes large or heavy products with high cost (S&H)‐to‐price ratios usually choose the PS strategy. Lastly, our empirical study also illustrates that the price adjustment behavior of retailers is affected by their shipping‐fee policies—for example, ZS retailers change their product prices almost 1.5 times more frequently than PS ones.     

联合订货区间值EOQ模型及变权Shapley值成本分摊方法

研究多个销售商企业组成联盟向一个供应商订购同种商品的联合订货问题。考虑到实际问题中很难预测到精确的需求，本文用区间表示单位时间需求量，研究允许缺货的销售商企业联合订货区间值EOQ模型，其中缺货完全回补。以联合订货平均成本最小为目标，结合连续有序加权集结算子求解出联合订货的周期、区间值订货量和区间值平均成本。定义变权Shapley值，给出区间值合作博弈的区间值变权Shapley值的求解方法，得出区间值变权Shapley值的表达式可直接利用相关联盟值的左、右端点计算得到。考虑联盟和局中人的相对重要性，结合需求率确定合成权重，提出基于区间值变权Shapley值的联合订货成本分摊方法。利用数值算例验证模型和方法的有效性。本文可为解决联合订货成本分摊问题提供决策参考。     

碳交易机制下零售商合作的费用分配研究

在一个由单供应商和多个零售商组成的二阶供应链中，研究碳交易机制下多零售商合作的订货决策问题。对完全信息下零售商合作的费用分配问题，应用合作博弈理论建立了费用分配的博弈模型，证明了博弈为子模博弈且设计了属于核心的费用分配方案，该方案不仅可通过总体单调分配机制实现而且可使大联盟长远稳定。对不完全信息下零售商合作的费用分配问题，证明了纯策略纳什均衡的存在性。研究结果表明，零售商的合作不仅能降低总费用，而且能降低碳排放量；各零售商在不完全信息下分担的费用大于完全信息下分担的费用。     

How Costs and Heterogeneous Consumer Price Sensitivity Interact with Add‐On Pricing

Firms often cite cost savings as a reason why they charge separately for add‐ons. Firms also often face situations where consumers' price sensitivity is correlated with their valuation of add‐ons. While cost savings may directly translate into profit gains in some scenarios, this study examines the strategic implications of add‐on pricing and is the first to suggest that cost savings from add‐on pricing may in fact result in profit loss for firms when consumers are heterogeneous in price sensitivity. This is because add‐on pricing can trigger a revenue loss that exceeds any cost savings, thus leading to a negative net profit change for competing firms. Even if firms have the capability to pre‐commit to not adopting add‐on pricing, we show that competing firms can be locked in a prisoner's dilemma where all choose to adopt add‐on pricing and lose profits (as compared to none adopting add‐on pricing). We further show the possibility that the greater the cost of providing the add‐on (and the greater the cost savings generated from add‐on pricing), the worse this profit loss gets.     

非瞬时补货下改良品联合采购决策

联合采购往往使订货批量成倍增加,从而更易享受供应商提供的价格折扣,因此联合采购受到零售商们的青睐。考虑由单供应商与多零售商组成的二级改良品供应链中,供应商对零售商提供非瞬时补货,分别建立零售商独立采购与联合采购的单位时间成本函数,求解出两种采购模式的最小单位时间成本并对之进行比较,得到联合采购优于独立采购的必要条件。同时,以联合采购的联盟成本作为分摊对象,应用多人合作博弈理论,将联合采购的成本分摊问题构造成多人合作博弈问题,给出最小核心法的成本分摊思路。通过数值算例演示成本分摊过程,给出净改良率对订货参数及成本参数的敏感性分析,并对四种成本分摊算法的分摊结果作出比较。     

Impact of Retailers with Knowledge of Supplier's Inventory on Supply Chain Performance

We model a supply chain consisting of a supplier and multiple retailers facing deterministic demand. We denote some retailers as strategic in the sense that given the supplier inventory information, they will implement the optimal stocking policy by incorporating such information. On the other hand, some retailers are denoted as naïve in the sense that they ignore supply information and resort to a simplistic ordering policy. Naïve retailers learn the optimal policy over time and adjust their orders accordingly. We study the dynamics of this game and investigate the impact of such strategic and naïve retailers on the cost, ordering pattern and stocking policies of all parties. We analyze the supply chain under two scenarios: the centralized supply chain where the objective is to minimize the total supply chain cost, and the decentralized supply chain where each self‐interested player minimizes its own cost in a Stackelberg game setting. We fully characterize the optimal policies under both centralized and decentralized scenarios and show that, surprisingly, the supply chain might be better off by virtue of naïve retailers. The result is driven by the fact that strategic and naïve players’ decisions shift the positioning of inventory in the supply chain with its final impact being determined by the relative costs of different retailer‐types. Our results also offer managerial insights into how access to supply information can improve supply chain performance.     

A Cooperative Savings Game Approach to a Time Sensitive Capacity Allocation and Scheduling Problem

We consider a competitive scheduling setting with arbitrary number of agents each having the option to utilize two parallel resources to satisfy its demand: (i) an in‐house resource dedicated to process only the tasks of each specific agent, and (ii) a flexible resource capable of processing all agents' workloads. In a noncooperative setting, each agent would determine how much of its demand it will subcontract to the flexible resource with the objective to deliver its entire demand as quickly as possible subject to the priority rules set by the owner of the flexible resource (i.e., third‐party). In this study, we also allow for agents to coalesce with other agents and update their initial subcontracting decisions to attain rescheduling savings. Evidently, a grand coalition of all agents can coordinate to achieve the maximum savings possible, but the resulting schedule may yield individual losses for a subset of agents (which we refer to as “losers”), thus necessitating a transfer payment scheme to distribute the rescheduling savings among the agents in an equitable way. We model the rescheduling interactions among the agents as a cooperative savings game, and propose savings distribution schemes that invoke the core allocation concept.     

Two efficient values of cooperative games with graph structure based on $$\tau $$-values

The paper is devoted to value concepts for cooperative games with a communication structure represented by a graph. Under assumptions that the players partition themselves into ‘components’ before realizing cooperation and the worth of the grand coalition not less than the sum of the worths of all components, the fair distribution of surplus solution and the two-step \(\tau \)-value are introduced as two efficient values for such games, each of which is an extension of the graph \(\tau \)-value. For the two efficient values, we discuss their special properties and we provide their axiomatic characterizations in views of those properties. By analysing an example applied to the two values, we conclude that the fair distribution of surplus solution allocates more surplus to the bigger coalitions and favors the powerful players, while the two-step \(\tau \)-value benefits the vulnerable groups and inspires to form small coalitions.     

具有联盟优先关系的模糊合作博弈的目标规划求解模型

用合作博弈研究实际管理问题中的分配方案时，常常存在一些不重要联盟或无效联盟，这些联盟影响公平合理的分配方案。因此，联盟的重要程度成为求解合作博弈必不可少的因素。本文考虑了联盟的重要性和局中人参与联盟的不确定性，研究了具有优先关系的模糊联盟合作博弈(简称为模糊合作博弈)。首先，借助于目标规划模型的优先因子可以表征联盟重要程度的思想，通过构建多优先级目标规划模型，得到模糊合作博弈新的解。其次，证明了构建的多优先级目标规划模型的解和模糊合作博弈的核心之间具有重要对应关系。最后，通过数值实例和比较分析，说明本文提出的多优先级目标规划模型求解模糊合作博弈问题的合理性和有效性。研究表明：(1)本文提出的多优先级目标规划模型考虑不同联盟重要程度，得到的解符合“多劳多得”原则，能够更公平合理解决实际管理中的分配问题。(2)本文的目标规划模型同时适用于求解存在联盟特征函数值缺失的合作博弈。与已有合作博弈的解进行比较分析，该模型无需估算无效联盟的特征函数缺失数据得到的分配值更为准确。从而，说明本文给出的目标规划求解模糊合作博弈解的模型，更符合许多管理学问题的实际情况。(3)通过多优先级目标规划模型最优解是否存在可判断模糊合作博弈的核心存在情况，若核心存在则该模型通过目标规划软件包可得到核心内的一个解，这样也得到了一个判断合作博弈核心是否存在的标准。(4)目标规划模型可弥补已有合作博弈解的一些不足，如核心可能为空集，Shapley值和最小二乘预核仁可能不满足个体合理性等。本文构建的多优先级目标规划模型不仅能求解联盟具有优先关系的模糊合作博弈，而且能够求解一般合作博弈的解，该目标规划模型作为合作博弈一种新的求解方法，能更有效地解决实际管理中的分配问题，具有更加广泛的应用价值。