Coordinating a two-level supply chain with delay in payments and profit sharing

Achieving effective coordination among suppliers and retailers has become a pertinent research issue in supply chain management. Channel coordination is a joint decision policy achieved by a supplier(s) and a retailer(s) characterized by an agreement on the order quantity and the trade credit scenario (e.g., quantity discounts, delay in payments). This paper proposes a centralized model where players in a two-level (supplier–retailer) supply chain coordinate their orders to minimize their local costs and that of the chain. In the proposed supply chain model the permissible delay in payments is considered as a decision variable and it is adopted as a trade credit scenario to coordinate the order quantity between the two-levels. Computational results indicate that with coordination, the retailer orders in larger quantities than its economic order quantity, with savings to either both players, or to one in the supply chain. Moreover, a profit-sharing scenario for the distribution of generated net savings among the players in the supply chain is presented. Analytical and experimental results are presented and discussed to demonstrate the effectiveness of the proposed model.     

贸易信用下考虑零售商违约风险的供应链协调问题研究

本文研究延迟支付和提前支付同时存在下的供应链协调问题。考虑由一个供应商和一个零售商构成的二级供应链,市场需求随机,延迟支付下零售商会增加订购数量,但由于其违约风险的存在,供应商会降低其交付量,最终导致供应商交付量小于零售商订购量,降低供应链收益。要求零售商提前支付部分货款则可以有效避免零售商的违约问题,通过建立延迟支付和提前支付同时存在下的零售商收益模型和供应商的收益模型,给出了零售商的最优订购量决策和供应商的最优交付量决策,通过调整延迟支付期限和提前支付比例,使得二者相等,并等于供应链整体收益最大化下的生产数量,实现供应链协调。最后通过数值算例分析了相关参数的敏感性等问题。     

Coordinating a three-level supply chain with delay in payments and a discounted interest rate

Both researchers and practitioners recognize the importance of the interactions between financial and inventory decisions in the development of cost effective supply chains. Moreover, achieving effective coordination among the supply chain players has become a pertinent research issue. This paper considers a three-level supply chain, consisting of a capital-constrained supplier, a retailer, and a financial intermediary (bank), coordinating their decisions to minimize the total supply chain costs. Specifically, we consider a retailer managing its cash through the supplier’s bank, in return for permissible delay in payments from the supplier. The bank, benefiting from increasing its cash holdings with the retailer’s cash deposits, offers the supplier a discount on its borrowing rate. We show that the proposed coordination mechanism achieves significant cost reduction, by up to 26.2%, when compared to the non-coordinated model. We also find that, with coordination, the retailer orders in larger quantities than its economic order quantity, and that a higher return on cash for the retailer leads to a higher order quantity. Furthermore, we empirically validate our proposed coordination mechanism, by showing that banks, retailers, and suppliers have much to gain through collaboration. Thus, using COMPUSTAT datasets for the years 1950 through 2012, we determine the most important factors that affect the behavior of the retailers and suppliers in granting and receiving trade credit. Our results indicate that engaging into such a coordination mechanism is a win–win situation to all parties involved.     

Optimal ordering policies for deteriorating items using a discounted cash-flow analysis when a trade credit is linked to order quantity

In today’s competitive market, in order to obtain a competition advantage, the supplier often offers the purchaser a longer permissible delay in payments or a price discount if the order quantity is greater than or equal to a predetermined quantity. As a result, in this paper, we establish an inventory model for the purchaser in which the supplier provides different trade credits. We then solve the inventory problem by using a discounted cash-flow (DCF) approach, characterize the optimal solution, and obtain some theoretical results to find the optimal order quantity and the optimal replenishment time. Finally, we provide several numerical examples to illustrate the results.     

基于订货阈值的供应商延期支付策略设计

针对完全信息下以供应商为核心企业的二级供应链库存系统,将全单位延期支付与部分延期支付两种手段相结合,并在考虑延期支付期限与订货量相关的条件下,设计了基于供应商视角和订货阈值的延期支付策略,从而得出此策略能使系统利润达到帕累托最优.最后,通过数值算例对相关结论进行了验证和灵敏度分析.     

An approach for community detection in social networks based on cooperative games theory

Detecting communities is of great importance in social network analysis. However it is an issue that has not yet been satisfactorily solved, despite the efforts made by interdisciplinary research communities over the past few years, because of the nature of complexity in deciding how community structures should be recognized. In this paper we propose an approach based on cooperative game theory for community detection in social networks. We regard individuals as players, and regard communities as coalitions formed by players, and model community detection problem as the formation and optimization of coalitions. Furthermore, we define coalition profile for players to indicate coalitions that players joined, the order of a coalition profile is defined as the number of coalitions in a coalition profile, and we introduce a utility function to measure preference of coalition profiles. Accordingly, we propose an algorithm to detect a coalition profile with maximal utility function values. We have implemented the algorithms developed in this study and experimental results demonstrate the effectiveness of our approaches.     

The stability of cooperative sourcing coalitions ‐ game theoretical analysis and experiment

Cooperative sourcing is when multiple firms form a coalition to merge similar processes using shared-service processing in order to leverage economies of scale and skill. This paper discusses how coalition partners should allocate coalition costs and benefits to ensure a stable coalition which minimizes the incentives for current or future coalition partners to withdraw from the coalition. The paper develops a formal cost allocation and benefit model which is then used in game theoretical analyses and bargaining experiments. The results show that proportional cost allocation is key to avoiding unstable coalitions. However, if coalition partners do not disclose their cost structures to facilitate a cooperative decision in favor of proportional cost allocation, but rather negotiate shared costs based on “closed books”, proportional cost allocation is rarely achieved. In such cases, the Shapley value has high predictive power and negotiators are in danger of making poor decisions that can lead to instable coalitions. These findings help sensitize managers to the structural threats inherent to multilateral negotiations of cooperative sourcing coalitions.     

A comprehensive note on “Lot‐sizing decisions for deteriorating items with two warehouses under an order‐size‐dependent trade credit”

To reduce inventory and increase sales, the supplier frequently offers the retailer a permissible delay in payments if the retailer orders more than or equal to a predetermined quantity. In 2012, Liao et al. proposed an economic order quantity model for a retailer with two warehouses when the supplier offers a permissible delay linked to order quantity. In this paper, we attempt to overcome some shortcomings of their mathematical model. Then, we apply some existing theoretical results in fractional convex programs to prove that the annual total variable cost is pseudoconvex. Hence, the optimal solution exists uniquely, which simplifies the search for the global minimum solution to a local minimum solution. Finally, we run a couple of numerical examples to illustrate the problem and compare the optimal solutions between theirs and ours.     

A decision rule for coordination of inventory and transportation in a two-stage supply chain with alternative supply sources

This paper deals with a two-stage supply chain that consists of two distribution centers and two retailers. Each member of the supply chain uses a (Q,R) inventory policy, and incurs standard inventory holding and backlog costs, as well as ordering and transportation costs. The distribution centers replenish their inventory from an outside supplier, and the retailers replenish inventory from one of the two distribution centers. When a retailer is ready to replenish its inventory that retailer must decide whether it should replenish from the first or second distribution center. We develop a decision rule that minimizes the total expected cost associated with all outstanding orders at the time of order placement; the retailers then repeatedly use this decision rule as a heuristic. A simulation study which compares the proposed policy to three traditional ordering policies illustrates how the proposed policy performs under different conditions. The numerical analysis shows that, over a large set of scenarios, the proposed policy outperforms the other three policies on average.     

Pricing,manufacturing and inventory policies for raw material in a three-level supply chain

We studied a decentralised three-layer supply chain including a supplier, a producer and some retailers. All the retailers order their demands to the producer and the producer order his demands to the supplier. We assumed that the demand is price sensitive and shortage is not permitted. The goal of the paper is to optimise the total cost of the supply chain network by coordinating decision-making policy using Stackelberg–Nash equilibrium. The decision variables of our model are the supplier's price, the producer's price and the number of shipments received by the supplier and producer, respectively. To illustrate the applicability of the proposed model numerical examples are presented.