Optimal pricing and order quantity for the newsvendor problem with free shipping

To attract and keep customers, companies, especially those in e-business, are increasingly offering free shipping to buyers whose order sizes exceed the free shipping quantity. In this paper, given the supplier offers free shipping and the retailer faces stochastic demand, we determine the retailer's (i.e., the newsvendor's) optimal order quantity and the optimal selling price simultaneously. We consider two different ways in which price affects the demand distribution, namely price only affects the location or scale of the demand distribution. We explicitly incorporate the supplier's quantity discount and transportation cost into the models. The transportation cost function is very general, which includes those most commonly used in the literature. We numerically examine the impacts of free shipping, quantity discount, transportation cost, and demand variance on the retailer's optimal order quantity and pricing decisions. We find that even though the retailer faces uncertain demand, free shipping can effectively encourage the retailer to order more of the good and can benefit the supplier, the retailer, and the end customers. An increase in transportation cost or a decrease in purchase price will induce the retailer to order more of the good and decrease the retail price. With increasing demand variance, the retailer should order more of the good. We also find that the newsvendor can cope with demand variance by taking advantage of free shipping.     

基于收益共享的供应链中断协调研究

本文假定市场需求不确定和供给存在中断危机，同时考虑订货过剩损失和缺货成本，研究了由零售商、主供应商和备份供应商组成的供应链网络，构建了收益共享合同协调模型，通过相关参数的设定达到供应链协调。供应链协调时的供货量及整体利润均大于分散模型；备份供应商的供货量及利润随着中断危机的增大而增加，零售商利润也随之增加。     

Coordination in a retailer-led supply chain through option contract

This paper develops a model to study channel coordination and risk sharing in a retailer-led supply chain. Such chains are characterized by a dominant retailer who aims to coordinate the upstream production quantity. We investigate a coordinating contract based on an option with two parameters. An option price is paid by the retailer for each additional unit of product reserved beyond the initial order. An exercise price serves as the unit purchasing price when the retailer sets a second order if realized demand is more than the initial order. A successful coordination needs two conditions. One condition is to maintain a negative correlation between exercise price and option price. Particularly, we draw the functional form. The other is that the firm commitment must be lower than the optimal production quantity in a centralized system. In a risk sharing mechanism, we prove that such a contract brings benefit to each party.     

Retailer policy, uncertainty reduction, and supply chain performance

We investigate how the retailer’s inventory policy affects the total cost of a serial supply chain. When the retailer uses the locally optimal (s,S) policy, there is randomness in order time and order quantity to the supplier whereas the supplier sees randomness only in order quantity for the suboptimal (R,T) policy and only in order time for another suboptimal (Q,r) policy. Using an extensive computational study, we find that the suboptimal policies perform better from the total supply chain perspective. The benefit of policy changes is magnified when the retailer costs are low, when the supplier costs are high, and when there is information sharing.     

Supply contract with options

The purpose of this paper is to analyze the impact of an option contract for two companies of a supply chain: retailer and supplier. With an option contract the retailer orders a quantity of units and has the right to modify his order if necessary. A model to calculate the performance of an option contract in terms of contract value for the two companies engaged is presented. The two considered cases are multiple suppliers and one retailer, and one supplier and one retailer. The performance improvement obtained using this kind of contract is compared by simulation.     

Optimal inventory policy with noninstantaneous receipt under trade credit

In the last two decades, the models for inventory replenishment policies under trade credit have been widely studied by several researchers. However, the extant papers only consider the effects of permissible delay in payments in the inventory systems. In some situations, the supplier also may offer a cash discount to encourage retailer to pay for his purchases quickly. On the other hand, an inventory model with instantaneous receipt is not a common feature in actual practice. For generality, this study develops an inventory model with noninstantaneous receipt under trade credit, in which the supplier provides not only a permissible delay but also a cash discount to the retailer. We then characterize the optimal solution and provide an easy-to-use criterion to find the optimal order strategies. Finally, several numerical examples are presented to illustrate the theoretical results.     

零售商的风险规避特性和公平偏好对绿色供应链运作的影响

针对市场需求的不确定性,本文通过建立风险规避型零售商与风险中性供应商的Stackelberg博弈模型,供应商为主导者,综合考虑零售商风险规避特性和公平偏好心理对该供应链运作产生的影响。研究发现,当风险规避型零售商不具有公平意识时,零售商的风险规避程度与供应商的批发价、绿色创新投入水平以及供应商和供应链整体的效用正相关;供应商的绿色成本系数的大小可影响风险规避程度对产品售价以及零售商效用的影响。当风险规避型零售商具有公平偏好时,零售商的公平偏好负向影响产品售价、批发价以及供应商绿色投入水平和供应商效用;零售商公平偏好对零售商以及供应链效用产生的影响受到零售商风险规避程度的影响。     

考虑质押物损耗的存货质押融资决策模型

质押物的完整性是关系存货质押融资业务能否顺利开展的重要问题,质押物损耗长期困扰各参与方,阻碍了存货质押融资业务的顺利开展。考虑质押物损耗和第三方物流企业对质押物监管所带来的损耗节约的基础上,研究了存货质押融资最优决策。研究表明:当零售商的初始现金余额很低时,零售商的最优订购数量随着初始现金余额的增加而减少,之后零售商最优订货量保持不变,直到初始现金余额大于某一水平时,零售商的最优订货量开始增加;在零售商贷款且不存在破产风险时,银行的收益随着零售商初始现金余额增加而减少;当风险估值是需求的增函数时,零售商的最优订货量随利率减少。     

前景理论框架下基于期望的损失厌恶报童博弈

本文运用前景理论,考虑了损失厌恶报童期望水平对其损失厌恶程度的影响,扩展了损失厌恶报童模型,分析了多个基于期望的损失厌恶报童向一个风险中性供应商竞争订货的情形,研究了报童相关参数对报童均衡总订货量的影响。在随机需求情形下引入期望参考利润水平,首先基于前景理论建立单个基于期望的损失厌恶报童效用函数,其次推导出多个基于期望的损失厌恶报童博弈模型,然后证明了该博弈模型对称纯策略纳什均衡的存在性和唯一性,推导出均衡总订货量的表达式并分析了均衡总订货量与报童数量、损失厌恶系数、期望水平的关系,最后通过算例论证了均衡总订货量与报童数量、损失厌恶系数和期望水平之间关系的正确性,进而比较分析了风险中性报童最优订货量、单个基于期望的损失厌恶报童最优订货量以及均衡总订货量之间的关系。结果表明,均衡总订货量随着报童数量的增多而增加,随着损失厌恶系数的增大而减少,随着期望水平的增大而减少;单个基于期望的损失厌恶报童最优订货量要小于风险中性报童最优订货量以及均衡总订货量。     

A JIT lot-splitting model for supply chain management: Enhancing buyer–supplier linkage

This study develops a buyer–supplier coordination model to facilitate frequent deliveries in small lot sizes in a manufacturing supply chain. The proposed model, based on the integrated total relevant costs of both buyer and supplier, determines optimal order quantity, the number of deliveries/setups, and shipping quantity over a finite planning horizon in a relatively simple JIT single buyer single supplier scenario. Under deterministic conditions for a single product, we show that the optimal delivery policy adopted by both buyer and supplier in a cooperative manner can be economically beneficial to both parties. It is shown that the optimal delivery size can be unique, regardless of the order quantity and the number of deliveries. Numerical results are also presented.     

Economic lot-sizing and dynamic quantity competition

We study a problem of dynamic quantity competition in continuous time with two competing retailers facing different replenishment cost structures. Retailer 1 faces fixed ordering costs and variable procurement costs and all inventory kept in stock is subject to holding costs. Retailer 2 only faces variable procurement costs. Both retailers are allowed to change their sales quantities dynamically over time. Following the structure of the economic order quantity (EOQ) model, retailer 1 places replenishment orders in batches and retailer 2 follows a just-in-time (JIT) policy. The objective of both retailers is to maximize their individual average profit anticipating the competitor's replenishment and output decisions. The problem is solved by a two-stage hierarchical optimization approach using backwards induction. The second-stage model is a differential game in output quantities between the two retailers for a given cycle length. At the first stage, the replenishment policy is determined. We prove the existence of a unique optimal solution and derive an open-loop Nash equilibrium. We show that both retailers follow contrary output strategies over the order cycle. The EOQ retailer, driven by inventory holding costs, decreases his market share whereas the output of the JIT retailer increases. Moreover, depending on the cost structure, the EOQ retailer might partially be a monopolist. At the first stage, the EOQ retailer determines the cycle length, anticipating the optimal output trajectories at the second stage.     

供应中断下双源采购的供应链契约设计

考虑由一个制造商和两个供应商构成的两级供应链契约设计问题,将可靠性服从随机分布的供应商作为主供应商,将完全中断供应商作为次供应商,建立以利润最大化为目标的签约和执行两阶段博弈的动态规划模型,得到制造商的最优契约设计。制造商根据产品零售价格的变化灵活做出只与一个供应商签约、与两个供应商同时签约或都不签约的决定,供应商根据契约设计内容决定自己的最优生产规模。研究表明：供应商最优生产规模与产品的单位生产成本呈负相关,与单位变动支付和单位惩罚成本呈正相关;次供应商的订货量与其本身的可靠性呈正相关,与主供应商的可靠性呈负相关;供应商的固定支付与其相应的可靠性呈负相关。     

Myopic optimal policy for a multi-period, two-delivery-lead-times, stochastic inventory problem with minimum cumulative commitment and capacity

This paper studies a single-product, multi-period, stochastic inventory problem that imposes the lower and upper bounds on the cumulative order quantity during a planning horizon and allows two delivery lead times. This model includes three features. The first one is that a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity during the planning horizon is constrained with the capacity. The second one is that the buyer agrees to purchase the product at least a certain percentage of the purchased capacity during the planning horizon. The third one is that the supplier allows the buyer to order the product with two-delivery-lead-times. We identify conditions under which a myopic ordering policy is optimal. We also develop an algorithm to calculate the optimal capacity when the minimum cumulative order quantity commitment is a certain percentage of the capacity. We then use the algorithm to evaluate the effect of the various parameters on the buyer’s minimum expected total cost during the planning horizon. Our computation shows that the buyer would benefit from the commitments and two-delivery-lead-times.     

基于利他行为下的闭环供应链决策研究

随着行为运营管理的发展,利他、公平、信任等行为得到广泛的关注。文章构建一个由供应商和零售商的闭环供应链,供应商负责旧产品回收再加工。将利他行为引入到供应链中,研究利他属性对供应链决策的影响。研究发现,在该模型的供应链中,供应商的利他属性,对于供应链的回收率、零售商的利润、供应商的效用、供应链的整体利润都是有益的。而零售商的利他行为,有利也有弊,带来的效益是局部的。然后通过数值分析对结论作出解释和说明。     

A multi-item supply chain with credit periods and weight freight cost discounts

It is possible to realize considerable savings by aggregating the replenishment of a variety of items in a multi-item supply chain. This joint multi-item replenishment policy has already been widely applied in a variety of industries. This type of policy may make it possible for the retailer to take advantage of transport economies of scale by the utilization of freight discounts for greater weight. In addition, a supplier will often extend forward financing to a retailer. In this paper, a multi-item supply chain with a credit period and weight freight cost discounts is considered. The retailer bears the freight costs, but the freight carrier provides freight-transport discounts that are positively related to the weight of the cargo transported. From both the individual and the channel perspectives, we deal with the dual problems of determining the ideal supplier credit period, and of the best way for the retailer to make multi-item replenishment and pricing decisions, while still maximizing profits. We outline the optimal properties and develop algorithms for solving the problems described, as well as discuss the impact of the freight cost discounts, the inventory holding cost, and the interest rate on the behavior of both parties.     

Inter-temporal inventory competition and the effects of capacity constraints

This paper addresses an intertemporal inventory competition between a supplier (a provider, manufacturer) and a retailer engaged in a supply chain. The paper's focus is on the effect of capacity constraints on both parties when demands are seasonal. The paper provides a comparative study of two solution approaches, one is based on supply chain competition and the other is based on system wide optimization. Our results demonstrate that with dynamic inventory competition, the retailer reduces inventory costs by reducing the response period to higher demands while increasing the supply requests compared to the system-wide optimal approach. As a result, the supplier's inventory costs increase. An example illustrating these particular facets of the problem and its application is presented and discussed in light of the supplier and the retailer coordinating policies.     

Streamlining inventory flows with time discounts to improve the profits of a decentralized supply chain

We consider a decentralized supply chain, whereby a supplier sells a product to a group of independent buyers, and develop a strategy for the supplier to offer an all-units price discount or cash rebate for orders that are synchronized with its replenishments. As synchronized orders can be met with inventory directly from receiving to shipping without warehousing, the proposed strategy streamlines system inventory flows to minimize inventory and, hence, the related costs. On the other hand, by increasing the replenishment interval of the supplier, the proposed strategy is able to induce buyers to order in large quantities and hence achieve the objectives of quantity discounts. We show that the proposed strategy can achieve nearly optimal (minimum) system cost, and is much more effective than the existing coordination strategies for decentralized supply chains in the literature.     

Optimal economic ordering policy with deteriorating items under different supplier trade credits for finite horizon case

This paper develops and solves a general finite horizon trade credit economic ordering policy for an inventory model with deteriorating items under inflation and time value of money when shortages are not allowed. The time horizon is divided into different cycles each of which has its own demand rate and its own trade credit period offered from the supplier to his retailer so that the retailer should pay his supplier before or after the end of the permissible trade credit of that cycle. Up to the end of the trade credit of a cycle, the retailer is free of charge, but he is charged on an interest for those items not being sold before this end. The retailer can also earn the interest of the money from the generated sales revenue in any cycle by depositing such revenue into an interest bearing account. The objective of the retailer is then to minimize his net total relevant costs. A closed form of this net total cost is derived and the resulting model is solved. Then rigorous mathematical methods are used to show that, under some seemingly possible conditions, there exist a unique vector of the relevant decision variables that solve the underlying inventory system. A numerical example which shows the applicability of the theoretical results is given.     

Replenish-up-to inventory control policy with random replenishment intervals

The multi period inventory problems have been studied under two main assumptions. Continuous review assumption where an order can be made at any time depending on inventory position and periodic review assumption where an order can be initiated only at discrete time epochs. In this study, we analyze a multi period inventory problem that falls under neither of these two assumptions. In the case we consider, there are periodic replenishments but the replenishment intervals are taken to be i.i.d. random variables. This setting represents the real life cases where a supplier visits a retailer with random inter arrival times and the retailer replenishes his inventories based on a replenish-up-to-level inventory control policy. We also assume that only a certain fraction of unmet demand is backordered and the rest of it is lost.In this setting under general distribution between replenishment epochs, we show the concavity of the expected profit function and give the condition that must hold for the optimal replenish-up-to-level. We also present the specific solutions and analysis under two different distributions, namely, uniform and exponential distributions, together with some numerical examples.     

An EOQ lot sizing model with random supplier capacity

This paper presents a general formulation of the inventory lot sizing model with random supplier capacity under the EOQ framework. For a general capacity distribution, we show that the expected cost per unit of time is a unimodal function and pseudo-convex in the ordering quantity. Moreover, we derive some simple data-dependent bounds for both optimal lot size and expected cost per unit of time. In order to illustrate the general model, three types of distributions for the random capacity are analyzed as special cases. These are the uniform, exponential, and truncated normal distributions. For each of these distributions, we find that the maximum cost penalty of using the EOQ lot size instead of the optimal one is almost negligible (not greater than 0.52%, 1.81%, and 0.91% for the uniform, exponential, and truncated normal distributions, respectively). In addition, we extend the general model to allow for the presence of defective units in the quantity received from the supplier. It is shown that this extra randomness does not affect the optimal ordering policy for the original model.