Multi-product newsvendor problem with value-at-risk considerations

We consider the single period stochastic inventory (newsvendor) problem with downside risk constraints. The aim in the classical newsvendor problem is maximizing the expected profit. This formulation does not take into account the risk of earning less than a desired target profit or losing more than an acceptable level due to the randomness of demand. We utilize Value at Risk (VaR) as the risk measure in a newsvendor framework and investigate the multi-product newsvendor problem under a VaR constraint. To this end, we first derive the exact distribution function for the two-product newsvendor problem and develop an approximation method for the profit distribution of the N-product case (N>2). A mathematical programming approach is used to determine the solution of the newsvendor problem with a VaR constraint. This approach allows us to handle a wide range of cases including the correlated demand case that yields new results and insights. The accuracy of the approximation method and the effects of the system parameters on the solution are investigated numerically.     

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.     

Impact of demand uncertainty on supply chain cooperation of single-period products

Cooperation is an approach of improving competitive advantages of a supply chain. A two-echelon supply chain consisting of a manufacturer and a retailer for a single-period product is studied, and retail-market demand uncertainty is described by coefficient of variation. We develop a cooperation mechanism to address the cooperation and its implementation between the manufacturer and the retailer, two market situations are considered: (i) the wholesale price and the order quantity are decision variables, (ii) the wholesale and the retail prices as well as the order quantity are decision variables. In both market situations, our research shows that: (1) the cooperation mechanism can improve the overall channel profits and the supply chain members’ allocated profits, (2) the described cooperation is conditional on retail-market demand uncertainty: it can be implemented if, and only if, the fluctuation of retail-market demand is relatively small and coefficient of variation of retail-market demand does not exceed an upper bound. Impacts of retail-market demand uncertainty on wholesale price, order quantity and/or retail price have also been investigated through analytical and numerical analyses. Although our research is based on the assumption that the manufacturer dominates the supply chain in the non-cooperative situation, which is not the case for most retailer-driven supply chains, this research is still significant on providing guidelines for practitioners in current China mid-level car market that is similar to situations described in the paper.     

Joint pricing and procurement of fashion products in the existence of clearance markets

This paper focuses on the joint pricing and procurement of fashion products in the existence of clearance markets. It is assumed that the expected regular season demand is a linear decreasing function of the price and the end of period excess inventory is sold at a known discounted price in a clearance market where the demand is a random variable that follows a general distribution. It is shown that the expected profit function is unimodal and the optimal procurement quantity and price can be found from the first order conditions. Existence of a clearance market increases the profit, price, and the procurement quantity. In order to prove this, the optimal procurement and pricing policy of a price-setting retailer who does not have a clearance market is provided. As opposed to the literature, it is shown that the expected profit function of this problem is unimodal as well. A numerical study demonstrating the magnitude of the increase in profit, procurement quantity, and price is reported.     

基于连锁零售企业退货管理的供应链协调机制研究

在对连锁零售企业退货物流网络结构进行分析的基础上,建立了与价格相关的随机需求下存在顾客退货和允许库存结转的单一供应商、单一连锁零售企业、单一产品的供应链模型。根据供应链一体化模式下得到的相关决策变量的一阶条件,论证基于回馈和惩罚的批发价格契约能够实现供应链的协调。研究表明,在给定回馈和惩罚因子的前提下,供应商可以通过调整目标订购数量来实现供应链整体利润的任意分配,并且当目标订购数量和回馈惩罚因子满足一定条件时,供应链的协调才是有效的,从而为连锁零售企业的退货物流管理提供了重要的理论依据。     

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。     

VMCI 下基于批发价决策权转移的供应链效率改进研究

本文在VMCI 模式下,考虑销售努力水平对市场需求的影响,研究批发价决策权由供应商转移至零售商的两级供应链效率改进问题。假定零售商决策批发价和销售努力水平,供应商决策寄售量,建立了零售商主导的Stackelberg 博弈模型,证明了集中决策下的最优解和分散决策下的均衡解均存在且唯一,集中决策下的寄售因子大于分散决策下的对应值。随后,引入收入共享与销售努力成本共担契约,论证了系统中寄售因子保持不变、批发价降低,且当契约参数满足一定条件时,可实现帕累托改进,实现供应链的效率改进。最后,分析了契约参数对于系统决策变量及利润的影响。     

Mean-downside-risk and mean-variance newsvendor models: Implications for sustainable fashion retailing

Newsvendor models have been well-established for studying supply chain management problems with fashionable products. In this paper, we explore the mean-downside-risk (MDR) and mean-variance (MV) newsvendor models under both the exogenous and endogenous retail price decision cases. We first construct analytical models with the MDR and MV objectives. We then show that the analytical solution schemes for both the MDR and MV problems are the same. With the measures for sustainability such as the expected quantity of goods leftover, the expected sales to expected goods leftover ratio, the rate of return on investment, and the probability of achieving a pre-determined profit target, we proceed to compare the levels of sustainability by the fashion retailers which employ the mean-risk and the risk neutral models. Insights are generated.     

On the convexity of newsvendor games

This study considers a simple newsvendor situation that consists of n retailers, all selling the same item with common purchasing costs and common selling prices. Groups of retailers might increase their expected joint profit by inventory centralization, which means that they make a joint order to satisfy total future demand. The resulting newsvendor games are shown to have non-empty cores in the literature. This study investigates convexity of newsvendor games. We focus our analysis on the class of newsvendor games with independent symmetric unimodal demand distributions after providing several examples outside this class that are not convex. Several interesting subclasses, containing convex games only, are identified. Additionally, we illustrate that these results cannot be extended to all games in this class.     

The component procurement problem for the loss-averse manufacturer with spot purchase

This paper studies the purchasing behaviour of a loss-averse engineer-to-order manufacturer, who purchases a key component for his final product from a supplier under a single-wholesale-price contract with spot purchase opportunities, where both the product demand and the component spot price are uncertain. Through newsvendor type of models, we analyze several key issues, including the effects of the manufacturer's loss aversion, and the effects of demand and spot price uncertainties on the manufacturer's decision behaviour. We find that the purchasing behaviour of the loss-averse manufacturer differs from those of the risk-neutral and risk-averse ones. Specifically, we identify some sufficient conditions under which the loss-averse manufacturer may purchase a larger order quantity in advance when demand becomes more uncertain or when the price becomes more uncertain. We also discuss the two-wholesale-price contract and show that fixing the emergency supply price may lead to a smaller order quantity.     

分散决策下的双渠道供应链补偿策略——基于消费者渠道选择行为

为了有效解决由于对消费者的争夺从而引发的渠道之间关于定价、服务水平、利润等方面的冲突,基于消费者渠道选择行为,构建了网络直销市场与传统零售市场需求模型和双渠道供应链利润模型,运用Stackelberg模型,在制造商与零售商实施分决策时,通过制造商对零售商实施补偿激励前后的对比,分析了消费者渠道选择行为对网络直销渠道和传统零售渠道定价、制造商与零售商利润以及供应链总利润的影响,并求得最优定价及制造商的最优补偿额度和零售商的最优销售努力水平,进行了不同情况下的双渠道供应链利润的比较分析。结果表明,无论制造商是否实施补偿激励,都应随着网络消费者比例的增加而增加其网络直销价格;零售商的零售渠道价格应根据网络消费者比例的增加先降低到一定水平后再提升。当更多的消费者选择网络直销渠道时,制造商的补偿激励水平和零售商的销售努力程度均会下降。制造商应提高其补偿水平,进而激发零售商提高销售的努力水平,并使双方利润及供应链总利润最大化。研究结果为基于消费者选择行为的供应链补偿研究提供了新方法,对双渠道的供应链补偿研究有借鉴意义。     

Coordination in retailer-carrier channels for long term planning

We study a retailer-carrier channel for the purpose of long term planning and coordination. Here, the term channel represents the business interaction between the retailer and the carrier. The retailer sells a particular item with price-dependent demand, whereas the carrier is responsible for transporting the item to the retailer's site. We characterize the profit functions of each channel member as well as the total channel profit. We consider two specific channel structures: (i) the centralized channel and (ii) the decentralized channel. Under the first channel structure, the goal is to set the retail price so as to maximize the total channel profit. Under the latter, the carrier and the retailer choose their own policy parameters, i.e., the freight rate for the carrier and the retail price for the retailer, so as to maximize their individual profits. We model the decentralized channel as a Stackelberg Game and propose a coordination mechanism between the retailer and the carrier in which the retailer signals a price multiplier to the carrier. We illustrate that this mechanism could provide win-win solutions for both parties and present analytical and numerical results on the efficiency of channel coordination. We demonstrate that coordination in retailer-carrier channels can be as promising as supplier-retailer channels. We also discuss the effects of retailer-carrier coordination on inventory levels.     

Impact of loss aversion on the newsvendor game with product substitution

This paper studies a newsvendor game in which two substitutable products are sold by two different retailers (newsvendors) with loss-averse preferences. Each loss-averse retailer facing stochastic customer demand and deterministic substitution rate will make an order quantity decision to maximize his expected utility. Since product substitution causes two retailers to make decisions in a competitive environment, game theory is used to find the retailers' optimal order quantities. It is shown that under certain conditions, there exists a unique Nash equilibrium in the newsvendor game. Under a symmetry assumption, each retailer's equilibrium order quantity is decreasing in the loss aversion coefficient and increasing in the substitution rate. Further, if the effect of loss aversion on the order quantity is strong enough to dominate the effect of competition, the total inventory level of a decentralized supply chain will be lower than that of a centralized supply chain. Numerical experiments are conducted to illustrate our results.     

Inventory decisions for substitutable products with stock-dependent demand

We study a retailer’s inventory policy for two products. The products are substitutable and have inventory dependent demand, so a higher inventory level of a product increases its sales. We model the joint effect of demand stimulation and product substitution on inventory decisions by considering a single-period, stochastic demand setting. We provide the first order optimality conditions for the profit maximizing order quantities and interpret them using marginal analysis. We also consider two heuristic solutions that separately account for either demand stimulation or product substitution. Our numerical analysis reveals that the optimal policy by appropriately using sales information that quantifies substitution and demand stimulation can produce significantly higher profits. The profit benefits are lessened under certain circumstances, such as when the two products have similar critical fractile values, suggesting that in such instances the heuristics may be used effectively.     

Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand

In this paper, a joint pricing and inventory control for non-instantaneous deteriorating items is developed. We adopt a price and time dependent demand function. Shortages is allowed and partially backlogged. The major objective is to determine the optimal selling price, the optimal replenishment schedule and the optimal order quantity simultaneously such that, the total profit is maximized. We first show that for any given selling price, optimal replenishment schedule exists and unique. Then, we show that the total profit is a concave function of price. Next, we present a simple algorithm to find the optimal solution. Finally, we solve a numerical example to illustrate the solution procedure and the algorithm.     

VERTICAL RESTRAINTS UNDER ASYMMETRIC INFORMATION: ON THE ROLE OF PARTICIPATION CONSTRAINTS*

The impact on vertical contracting of a type‐dependent reservation utility is investigated within a sequential monopolies environment with asymmetric information. The welfare and private properties of contracts controlling both the retail price and the sales level are compared with those restricting only sales. When firms choose contracts non‐cooperatively, retail price restrictions are desirable for the upstream supplier although detrimental to consumers, whenever the retailer reservation utility has a relevant impact on optimal contracts. If this impact is relatively weak and contracts are chosen cooperatively, vertical price control fails to maximize firms' joint‐profit although it would be beneficial to consumers.     

Revenue Sharing and Vertical Control in the Video Rental Industry

Revenue sharing contracts, in which retailers pay a royalty on sales to their suppliers, are now widely used in the video rental industry. We show that revenue sharing is valuable in vertically separated industries in which demand is either stochastic (unpredictable) or variable (e.g., systematically declining), downstream inventory is chosen before demand is realized and downstream firms engage in intrabrand competition. Unlike two-part tariffs, revenue sharing achieves the first best outcome by softening retail price competition without distorting retailers' inventory decisions. Our theories are also consistent with trends in prices and availability following retailers' adoption of revenue sharing contracts.     

Regulation of international roaming in the European Union—Lessons learned

This paper analyzes the evolution of prices and competition in intra-EU international roaming markets. It addresses three main research questions: (i) to what extent have market forces by themselves brought competition to retail roaming markets? (ii) Has the evolution of market dynamics in wholesale roaming improved competition? (iii) Is wholesale regulation sufficient to lead to a reduction in retail roaming prices? Data show that there has been little price-based competition both at wholesale and retail levels, despite prices being well above costs and the significant margins allowed by regulation. Available data from the period preceding the entry into force of the first EU roaming regulation also point to the same conclusion. Lack of competitive pressure in retail roaming markets and inelastic demand give little incentives for retail roaming service providers to lower prices. Wholesale international roaming markets have complex competition dynamics. They are characterized by the reciprocity of wholesale roaming agreements and traffic internalization inside transnational groups. These circumstances limit price competition at the wholesale level. The traditional regulatory approach applied to electronic communication markets has been primarily focused on wholesale regulation. However, empirical evidence shows that even if wholesale charges are reduced, retail roaming markets continue to operate at very high retail margins (for example, more than 200% retail mark-up over wholesale charges for data roaming services and incoming calls). This proves that in international roaming markets wholesale charge reductions are not necessarily passed on to retail prices. It can thus be inferred that wholesale price regulation alone is in most cases not sufficient to ensure that benefits are passed through to end users.     

考虑营销成本的库存与运输联合优化三阶段决策模型研究

一般来说,个体最优和整体最优是不一致的,二者之间存在着偏差,这一偏差就是分散优化带来的效率损失。库存与运输联合优化（ITIO）将物流系统中的库存控制和运输管理融合到一个大问题中,去寻求这一联合问题而非单个问题的最优解决方案,可以最优化整个配送系统的运营成本。本文在考虑营销成本条件下,建立ITIO三阶段决策模型,并求解分析模型性质。研究表明：ITIO零售价和营销成本与需求的营销成本弹性、零售商订购成本、供应商生产启动成本、供应商生产成本、运输固定成本和运输可变成本正相关;与需求函数的价格弹性和订货批量负相关;当订购数量相同时,零售商单独优化的营销成本大于ITIO联合优化的营销成本。     

The effect of advertising on the distribution-free newsboy problem

Advertising is very important for the newsboy problem because the shelf-life of the newsboy product is short and advertising may increase sales to avoid overstocking. In this paper, models to study the effect of advertising are developed for the distribution-free newsboy problem where only the mean and variance of the demand are known. As in Khouja and Robbins (2003), it is assumed that the mean demand is an increasing and concave function of advertising expenditure. Three cases are considered: (1) demand has constant variance, (2) demand has constant coefficient of variation, and (3) demand has an increasing coefficient of variation. This paper provides closed-form solutions or steps to solve the problem. Numerical results of the model are also compared with those from other papers. The effects of model parameters on optimal expenditure on advertising, optimal order quantity, and the lower bound on expected profit are derived or discussed.