The price-setting newsvendor with service and loss constraints

Current performance measurement systems consider not only financial measures, like costs and profits, but also non-financial indicators with respect to customer service, quality and flexibility. Using the newsvendor model, we analyse the respective influence of these possibly conflicting performance measures on important operations and marketing decisions, for instance the order quantity and the selling price of a product. As in the classical newsvendor model for price-independent as well as price-dependent demand distribution, the objective of the firm is to maximise expected profit. In this paper, we also consider a service constraint—a lower bound for the level of product availability—and a loss constraint—an upper bound for the probability of a loss occurring. For both models, we provide conditions for the existence of solutions. We then analyse the influence of demand variability using a set of conditions specifying the quantiles of the predetermined performance measures: a higher variability of demand implies a smaller admissible region of the decision variables. In the price-independent case, the optimal solution has a control-limit structure: the optimal order quantity is thus given either by the classical newsvendor solution or by the control-limits corresponding to the constraints. In the price-setting model with multiplicative demand, this structure is used to check whether small admissible prices are determined by the service constraint or by the loss constraint. Using these structural results, a procedure is developed to more easily enable the computation of the optimal values of the order quantity, selling price and expected profit.     

Late season low inventory assortment effects in the newsvendor problem

The assumption of the newsvendor being able to satisfy demand as long as on-hand inventory is positive does not hold for a non-homogenous product. Consumers who do not find a unit of the product which satisfies their secondary features preferences may not purchase the product even though the newsvendor has positive on-hand inventory. This is likely to occur late in the season as inventory level declines. We solve a newsvendor problem in which the probability of purchase by consumers is increasing in on-hand inventory for any inventory level below that which is needed to have a complete assortment. We identify the sufficient optimality condition for the order quantity. We show that, unlike the case of inventory-dependent demand models in the literature, the optimal order quantity may decrease due to the assortment effect. We investigate two types of pre-end of season discounts, immediate all-units and delayed, as ways to mitigate the late season assortment effect and show that in some cases, they can increase the newsvendor׳s profit and free up the shelf space for other products.     

The newsvendor problem with barter exchange

Barter exchange, as an alternative to move distressed inventory, has become increasingly popular in business. Many companies barter their unsold product for the product they need via barter exchange platforms at full prices. In this paper we consider the newsvendor problem with the barter exchange option. A retailer (the newsvendor) facing stochastic demand not only sells its product, but also buys other product that it needs from the market. It either trades its unsold product for the product it needs on a barter platform or disposes of its unsold product at discounted prices at the end of the selling season like in the classical newsvendor model. We derive the retailer’s optimal order quantity, then analytically and numerically examine the impacts of barter on the retailer’s inventory decisions and profit. We find that barter exchange can help the retailer to manage demand uncertainty and improve profit. The optimal order quantity decreases with barter commission and barter uncertainty, while increases with demand uncertainty and the value of the product that the retailer needs. Barter is more advantageous with lower barter commission, larger demand uncertainty, lower barter uncertainty, and higher value of the product it needs.     

Price-setting newsvendor with strategic consumers

We consider a newsvendor who sells a single product over a single season with the objective of determining both the selling price and stock quantity to maximize the expected profit. The customers are strategic and we consider two demand cases: additive and multiplicative. For each case, we derive the newsvendor׳s optimal decisions and demonstrate that neglecting the price-sensitivity of demand leads the newsvendor to make sub-optimal decisions. Moreover, we show that under certain conditions, strategic consumer behavior may positively affect the newsvendor׳s optimal expected profit in the additive demand case.     

基于预期的报童问题研究

Koszegi与Rabin认为参照点往往由决策者的理性预期确定，本文选取报童的预期作为参照点，利用参照依赖偏好理论对报童问题进行了研究。研究发现，基于预期的报童的最优订货量不仅与货物销售的概率分布、价格等有关还与报童的损失厌恶程度有关。如果报童是损失厌恶的，报童的订货量要小于经典报童问题的订货量；反之，报童的订货量则大于经典报童问题的订货量，该结论与大部分实证结果是一致的。最后，用算例来验证了文中有关结论的正确性。     

On the benefits of operational flexibility in a distribution network with transshipment

We consider a centralized distribution network with multiple retailers who receive replenishment inventory to satisfy customer demand of the local markets. The operational flexibility of the network is defined as the opportunity that one retailer's excess inventory can be transferred to satisfy other retailers’ unmet customer demand due to stock-outs. A general modeling framework is developed to optimize retailers’ order quantities under any possible flexibility level of a stylized two-stage distribution network. We apply the framework to formulate and solve the transshipment problem of a distribution network with three retailers. Six typical flexibility levels are investigated to make the comparison study on the firm's profit performance under three ordering quantity policies: average demand, newsvendor order quantity, and optimal order quantity. We find that the operational flexibility and system optimization are complements to the firm's performance. The ordering policy with newsvendor ordering quantity can perform fairly well with moderate flexibility level when compared with the optimized ordering policy with full flexibility.     

考虑战略顾客行为时的供应链性能分析与协调

动态定价策略的广泛应用使得越来越多的顾客具有了战略性,战略顾客会根据产品在销售期内的价格路径确定最优购买时机,零售商则根据顾客的购买行为确定订货数量和销售价格.研究了双方静态博弈时的理性预期均衡解和零售商进行数量承诺时的情形.研究表明:理性预期均衡时的最优销售价格、最优存货数量和最优期望利润分别小于标准报童模型的情形;数量承诺时的最优存货数量小于理性预期均衡时的最优存货数量;最优期望利润则大于理性预期均衡时的最优期望利润,并且在一定条件下可能会大于标准报童模型的最优期望利润,战略顾客行为的存在对零售商可能有利.最后分析了在分散式供应链中如何利用收入分享契约和数量折扣契约实现供应链协调.     

The loss-averse newsvendor problem

Newsvendor models are widely used in the literature, and usually based upon the assumption of risk neutrality. This paper uses loss aversion to model manager's decision-making behavior in the single-period newsvendor problem. We find that if shortage cost is not negligible, then a loss-averse newsvendor may order more than a risk-neutral newsvendor. We also find that the loss-averse newsvendor's optimal order quantity may increase in wholesale price and decrease in retail price, which can never occur in the risk-neutral newsvendor model.     

Decision making in the newsvendor problem: A cross-national laboratory study

In this paper, we conduct a laboratory experiment using the classic newsvendor problem to examine cross-national differences in inventory ordering patterns between Chinese and American decision makers based on a theoretical examination of the role of the Doctrine of the Mean in Chinese decision making. Drawing on the theory of context-dependent preferences (specifically extremeness aversion), we also revisit the flat-maximum hypothesis of Bolton and Katok [12], i.e., “thinning the set of order options leads to newsvendor decisions that achieve a higher proportion of maximum expected profit.” The results show that the “pull-to-center” effect is more prominent for Chinese than Americans, i.e., average order quantities of Chinese subjects are closer to the anchor of mean demand than those of American subjects. Furthermore, we find that thinning the set of order options such that the optimal order quantity is a middle option, not an extreme option in the choice set, leads to better performance in newsvendor decisions, which complements the flat-maximum hypothesis.     

Optimal ordering and pricing decisions for a target oriented newsvendor

This paper is the first to study pricing and target oriented decision making together in the newsvendor model. Specifically, this paper studies a newsvendor who decides on order quantity and selling price to maximize the probability of achieving both profit and revenue targets simultaneously. First, it is shown that the probability of a newsvendor achieving both targets depends critically on the relative magnitudes of the profit margin and the ratio between the profit target and the revenue target. Second, the closed-form expressions of the optimal order quantity, the optimal selling price, and the maximal profit and revenue probability are obtained. It is shown that if the product has greater price elasticity, the best strategy is always to price lower and order more.     

Updating Inventories of Substitutable Resources in Response to Forecast Updates

We show simple yet optimal results to update the inventory/capacity levels, expected profit, fill rates, and service levels of substitutable resources in response to an updating of the mean demand forecasts for the resources. We find that a change in the mean demand of one resource does not affect the optimal inventory level of any other resource. The results are obtained for demands with location‐scale distribution, and for a revenue structure satisfying a triangle property such that the manager will always use the inventory of a resource to meet her own demand first before using it for substitution. The results for updating the performance measures also extend to managers who maintain non‐optimal inventory/capacity levels. Implications for procurement, sales and operational planning, and multi‐store operations are discussed.     

延迟支付下短生命周期产品批发价契约研究

在需求随机且允许延迟支付的情况下,如果零售商的销售款不足以清偿应支付给制造商的货款,制造商将承担一定的回款风险。对此,以报童模型为基础,针对短生命周期产品建立了延迟支付下的批发价契约模型。分析表明,如果需求分布是IGFR,那么对于一定的批发价,零售商有确定的最优订货批量。制造商的预期利润是批发价的递增函数。制造商根据零售商至少应获得的预期利润来确定批发价。当满足一定条件时供应链能够实现协调,但这是一种系统利润分配缺乏柔性的协调。     

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

We consider a periodic‐review inventory system with regular and expedited supply modes. The expedited supply is faster than the regular supply but incurs a higher cost. Demand for the product in each period is random and sensitive to its selling price. The firm determines its order quantity from each supply in each period as well as its selling price to maximize the expected total discounted profit over a finite or an infinite planning horizon. We show that, in each period if it is optimal to order from both supplies, the optimal inventory policy is determined by two state‐independent thresholds, one for each supply mode, and a list price is set for the product; if only the regular supply is used, the optimal policy is a state‐dependent base‐stock policy, that is, the optimal base‐stock level depends on the starting inventory level, and the optimal selling price is a markdown price that decreases with the starting inventory level. We further study the operational impact of such supply diversification and show that it increases the firm's expected profit, reduces the optimal safety‐stock levels, and lowers the optimal selling price. Thus that diversification is beneficial to both the firm and its customers. Building upon these results, we conduct a numerical study to assess and compare the respective benefit of dynamic pricing and supply diversification.     

A heuristic approach to in-season capacity allocation in a multi-product newsvendor model

Based on an actual problem, we develop and test two heuristics for optimizing the newsvendor’s response to new in-season demand information for a multi-product single-period problem. In this model, in addition to the quantities produced prior to the beginning of the selling season, the newsvendor can produce additional quantities of some products after the selling season begins. Sales data of all products is updated daily, and using these updates, the newsvendor can test if the quantities already produced are still optimal. If the newsvendor finds that the actual demand of a product up to a point in time indicates that the quantity already produced is too small, then the product becomes a candidate for an incremental production quantity. In Heuristic I, we fix the pre-season production quantities to those that are optimal for the classic newsvendor model. In Heuristic II, because the newsvendor may have some recourse during the selling season, we allow for reductions in the pre-season production quantities from the optimal classic newsvendor model production quantities. Using a simulation experiment, we show that even under an unbiased forecast, both heuristics result in higher profit, with Heuristic II outperforming Heuristic I. The increase in profits from using the heuristics increases significantly with the number of products for which the forecast is biased. In addition, the improvements in profits decrease significantly as the lead time and the penalty for late production increase.     

Evaluating manufacturer's buyback policies in a single-period two-echelon framework under price-dependent stochastic demand

This paper attempts to model the profitability of a secondary market, in a newsvendor setting, to a profit-maximizing manufacturer, who is offering to the retailer a buyback policy for the unsold merchandise left at the end of the selling season. With a buyback agreement, the manufacturer shares the risks of demand uncertainty, thus inducing the buyer to place larger orders. The manufacturer's risk is mitigated to some extent by the availability of an extra market to dispose off the unsold merchandise. Both parties are risk-neutral profit-maximizers and both have the same information about the final demand for the product and its uncertainty. The manufacturer's decision is to arrive at an optimal wholesale price and the buyback price. Based on this offer, the retailer in turn sets the optimal amount of merchandise to purchase, as well as the unit selling price to meet a price-dependent uncertain demand for the merchandise in question. Due to the difficulty of obtaining analytical results, we have undertaken a numerical analysis to (i) compare the optimal policies across demand functions and error structures for three situations namely the no-incentive case and the buyback policies with and without a secondary market; (ii) indicate the conditions whereby the trade incentive is beneficial to both parties; (iii) assess the efficacy of the policies using two other performance indices (probability of achieving a target profit, and pass-through ratios) alternate to profit maximization; and (iv) conjecture the conditions for successful buyback policies and the nature of the benefits from the secondary market.     

Mean–variance analysis of the newsvendor model with stockout cost

We study the risk-averse newsvendor model with a mean–variance objective function. We show that stockout cost has a significant impact on the newsvendor's optimal ordering decisions. In particular, with stockout cost, the risk-averse newsvendor does not necessarily order less than the risk-neutral newsvendor. We illustrate this finding analytically for the case where the demand follows the power distribution.     

多类顾客环境下报童模型中库存分配策略研究

考虑一个报童模型中多类顾客的库存分配问题,将顾客按照他们愿意支付价格的高低划分为不同级别。零售商在销售期初决定产品订货量,并在销售期内决定接受或者拒绝不同顾客的需求,以最大化销售期内的期望总利润。将销售期分成大量足够小的时间单位,通过建立一个反向Bellman动态规划方程,以优化每个时间单位内的库存分配策略,并得到了零售商最优的期初订货量。通过与没有库存分配策略下零售商的期望利润进行比较,算例分析得出库存分配策略可以大幅提高零售商的利润。这主要是因为通过库存分配可以使得零售商从高端顾客中获取更多利润,同时能够减小期初的订货量,以节约采购成本和库存持有成本。     

基于资金供应链价值视角的最优现金持有方案研究

内部资金的配置不当常常引发公司高层的控制权争夺而损害公司利益。在投资项目中如何设计包含预期投资收入和现金分红比例组合要素在内的最优现金持有方案以提升公司价值成为公司所有者和高管共同面临的问题。本文借鉴报童模型,以公司所有者为先行者,建立了两者之间的斯塔克伯格博弈模型,分析最优现金持有方案的设置及其对公司所有者和高管的影响。研究发现:风险中性的公司所有者总会接受高管内部参股投资,并设置行业现金分红比例以给予高管资金使用方便;最优现金持有方案下,高管总会倾向于选择内部参股而不选择外部投资;此时,公司所有者的收益和资金供应链的效率都会提高,而高管选择外部引资是否能提高收益则取决于已有的薪酬合同水平。研究结论既支持了内部资金市场的"收集有利信息"假说,同时也对公司所有者在控制权私利倾向较强的职业经理人市场中如何科学决策有着重要的借鉴意义。     

A competitive multiple-product newsboy problem with partial product substitution

This paper studies a multi-product competitive newsboy problem with shortage penalty cost and partial product substitution. We characterize the unique Nash equilibrium of the competitive model and analyze some properties of the equilibrium. An iterative algorithm is developed on the basis of approximating the effective demand as well as the expected profit function for each product. Numerical experiments are conducted to illustrate the impacts of product substitution, demand correlation and demand variation on the optimal order quantities and the corresponding expected profits, and to compare the total optimal inventory level of the competitive case with that of the centralized case. The conclusion that competition always results in a higher total inventory level, even under the effect of product substitution is drawn in the symmetric case.     

Exact closed-form solutions for “optimal inventory model for items with imperfect quality and shortage backordering”

Wee et al. [Optimal inventory model for items with imperfect quality and shortage backordering. Omega 2007;35(1):7–11] recently contributed an optimal inventory model for items with imperfect quality and shortage backordering. This article revisits their study and applies the well-known renewal-reward theorem to obtain a new expected net profit per unit time. We derive the exact closed-form solutions to determine the optimal lot size, backordering quantity and maximum expected net profit per unit time, specifically without differential calculus. We also solve the same model algebraically from another direction, which has been mentioned, but the process has not been finished yet. The problem parameter effects upon the optimal solutions are examined analytically and numerically.