Fulfillment by Amazon versus fulfillment by seller: An interpretable risk-adjusted fulfillment model

With dual-channel choices, E-retailers fulfill their demands by either the inventory stored in third-party distribution centers, or by in-house inventory. In this article, using data from a wedding gown E-retailer in China, we analyze the differences between two fulfillment choices—fulfillment by Amazon (FBA) and fulfillment by seller (FBS). In particular, we want to understand the impact of FBA that will bring to sales and profit, compared to FBS, and how the impact is related to product features such as sizes and colors. We develop a risk-adjusted fulfillment model to address this problem, where the E-retailer's risk attitude to FBA is incorporated. We denote the profit gaps between FBA and FBS as the rewards for this E-retailer fulfilling products using FBA, our goal is to maximize the E-retailer's total rewards using predictive analytics. We adopt the generalized linear model to predict the expected rewards, while controlling for the variability of the reward distribution. We apply our model on a set of real data, and develop an explicit decision rule that can be easily implemented in practice. The numerical experiments show that our interpretable decision rule can improve the E-retailer's total rewards by more than 35%.     

Inventory transshipment game with limited supply: Trap or treat

Inventory transshipment is generally shown to be beneficial to retailers by matching their excess demand with surplus inventory. We investigate an inventory transshipment game with two newsvendor-type retailers under limited total supply and check whether the retailers are better off than the case without transshipment. We derive the ordering strategies for the retailers and show that unlike the unlimited supply case, a pure Nash equilibrium only exists under certain conditions. Furthermore, contrary to the conventional wisdom, we show that inventory transshipment may not always benefit both retailers. Although one of the retailers is guaranteed to be better off, the other could be worse off. The decision criteria are then provided for the retailers to determine if they will benefit from the exercise of inventory transshipment. Numerical study indicates that the carefully chosen transshipment prices play an important role in keeping inventory transshipment beneficial to both retailers. Subsequently, a coordinating mechanism is designed for the retailers to negotiate transshipment prices that maximize the total profit of the two retailers while keeping each of them in a beneficial position.     

Optimal control of a capacitated inventory system with multiple demand classes

This article studies the optimal control of a periodic‐review make‐to‐stock system with limited production capacity and multiple demand classes. In this system, a single product is produced to fulfill several classes of demands. The manager has to make the production and inventory allocation decisions. His objective is to minimize the expected total discounted cost. The production decision is made at the beginning of each period and determines the amount of products to be produced. The inventory allocation decision is made after receiving the random demands and determines the amount of demands to be satisfied. A modified base stock policy is shown to be optimal for production, and a multi‐level rationing policy is shown to be optimal for inventory allocation. Then a heuristic algorithm is proposed to approximate the optimal policy. The numerical studies show that the heuristic algorithm is very effective. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 43–58, 2011     

Market entry strategy in the presence of market spillovers and efficiency differentiation

Firms form various alliances or use brand extensions to enter new markets in order to improve their operational efficiency and create a positive spillover. However, they do not always know the implications of these strategies for market entry and multimarket competition because the sale of products in one market can have negative spillover effects on product sales in other markets. We present an analytical framework to examine whether and how (i.e., by choosing alliance entry or independent entry) competing firms should enter a market in a situation where market spillovers occur when a firm enters a spillover-producing market to sell products that may increase or decrease the consumers' willingness to pay for products in the primary market. Our analysis shows that the operational efficiency (or quality differentiation ability) of firms in a spillover-producing market varies, and hence, the impact of market spillovers differs for firms. We identify the key factors, such as bargaining power, brand value difference in the primary market, and the extent of efficiencies and spillovers, that determine the firms benefitting from the different entry strategies. Specifically, we show that firms would be more willing to choose an alliance strategy to enter a spillover-producing market if the negative spillover is small and alliance efficiency is high. In contrast, if an alliance entry is not favored, the firms' relative operational efficiency is crucial for them to decide whether to enter the market independently under moderate spillover conditions. Finally, we show the implications of market entry strategies for managers.     

Dynamic inventory management with cash flow constraints

In this article, we consider a classic dynamic inventory control problem of a self‐financing retailer who periodically replenishes its stock from a supplier and sells it to the market. The replenishment decisions of the retailer are constrained by cash flow, which is updated periodically following purchasing and sales in each period. Excess demand in each period is lost when insufficient inventory is in stock. The retailer's objective is to maximize its expected terminal wealth at the end of the planning horizon. We characterize the optimal inventory control policy and present a simple algorithm for computing the optimal policies for each period. Conditions are identified under which the optimal control policies are identical across periods. We also present comparative statics results on the optimal control policy. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

Capacity games for partially complementary products under multivariate random demands

In this study, we consider n firms, each of which produces and sells a different product. The n firms face a common demand stream which requests all their products as a complete set. In addition to the common demand stream, each firm also faces a dedicated demand stream which requires only its own product. The common and dedicated demands are uncertain and follow a general, joint, continuous distribution. Before the demands are realized, each firm needs to determine its capacity or production quantity to maximize its own expected profit. We formulate the problem as a noncooperative game. The sales price per unit for the common demand could be higher or lower than the unit price for the dedicated demand, which affects the firm's inventory rationing policy. Hence, the outcome of the game varies. All of the prices are first assumed to be exogenous. We characterize Nash equilibrium(s) of the game. At the end of the article, we also provide some results for the endogenous pricing. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 59: 146–159, 2012     

Oligopolistic contracting: Channel coordination under competition

We study contracts between a single retailer and multiple suppliers of two substitutable products, where suppliers have fixed capacities and present the retailer cost contracts for their supplies. After observing the contracts, the retailer decides how much capacity to purchase from each supplier, to maximize profits from the purchased capacity from the suppliers plus his possessed inventory (endowment). This is modeled as a noncooperative, nonzero‐sum game, where suppliers, or principals, move simultaneously as leaders and the retailer, the common agent, is the sole follower. We are interested in the form of the contracts in equilibrium, their effect on the total supply chain profit, and how the profit is split between the suppliers and the retailer. Under mild assumptions, we characterize the set of all equilibrium contracts and discuss all‐unit and marginal‐unit quantity discounts as special cases. We also show that the supply chain is coordinated in equilibrium with a unique profit split between the retailer and the suppliers. Each supplier's profit is equal to the marginal contribution of her capacity to supply chain profits in equilibrium. The retailer's profit is equal to the total revenue collected from the market minus the payments to the suppliers and the associated sales costs.     

Spatial pricing and product allocation in online retailing

Spatial pricing means a retailer price discriminates its customers based on their geographic locations. In this article, we study how an online retailer should jointly allocate multiple products and facilitate spatial price discrimination to maximize profits. When deciding between a centralized product allocation ((i.e., different products are allocated to the same fulfillment center) and decentralized product allocation (ie, different products are allocated to different fulfillment centers), the retailer faces the tradeoff between shipment pooling (ie, shipping multiple products in one package), and demand localization (ie, stocking products to satisfy local demand) based on its understanding of customers' product valuations. In our basic model, we consider two widely used spatial pricing policies: free on board (FOB) pricing that charges each customer the exact amount of shipping cost, and uniform delivered (UD) pricing that provides free shipping. We propose a stylized model and find that centralized product allocation is preferred when demand localization effect is relatively low or shipment pooling benefit is relatively high under both spatial pricing policies. Moreover, centralized product allocation is more preferred under the FOB pricing which encourages the purchase of virtual bundles of multiple products. Furthermore, we respectively extend the UD and FOB pricing policies to flat rate shipping (ie, the firm charges a constant shipping fee for each purchase), and linear rate shipping (ie, the firm sets the shipping fee as a fixed proportion of firm's actual fulfillment costs). While similar observations from the basic model still hold, we find the firm can improve its profit by sharing the fulfillment cost with its customers via the flat rate or linear rate shipping fee structure.     

Dynamic learning,pricing, and ordering by a censored newsvendor

We address the problem of determining optimal ordering and pricing policies in a finite‐horizon newsvendor model with unobservable lost sales. The demand distribution is price‐dependent and involves unknown parameters. We consider both the cases of perishable and nonperishable inventory. A very general class of demand functions is studied in this paper. We derive the optimal ordering and pricing policies as unique functions of the stocking factor (which is a linear transformation of the safety factor). An important expression is obtained for the marginal expected value of information. As a consequence, we show when lost sales are unobservable, with perishable inventory the optimal stocking factor is always at least as large as the one given by the single‐period model; however, if inventory is nonperishable, this result holds only under a strong condition. This expression also helps to explain why the optimal stocking factor of a period may not increase with the length of the problem. We compare this behavior with that of a full information model. We further examine the implications of the results to the special cases when demand uncertainty is described by additive and multiplicative models. For the additive case, we show that if demand is censored, the optimal policy is to order more as well as charge higher retail prices when compared to the policies in the single‐period model and the full information model. We also compare the optimal and myopic policies for the additive and multiplicative models. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

One- and two-stage scheduling of two products with distributed inserted idle time: The benefits of a controllable production rate

Consider the problem of scheduling two products on a single machine or through two machines in series when demand is constant and there is a changeover cost between runs of different products on the same machine. As well as setting batch sizes, it is assumed that the production scheduler can choose the production rate for each product, provided an upper bound is not exceeded. This is equivalent to permitting distributed inserted idle time over the production run. It is shown that characteristic of the optimum schedule is that there is no idle time concentrated between runs; it is all distributed over the run. If the inventory charge is based on average inventory then one product is always produced at maximum rate on the bottleneck stage; however, if there is an inventory constraint based on maximum inventory then in the single-stage case it can occur that neither product is produced at maximum rate.     

A dynamic,nonstationary inventory problem for a price/quantity setting firm

A dynamic and nonstationary model is formulated for a firm which attempts to minimize total expected costs over a finite planning horizon. The control variables are price and production. The price p and the demand ζ are linked through the relationship ζ = g(p) + η, where g(p) is the riskless demand curve and η is a random variable. The general model allows for proportional ordering costs, convex holding and stockout costs, downward sloping riskless demand curve, backlogging, partial backlogging, lost sales, partial spoilage of inventory, and two modes of collecting revenue. Sufficient conditions are developed for this problem to have an optimal policy which resembles the single critical number policy known from stochastic inventory theory. It is also shown what set of parameters will satisfy these sufficiency conditions.     

On the (S − 1, S) lost sales inventory model with priority demand classes

In this paper an inventory model with several demand classes, prioritised according to importance, is analysed. We consider a lot‐for‐lot or (S ? 1, S) inventory model with lost sales. For each demand class there is a critical stock level at and below which demand from that class is not satisfied from stock on hand. In this way stock is retained to meet demand from higher priority demand classes. A set of such critical levels determines the stocking policy. For Poisson demand and a generally distributed lead time, we derive expressions for the service levels for each demand class and the average total cost per unit time. Efficient solution methods for obtaining optimal policies, with and without service level constraints, are presented. Numerical experiments in which the solution methods are tested demonstrate that significant cost reductions can be achieved by distinguishing between demand classes. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 593–610, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10032     

Network disconnection problems in a centralized network

We consider three network disconnection problems in a centralized network where a source node provides service to the other nodes, called demand nodes. In network disconnection problems, each demand node gets a certain benefit when connected to a source node and a network attacker destroys edges to prevent demand nodes from achieving benefits. As destroying edges incurs expenses, an attacker considers the following three different strategies. The first is to maximize the sum of benefits of the disconnected nodes while keeping the total edge destruction cost no more than a given budget. The second is to minimize the total destruction cost needed to make a certain amount of benefits not accomplished. The last is to minimize the ratio of the total destruction cost to the benefits not accomplished. In this paper, we develop exact algorithms to solve the above three problems. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Pricing and inventory management during new product introduction when shortage creates hype

In this study, we analyze the joint pricing and inventory management during new product introduction when product shortage creates additional demand due to hype. We develop a two‐period model in which a firm launches its product at the beginning of the first period, before it observes sales in the two periods. The product is successful with an exogenous probability, or unsuccessful with the complementary probability. The hype in the second period is observed only when the product is successful. The firm learns the actual status of the product only after observing the first‐period demand. The firm must decide the stocking level and price of the product jointly at the beginning of each of the two periods. In this article, we derive some structural properties of the optimal prices and inventory levels, and show that (i) firms do not always exploit hype, (ii) firms do not always increase the price of a successful product in the second period, (iii) firms may price out an unsuccessful product in the first period if the success probability is above a threshold, and (iv) such a threshold probability is decreasing in the first‐period market potential of the successful product. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 304–320, 2015     

Integrating decisions with advance supply information in an assemble-to-order system

We study a periodic-review assemble-to-order (ATO) system with multiple components and multiple products, in which the inventory replenishment for each component follows an independent base-stock policy and stochastic product demands are satisfied according to a First-Come-First-Served rule. We assume that the replenishment for various component suffers from lead time uncertainty. However, the decision maker has the so-called advance supply information (ASI) associated with the lead times and thus can take advantage of the information for system optimization. We propose a multistage stochastic integer program that incorporates ASI to address the joint optimization of inventory replenishment and component allocation. The optimal base-stock policy for the inventory replenishment is determined using the sample average approximation algorithm. Also, we provide a modified order-based component allocation (MOBCA) heuristic for the component allocation. We additionally consider a special case of the variable lead times where the resulting two-stage stochastic programming model can be characterized as a single-scenario case of the proposed multistage model. We carry out extensive computational studies to quantify the benefits of integrating ASI into joint optimization and to explore the possibility of employing the two-stage model as a relatively efficient approximation scheme for the multistage model.     

引入价格因素的网络资源分配模型与算法实现

引入价格因素,针对网络资源分配提出PE-EMRA网络资源分配模型,并给出算法实现。PE-EMRA模型综合考虑带宽、缓冲等多种网络资源,调节并限制各业务类流量,使系统总效率最大化。该方法可有效提高资源利用率,提供服务质量保证,并具有配置灵活、实现代价小等特点。     

Optimal advertising and inventory control of perishable goods

The primary goal of this article is to extend the results of a previous article to the case where the effect of advertisement on sales lasts more than one period. Monotonicity of the optimal advertising and inventory policies in the various factors is investigated. Also, attention will be focused on the relationship between the fluctuations over time of the optimal policies and the variations over time of the factors involved, such as demand distributions and holding costs. For example, if over a finite interval the demand decreases from one period to the next, reaches a minimum, and then increases, then the optimal advertising policy will produce the opposite effect. The period of minimum demand never precedes that of maximum goodwill; moreover, the optimal inventory level decreases while the demand decreases. Finally, when demand distributions are just translates of one another, the results of this article can be extended to nonperishable goods.     

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

Vendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Does defence expenditure have a spillover effect on income inequality? A cross-regional analysis in China

China’s defence expenditure has been growing rapidly along with GDP growth during the past two decades. Meanwhile, the income gap has continued to increase. There are conflicting views regarding whether the defence expenditure is capable of reducing income inequality. Therefore, this paper investigates the existence of any spillover effect of defence expenditure on income inequality, with a special focus on the regional differences among 31 provinces and 7 military regions in China. We extend panel cointegration and the impulse response function by using panel data during the period of 1997–2012. The empirical results show that the defence expenditure has an impact on income inequality, and the effect varies over different regions in China. The defence expenditure has a spillover effect on income inequality in the full sample panel and the southeastern panel. An increase in the defence expenditure does not crowd out social welfare spending due to the high level of economic development and government expenditure. On the contrary, in the northern panel, the effect is opposite because of the unbalanced economic development levels within the panel. Beijing as the capital of China, benefits more from the expansion of defence expenditure thus widening the income gap. In addition, the impulse response analyses further confirm a stronger effect of the defence expenditure on income inequality in the northern and the southeastern panels over a short period.     

Stability of information‐sharing alliances in a three‐level supply chain

In their recent article, Leng and Parlar (L&P) (2009) analyze information‐sharing alliances in a three‐level supply chain (consisting of a manufacturer, a distributor, and a retailer) that faces a nonstationary end demand. Supply chain members can share demand information, which reduces information distortion and thus decreases their inventory holding and shortage costs. We expand the results from L&P by considering dynamic (farsighted) stability concepts. We use two different allocation rules and show that under some reasonable assumptions there should always be some information sharing in this supply chain. We also identify conditions under which the retailer in a stable outcome shares his demand information with the distributor, with the manufacturer, or with both remaining supply chain members. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010