The newsvendor problem: Review and directions for future research

In this paper, we review the contributions to date for analyzing the newsvendor problem. Our focus is on examining the specific extensions for analyzing this problem in the context of modeling customer demand, supplier costs, and the buyer risk profile. More specifically, we analyze the impact of market price, marketing effort, and stocking quantity on customer demand; how supplier prices can serve as a coordination mechanism in a supply chain setting; integrating alternative supplier pricing policies within the newsvendor framework; and how the buyer’s risk profile moderates the newsvendor order quantity decision. For each of these areas, we summarize the current literature and develop extensions. Finally, we also propose directions for future research.     

Analysis of a newsvendor which has errors in inventory data records

Although supply chain scholars very often assume the availability of error free data pertaining to the flow of goods that come in and go out of an inventory system as well as the on hand inventory level, some recent investigations show that this may not be true even in facilities where advanced item identification and data capture technologies such as the barcode system are used. This paper proposes a single period model where the inventory data capture process using the barcode system is prone to errors that lead to inaccuracies. In the first part of our work, we derive analytically the optimal policy in presence of errors when both demand and errors are uniformly distributed. In the second part, we examine quantitatively the impact of record inaccuracies on the performance of an inventory system, in terms of additional overage and shortage costs incurred.     

A fuzzy newsvendor approach to supply chain coordination

In the absence of a clear command and control structure, a key challenge in supply chain management is the coordination and alignment of supply chain members who pursue divergent and often conflicting goals. The newsvendor model is typically used as a framework to quantify the cost of misalignment and to assess the impact of various coordination initiatives. The application of the newsvendor framework, however, requires the specification of some probability distribution for the sources of uncertainty, and in particular, for the market demand. The specification of an adequate demand distribution becomes difficult in the absence of statistical data. We therefore consider a fuzzy approach to the newsvendor problem. We use several fuzzy parameters in the model for the demand, the wholesale price, and the market sales price. We solve the fuzzy newsvendor problem to study three coordination policies: quantity discounts, profit sharing, and buyback. For each coordination policy, the optimal order quantity of the retailer is computed. The possible profits of the members in the supply chain are calculated with minimum sharing of private information. We further extend the fuzzy newsvendor model to a setting with a single manufacturer and multiple retailers under the assumption of ample capacity for the manufacturer. Detailed numerical examples are also provided.     

A multi-product risk-averse newsvendor with exponential utility function

We consider a multi-product newsvendor using an exponential utility function. We first establish a few basic properties for the newsvendor regarding the convexity of the model and monotonicity of the impact of risk aversion on the solution.When the product demands are independent and the ratio of the degree of risk aversion to the number of products is sufficiently small, we obtain closed-form approximations of the optimal order quantities. The approximations are as easy to compute as the risk-neutral solution. We prove that when this ratio approaches zero, the risk-averse solution converges to the corresponding risk-neutral solution. When the product demands are positively (negatively) correlated, we show that risk aversion leads to lower (higher) optimal order quantities than the solution with independent demands.Using a numerical study, we examine convergence rates of the approximations and thoroughly study the interplay of demand correlation and risk aversion. The numerical study confirms our analytical results and further shows that an increased risk aversion does not always lead to lower order quantities, when demands are strongly negatively correlated.     

The newsvendor problem with an in-season price adjustment

Consider a retailer stocking a seasonal item facing a stochastic demand where information about the demand becomes more accurate as the selling season progresses. The retailer places orders before the start of the season and in-season reorders are not possible. This article extends the classical newsvendor model by allowing the retailer to make an in-season price adjustment after conducting a review and using the realized demand to obtain an accurate estimate of the remaining demand. Our results include answers to the following questions. What price should the retailer choose? How much should the retailer have ordered at the start of the season given the option of adjusting prices in-season? This model was motivated by a problem in car rental revenue management and has applications in perishable assets revenue management (PARM), where price adjustments are needed towards the end of the selling season.     

Nash game model for optimizing market strategies,configuration of platform products in a Vendor Managed Inventory (VMI) supply chain for a product family

This paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies, platform product configuration and inventory policies in a VMI (Vendor Managed Inventory) supply chain. The manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers. Multiple types of products are substitutable each other to end customers. The manufacturer makes its decision on raw materials’ procurement, platform product configuration, product replenishment policies to retailers with VMI, price discount rate, and advertising investment to maximize its profit. Retailers in turn consider the optimal local advertising investments and retail prices to maximize their profits. This problem is modeled as a dual simultaneous non-cooperative game (as a dual Nash game) model with two sub-games. One is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers. This paper combines analytical, iterative and GA (genetic algorithm) methods to develop a game solution algorithm to find the Nash equilibrium. A numerical example is conducted to test the proposed model and algorithm, and gain managerial implications.     

A multi-item newsvendor problem with preseason production and capacitated reactive production

Given items with short life cycles or seasonal demands, one can potentially improve profits by producing during the selling season, especially when its production capacity is substantial. We develop a two-stage, multi-item model incorporating reactive production that employs a firm’s internal capacity. Production occurs in an uncapacitated preseason stage and a capacitated reactive stage. Demands occur in the reactive stage. Reactive capacities are pre-allocated to each item in the preseason stage and cannot be changed during the reactive stage. Reactive production occurs during the selling season with full knowledge of demands. The objective is expected profit maximization. Unsatisfied demand is lost. The revenue, salvage value, and production and lost sales costs are proportional. Assuming no fixed costs, we present a simple algorithm for computing optimal policies. For a model with fixed costs for allocating preseason stage production and reactive stage capacity to product families, we characterize optimal policies and develop optimal and heuristic algorithms.     

Stability and monotonicity in newsvendor situations

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization. However, we assume that the retailers impose some level of stock that should be dedicated to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where several model cost parameters and the retailers’ dedicated stock levels can change. We investigate how the profit division might be affected by these changes. We focus on four monotonicity properties. We identify several classes of games with retailers, where some of the monotonicity properties hold. Moreover, we show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general, when changes in dedicated stock levels are in concern.     

Cooperative game theory approach to allocating benefits of horizontal cooperation

Logistics costs in general, and transportation costs in particular, represent a large fraction of the operating costs of many companies. One way to try to reduce these costs is through horizontal cooperation among shippers. Thus, when the transportation needs of two or more companies are merged, their collective transportation requirements can be met at lower cost. The attainable cost savings are due to economies of scale, which translate into cheaper rates due to increased negotiation power, use of larger vehicles and bundling of shipments. In this paper, a linear model is presented and used to study the cost savings that different companies may achieve when they merge their transportation requirements. On the one hand, solving this optimization model for different collaboration scenarios allows testing and quantifying the synergies among different potential partners, thus identifying the most profitable collaboration opportunities. On the other, the problem of allocating the joint cost savings of the cooperation is tackled using cooperative game theory. The proposed approach is illustrated with an example in which different cooperative game solution concepts are compared. Extensive numerical experiments have also been carried out to gain insight into the properties of the corresponding cost savings game and the behavior of the different solution concepts.     

Repeated Games with Bonuses

This paper deals with 2-player zero-sum repeated games in which player 1 receives a bonus at stage t if he repeats the action he played at stage t−1. We investigate the optimality of simple strategies for player 1. A simple strategy for player 1 consists of playing the same mixed action at every stage, irrespective of past play. Furthermore, for games in which player 1 has a simple optimal strategy, we characterize the set of stationary optimal strategies for player 2.     

A note on channel performance under consignment contract with revenue sharing

Wang et al. [Y. Wang, L. Jiang, Z.J. Shen, Channel performance under consignment contract with revenue sharing. Management Science 50 (2004), 34–47] indicate that a decentralized supply chain cannot be perfectly coordinated. This note provides a cooperative game model that implements profit sharing between the manufacturer and the retailer to achieve their cooperation. When the manufacturer and the retailer are assumed to be risk-neutral, under a very mild restriction on the demand distribution function, the cooperative game model can achieve its unique equilibrium solution in iso-price-elastic or linear demand case. Under the revenue sharing agreement attached with the equilibrium payment scheme, the decentralized supply chain can be perfectly coordinated.     

Benefits of co-operation in a production distribution environment

We model co-operation in a typical production distribution setting that contains one capacitated supplier producing and distributing a single product to many identical retailers who are facing i.i.d. end-item demands from the consumers. We consider three inventory allocation mechanisms, representing varying degrees of co-operation, at the supplier: (1) the orders from the retailers are filled in a predetermined sequence; (2) the orders from the retailers are filled after taking into account their current inventories; and (3) the orders from the retailers are filled assuming that the product can also be shipped from one retailer to another. We estimate the benefits due to co-operation in this supply chain and study the effect of various system parameters on these benefits. An extensive computational study indicated that the benefits of co-operation in this production distribution environment decrease with increase in the supplier capacity, increase in the number of retailers, decrease in penalty cost, and decrease in consumer demand variance.     

Agricultural planning of annual plants under demand,maturation, harvest,and yield risk

In this study we present a planning methodology for a firm whose objective is to match the random supply of annual premium fruits and vegetables from a number of contracted farms and the random demand from the retailers during the planning period. The supply uncertainty is due to the uncertainty of the maturation time, harvest time, and yield. The demand uncertainty is the uncertainty of weekly demand from the retailers. We provide a planning methodology to determine the farm areas and the seeding times for annual plants that survive for only one growing season in such a way that the expected total profit is maximized. Both the single period and the multi period cases are analyzed depending on the type of the plant. The performance of the solution methodology is evaluated by using numerical experiments. These experiments show that the proposed methodology matches random supply and random demand in a very effective way and improves the expected profit substantially compared to the planning approaches where the uncertainties are not taken into consideration.     

Single-vendor multi-buyer inventory coordination under private information

This paper considers the problem of coordinating a single-vendor multi-buyer inventory system when there are privacy restrictions in the information required to solve the problem. The objective function and cost parameters of each facility are regarded as private information that no other facilities in the system have access to. Moreover, each facility is responsible to specify its own replenishment policy. The objective is to minimize the total average setup/ordering and inventory-related cost. Solution methodologies under private and global information are developed to find two types of nested power-of-two stationary policies. The first policy assumes all the buyers must replenish simultaneously. The second policy is a more general case where the common replenishment assumption is relaxed. A simple form of information exchange is uncovered that allows the solution methodologies for private and global information yield the same results. The experimental results suggest that the performance of the proposed heuristics is comparable or better than an existing method.     

A (Q, R) inventory replenishment model with two delivery modes

Although splitting shipments across multiple delivery modes typically increases total shipping costs as a result of diseconomies of scale, it may offer certain benefits that can more than offset these costs. These benefits include a reduction in the probability of stockout and in the average inventory costs. We consider a single-stage inventory replenishment model that includes two delivery modes: a cheaper, less reliable mode, and another, more expensive but perfectly reliable mode. The high-reliability mode is only utilized in replenishment intervals in which the lead time of the less-reliable mode exceeds a certain value. This permits substituting the high-reliability mode for safety stock, to some degree. We characterize optimal replenishment decisions with these two modes, as well as the potential benefits of simultaneously using two delivery modes.     

On a multi-period supply chain system with supplementary order opportunity

This paper considers a supplementary supply–order system in a multi-period situation. In each period, the buyer first places an initial order based on the demand prediction; he has the opportunity to place a supplementary order with the supplier after the demand of that period is realized. The supplier maintains an inventory, and decides the quantity to be produced and the quantity to be provided for the supplementary order in each time period. We formulate the problem as a multi-period inventory game, and derive the optimal production and order policies for the supplier and buyer, respectively. The existence and uniqueness of Nash equilibrium is proved in the generalized multi-period setting, and the closed-form Nash equilibrium solution is obtained when the parameters are stationary. Numerical study is performed to reveal more managerial insights. We find that the supplementary supply–order mechanism, if designed properly, can effectively improve the multi-period supply chain performance.     

Comparing improvement strategies for inventory inaccuracy in a two-echelon supply chain

Classical inventory theory often assumes no discrepancies between recorded inventory and actual inventory. However, inventory records are usually inaccurate due to many reasons in practice. For example, inventory shrinkage refers to the difference between booked inventory that a company should have as a result of its sales, purchasing, and manufacturing processes and actual inventory that it has on hand. This paper concerns the impact of inventory shrinkage to a supply chain and investigates different strategies to deal with inventory shrinkage. We consider a single-period two-echelon supply chain consisting of a Stackelberg manufacturer and a retailer whose inventory is subject to shrinkage errors. Our analysis is based on a single-period newsvendor model and considers the following cases of order decisions: (a) the retailer ignores the inventory errors; (b) the retailer estimates the errors; (c) the retailer shares the inventory error information with the manufacturer; and (d) RFID technology is used to reduce or eliminate the errors. The first case is the base strategy and a common practice for many supply chains, the other two represent certain non-technological strategies of the retailer when dealing with inventory inaccuracy, and the last one represents a technology improvement strategy by the manufacturer to reduce or eliminate inventory shrinkage errors. We compare these improvement strategies and derive critical tag price for RFID implementation as a technological remedy for the inventory inaccuracy problem. Conditions for the profitability of RFID adoption are discussed.     

Inventory systems with stochastic demand and supply: Properties and approximations

We model a retailer whose supplier is subject to complete supply disruptions. We combine discrete-event uncertainty (disruptions) and continuous sources of uncertainty (stochastic demand or supply yield), which have different impacts on optimal inventory settings. This prevents optimal solutions from being found in closed form. We develop a closed-form approximate solution by focusing on a single stochastic period of demand or yield. We show how the familiar newsboy fractile is a critical trade-off in these systems, since the optimal base-stock policies balance inventory holding costs with the risk of shortage costs generated by a disruption.     

基于需求和生产成本偏差的Cournot竞争供应链协调

分析一个供应商和两个Cournot竞争零售商组成的供应链系统的协调问题.首先证明收益共享合约在稳定条件下能实现该供应链协调;当突发事件导致零售商面临的需求规模和供应商的生产成本同时与其预测值发生偏差时,为使供应链收益最大,提出了调整生产计划和零售价格的协调策略,进一步证明了改进的收益共享合约可协调需求和成本偏差的分权供应链;最后进行了数值实验.