A review of non-cooperative newsvendor games with horizontal inventory interactions

There are numerous applications of game theory in the analysis of supply chains where multiple actors interact with each other in order to reach their own objectives. In this paper we review the use of non-cooperative game theory in inventory management within the newsvendor framework describing a single period inventory control model with the focus on horizontal interactions among multiple independent newsvendors. We develop a framework for identifying these types of horizontal interactions including, for example, the models with the possibility of inventory sharing via transshipments, and situations with substitutable products sold by multiple newsvendors. Based on this framework, we discuss and relate the results of prior research and identify future research opportunities

TECHNICAL NOTE—Robust Newsvendor Competition Under Asymmetric Information

We generalize analysis of competition among newsvendors to a setting in which competitors possess asymmetric information about future demand realizations, and this information is limited to knowledge of the support of demand distribution. In such a setting, traditional expectation-based optimization criteria are not adequate, and therefore we focus on the alternative criterion used in the robust optimization literature: the absolute regret minimization. We show existence and derive closed-form expressions for the robust optimization Nash equilibrium solution for a game with an arbitrary number of players. This solution allows us to gain insight into the nature of robust asymmetric newsvendor competition. We show that the competitive solution in the presence of information asymmetry is an intuitive extension of the robust solution for the monopolistic newsvendor problem, which allows us to distill the impact of both competition and information asymmetry. In addition, we show that, contrary to the intuition, a competing newsvendor does not necessarily benefit from having better information about its own demand distribution than its competitor has

Behavioral analyses of retailers’ ordering decisions

The main objective I pursue in this thesis is to better understand how different factors may independently and in combination influence retailers' ordering decisions under different supply chain structures (single agent and multi agent), different demand uncertainty (deterministic and stochastic), and different interaction among retailers (no interaction, competition and cooperation). I developed three different studies where I build on different formal management model and then run multiple behavioral studies to better understand subjects’ behavior. The first study analyzes order amplification in a single-supplier single-retailer supply chain. I used a behavioral experiment to test retailers’ orders under different ordering delays and different times to build supplier’s capacity. Results provide (i) a better understanding of the endogenous dynamics leading to retailers’ ordering amplification, and (ii) a description of subjects’ biases and deviation from optimal trajectories; despite subjects have full information about the system structure. The second study analyzes how order amplification can also take place when there is fierce retailer competition and limited supplier capacity. I study how different factors (different time to build supplier capacity, different levels of competition among retailers, different magnitudes of supply shortage and different allocation mechanisms) may independently and in combination influence retailers’ order in a system with two retailers under supply competition. Results show that (i) the bullwhip effect persists even when subjects do not have incentives to deviate, (ii) subjects amplify their orders in an attempt to build an unnecessary safety stock to respond to potential deviations from the other retailers, and (iii) retailers’ underperformance varies with the allocation mechanism used by the supplier. In the last study, I analyze retailers’ orders in a system where there is uncertainty in the final customer demand. I experimentally explore the effect of transshipments among retailers in a single-supplier multi-retailer supply chain. Specifically, I explore retailers’ orders under different profit and communication conditions. In addition, I integrate analytical and behavioral models to improve supply chain performance. Results show that (i) the persistence of common biases in a newsvendor problem (pull-to-center, demand chasing, loss aversion, psychological disutility), (ii) communication could improve coordination and may reduce demand chasing behavior, (iii) supply chain performance increases with the use of behavioral strategies embedded within a traditional optimization model, and (iv) dynamic heuristics improve overall coordination, outperforming a simple Nash Equilibrium strategy

Joint Pricing and Purchasing Decisions for the Dual-Channel Newsvendor Model with Partial Information

We investigate a joint pricing and purchasing problem for the dual-channel newsvendor model with the assumption that only the mean and variance of the demand are known. The newsvendor in our model simultaneously distributes a single product through traditional retail and Internet. A robust optimization approach that maximizes the worst-case profit is adapted under the aforementioned conditions to model demand uncertainty and linear clearing functions that characterize the relationship between demand and prices. We obtain a close-form expression for the robust optimal policy. Illustrative simulations and numerical experiments show the effects of several parameters on the optimal policy and on newsvendor performance. Finally, we determine that the gap between newsvendor performance under demand certainty and uncertainty is minimal, which shows that the robust approach can significantly improve performance

Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand

This paper considers the classical Newsvendor model, also known as the Newsboy problem, with the demand to be fully observed and to follow in successive inventory cycles one of the Exponential, Rayleigh, and Log-Normal distributions. For each distribution, appropriate estimators for the optimal order quantity are considered, and their sampling distributions are derived. Then, through Monte-Carlo simulations, we evaluate the performance of corresponding exact and asymptotic confidence intervals for the true optimal order quantity. The case where normality for demand is erroneously assumed is also investigated. Asymptotic confidence intervals produce higher precision, but to attain equality between their actual and nominal confidence level, samples of at least a certain size should be available. This size depends upon the coefficients of variation, skewness and kurtosis. The paper concludes that having available data on the skewed demand for enough inventory cycles enables (i) to trace non-normality, and (ii) to use the right asymptotic confidence intervals in order the estimates for the optimal order quantity to be valid and precise.Inventory Control; Newsboy Problem; Skewed Demand; Exact and Asymptotic Confidence Intervals; Monte-Carlo Simulations

Optimal Decisions of a Supply Chain with Two Risk-Averse and Competing Retailers under Random Demand

This paper investigates the optimal decisions in a decentralized supply chain consisting of one manufacturer and two competing retailers who face price-sensitive and stochastic demand. The retailers are risk averse with conditional value at risk (CVaR) as their risk measure, and the manufacturer is a risk-neutral agent. We construct manufacturer-Stackelberg games with retailers, who engage in horizontal price competition. For the multiplicative demand model and expected demand as an exponential function of both prices, we show that there exists the optimal pricing-ordering joint decision uniquely. We then explore the influence of the price sensitivity, risk aversion, and retail competition on optimal decisions and channel efficiency. The results show that retail competition contributes to manufacturer and improves channel efficiency of the decentralized supply chain. When the retailers are more risk averse, the channel efficiency becomes much lower. However, the level of retailers’ risk aversion has no significant impact on the manufacturer’s optimal wholesale price and retailer’s optimal selling price

Coordinating a Supply Chain With a Manufacturer-Owned Online Channel: A Dual Channel Model Under Price Competition

We consider a dual channel supply chain in which a manufacturer sells a single product to end-users through both a traditional retail channel and a manufacturer-owned direct online channel. We adopt a commonly used linear demand substitution model in which the mean demand in each channel is a function of the prices in each channel.We model each channel as a news vendor problem, with price and order quantity as decision variables. In addition, the manufacturer must choose the wholesale price to charge to the independent retailer. We analyze the optimal decisions for each channel and prove the existence of a unique equilibrium for the system. We compare this equilibrium solution to the solution for an integrated system, in which the manufacturer owns both the online store and the retailer. To enable supply chain coordination, we propose two contract schemes: a modified revenue-sharing contract and gain/loss sharing contract. We show that, in cases where the retail channel has a larger market than the online channel, such contracts enable the manufacturer to maintain price discrimination, selling the products in different channels at different prices. Finally, we perform a comprehensive numerical study to consider the impact of the model parameters on the equilibrium and to demonstrate the performance of the proposed coordination contracts. We conclude that coordination is most critical for products which are highly price sensitive and for systems in which the online and traditional retail channels are not viewed as close substitutes

Disaster relief inventory management: horizontal cooperation between humanitarian organizations

Cooperation among humanitarian organizations has attracted increasing attention to enhance effectiveness and efficiency of relief supply chains. Our research focuses on horizontal cooperation in inventory management which is currently implemented in the United Nations Humanitarian Response Depot (UNHRD) network. The present work follows a two-step research approach, which involves collection of empirical data and quantitative modeling to examine and overcome the coordination challenges of the network. Our interviews with members of the network identified several managerial issues for sustainable cooperative inventory management that the UNHRD network pursues. Using a newsvendor model in the context of non-cooperative game theory, our research has explored member humanitarian organizations' incentive of joining the network, a coordination mechanism which achieves system optimality, and impacts of members' decisions about stock rationing. Our results indicate that behaviors of member HOs do not necessarily align with the UNHRD's expectation. Our results suggest that for system optimality, a system coordinator should carefully assess the circumstances, including demand coefficient and stock rationing. Our research also proposes a policy priority for the first-best system optimal inventory management

An Elasticity Approach to the Newsvendor with Price Sensitive Demand

Cataloged from PDF version of article.We introduce a measure of elasticity of stochastic demand, called the elasticity of the lost-sales rate, which offers a unifying perspective on the well-known newsvendor with pricing problem. This new concept provides a framework to characterize structural results for coordinated and uncoordinated pricing and inventory strategies. Concavity and submodularity of the profit function, as well as sensitivity properties of the optimal inventory and price policies, are characterized by monotonicity conditions, or bounds, on the elasticity of the lost-sales rate. These elasticity conditions are satisfied by most relevant demand models in the marketing and operations literature. Our results unify and complement previous work on price-setting newsvendor models and provide a new tool for researchers modeling stochastic price-sensitive demand in other contexts

An Experimental Investigation of Outsourcing through Competition

Our research uses laboratory experiments to examine the theoretical results of competition between suppliers in an outsourcing setup. We consider a supply chain in which a single buyer needs to outsource the manufacturing of a product among N potential suppliers. The buyer allocates demand to suppliers not on the basis of price, but rather on service. We analyze the levels of service suppliers will decide to provide when competing on three different criteria specified by the buyer. For the first, suppliers compete by providing the buyer a specific service level (fill-rate), and for the second by maintaining a specific quantity of on-hand inventory. For the third criteria, suppliers compete based on a parameter designed to optimize the supply chain in favor of the buyer. Prior research and existing theory predict that the decisions will reach stability at the Nash equilibrium for all three types of competition. Theory also predicts these equilibrium points will be ordered, from competitions based on service level as the lowest and those based on the optimal criteria as the highest. Our experimental results show that the equilibrium points reached by subjects are in fact ordered as theory predicts. However, there are large and statistically significant differences between those equilibrium points and the theoretical predictions. Using the Quantal Response Equilibrium (QRE) we show that random errors can explain some of these discrepancies. Our analyses also suggest that, under optimal criteria for competition, other behavioral factors such as rival chasing and loss aversion can play an influential role