Single-period Newsvendor Problem Research Articles

A dynamic mobile production capacity and inventory control problem

We analyze a problem of dynamic logistics planning given uncertain demands for a multi-location production-inventory system with transportable modular production capacity. In such systems, production modules provide capacity, and can be moved from one location to another to produce stock and satisfy demand. We formulate a dynamic programming model for a planning problem that considers production and inventory decisions, and develop suboptimal lookahead and rollout policies that use value function approximations based on geographic decomposition. Mixed-integer programming formulations are provided for several single-period optimization problems that define these policies. These models generalize a formulation for the single-period newsvendor problem, and in some cases the feasible region polyhedra contain only integer extreme points allowing efficient solution computation. A computational study with stationary demand distributions, which should benefit least from mobile capacity, provides an analysis of the effectiveness of these policies and the value that mobile production capacity provides. For problems with 20 production locations, the best suboptimal policies produce on average 13% savings over fixed capacity allocation policies when the costs of module movement, holding, and backordering are accounted for. Greater savings result when the number of locations increases.

Mean-variance analysis of the newsvendor problem with price-dependent, isoelastic demand

We present a mean-variance analysis of the single-product, single-period newsvendor problem with two decision variables, price and stock quantity. The demand is price-dependent, multiplicative, and isoelastic, and the product sold is price-elastic. The main goal of this paper is to completely characterize a framework where most risk sensitivities can be studied and find conditions under which the unimodality of this mean-variance performance measure is guaranteed. We aim at presenting these conditions in terms of a metric that can capture managerial attention. To this end we use the lost sales rate (LSR) elasticity, as it relates directly to the retailer’s level of service. The main contribution of this paper is that, with very few and mild assumptions, we complement currently existing results for the uniqueness of the solution in the presence of price-inelastic products by extending the applicability of the LSR elasticity to the problem with price-elastic goods and assess its unimodality when the decision maker is risk-neutral or risk-sensitive. Finally, we compare the results under this model with others previously obtained for additive demand models, and we emphasize the reasons that make it difficult to attain similar results with an isoelastic demand model.

A distribution free newsvendor model with consignment policy and retailer’s royalty reduction

Reducing the system cost and achieving significant profit are the key factors for every successful business sector. A consignment contract under distribution-free approach may be a fruitful combination to achieve a profitable business. This model deals with a single-period newsvendor problem with a consignment policy. The consignment policy is an agreement between any two parties, named as the consignor and the consignee. Under Stackelberg approach, firms act as leader and follower. Both parties carry some parts of the holding cost instead of one. A new policy for paying the fixed fee to the consignee is introduced. This paper considers no specific probability distribution for customer’s demand except a known mean and standard deviation. An efficient approach is proposed to reduce the retailer’s cost and building a sustainable consignment contract. The solution of this model is obtained using distribution free approach. A comparison between the traditional supply chain policy and the consignment policy is established. The price-sensitivity on demand is analysed. Some numerical examples and graphical representations are given for both traditional and consignment policy. Result proves that consignment policy is dominating over the traditional policy and a significant reduction of retailer’s royalty is found.

Single-period newsvendor problem under random end-of-season demand

Newsvendor problems, which have attracted the attention of researchers since 1950s, have wide applications in various industries. There have been many extensions to the standard single-period newsvendor problem. In this paper, we consider the single-period, single-item and single-stage newsvendor problem under random end-of- season demand and develop a model to determine the optimal order quantity and expected profit. We prove that the optimal order quantity and expected profit thus obtained are lower than their respective values obtained from the standard newsvendor formulation. We also provide numerical examples and perform sensitivity analyses to compute the extent of deviations of the ‘true’ optimal solutions from the newsvendor solutions. We observe that the deviations are most sensitive to the ratio of the means of the demand distributions. The deviations are also found sensitive to the contribution margin, salvage price, coefficients of variation of the demand distributions and correlation between seasonal and end-of-season demands. We provide broad guidelines for managers as to when the model developed in this paper should be used and when the standard newsvendor formulation would suffice to determine the order quantity.

Channel Coordination in a Multi-Period Newsvendor Model with Dynamic, Price-Dependent Stochastic Demand

In this study, we extend the single-period newsvendor problem with stochastic demand into a multi-period and time-dependent one and find a solution for it. We analyze the multi-period newsvendor problem with stochastic demand in a Stackelberg framework where the wholesaler is the leader and the retailer (newsvendor) is the follower. We use an additive-multiplicative structure for the demand so that both its mean and variance are considered as functions of the current retail price. Moreover, in our model, the demand mean and variance can be either time-dependent or autonomous with respect to time. A price-dependent memory function is also embedded in this representation of demand that carries the effect of demand level at present over to the demand in future. This leads to a strategic game in which the players must balance immediate high profits with reduced future earnings. We propose a complete solution to this stochastic multi-period Stackelberg game, covering cases with finite and infinite horizons. The theory is illustrated by using Cobb-Douglas demand functions as the deterministic part, while a random variable brings in stochasticity into the model. Because our theory is very flexible with respect to the assumptions made about the demand, market memory, and the behavior of the two agents, it is applicable to a wide variety of functional forms and capable to model many different economic contexts.

A price-setting newsvendor problem under mean-variance criteria

The single-product, single-period newsvendor problem with two decision variables, namely price and stock quantity, is considered. The performance measure, in addition to the expected revenue, includes the variance of the income scaled with a risk parameter. We present conditions for the concavity of this risk-sensitive performance measure and the uniqueness of the optimal solution for both risk-averse and risk-seeking cases under the additive demand model, and compare the results to others previously published. These conditions are introduced in terms of the lost sales rate elasticity. Furthermore, we provide numerical examples that aim to endorse the theoretical results herein explained.

Production-Distribution Planning for a Two-Echelon Decentralized Supply Chain Coordinated with Revenue Sharing Mechanisms

This study presents a model for multi-product, multi-period production-distribution planning with revenue sharing for a two-echelon decentralized supply chain. The model incorporates a revenue sharing mechanism that is used to coordinate the two echelons and considers the distributor's ordering behavior under uncertain demands which is formulated by a single-period news-vendor problem. Since the model is a mixed-integer, nonlinear programming problem, a heuristic is proposed. The heuristic determines not only the production quantities and product flows for the supply chain network but also the wholesale prices between the two echelons. The proposed heuristic is evaluated against the optimal solution values and the computation times obtained by solving the model as a mixed-integer, nonlinear programming problem. The experiments employ the solution gap ratio and time-saving ratio to measure the solution quality and the computation efficiency for the proposed heuristic. The average solution gap was 3.564%. The maximum average time-saving ratio was 870.651 at the large supply chain environment. The results show that the proposed heuristic is effective and efficient in terms of solution quality and computation time.

Determining optimal price and order size for a price setting newsvendor under cycle service level

There has been significant interest in the single period newsvendor problem where, besides determining the order size, the decision maker has to set the selling price. The model is applicable when demand for the product is a stochastic function of the selling price. Although there have been several studies, the problem needs exploration given that retailers prefer using service level rather than the shortage cost to model the economic consequence of a stock out. We analyze the problem using a chance constrained formulation and provide a procedure for determining the optimal price and order size for a price-setting newsvendor.

The risk averse newsvendor problem from rank-dependent expected utility approach

This paper examines the single-period newsvendor problem where the risk averse newsvendor with rank-dependent expected utility (RDEU) determines the optimal order of newspapers for sale. Compared with the expected-utility (EU) newsvendor model, the effect of risk averse under RDEU on optimal order quantity is more significant and a closed-form solution is derived for dual-utility (DU) theory. The optimal order for RDEU newsvender is less than that for DU one. It follows that the optimal order for EU newsvender is less than that for expected-profit (EP) one. On the other hand, the optimal order for RDEU newsvender is less than that for EU one. In particular, the optimal order for DU newsvender is less than that for EP one. Effect of changes in risk aversion degree is also explored.

Effects of higher order moments on the newsvendor problem

In this paper, we propose a stochastic programming model for the well-known single-period newsvendor problem by adopting the conditional Value-at-Risk (CVaR) as the risk metric in the objective function. The demand uncertainty is modeled in terms of discrete scenarios that reflect the empirical distributions implied by market demand data. Our numerical results demonstrate that the higher order moments (skewness and kurtosis) of demand have obvious effects on the newsvendor problem, and the stochastic programming framework provides a flexible and effective decision support tool for the newsvendor problem.

Coordination Scheme for Restructuring Business Operation of the Single Period Newsvendor Problem

This paper presents a coordination scheme for a single period newsvendor problem when both supplier and retailer of the supply chain agree to change the business operation from a market decision power sharing system (Model 1) to a unique decision maker system (Model 2). The supplier is assumed to be a risk-averse decision maker and he will undertake the product quality risk in both models. Model 1 is game theoretic, where the supplier controls the wholesale price, but the retailer controls the order quantity and market price. The bargaining process ends when the supplier has found a wholesale price that maximizes the value of his sales revenue minus the product quality cost. Model 2 is a centralized system where the supplier possesses all decision powers of the market. In general, Model 2 will generate higher total revenue than Model 1. The aim of this research is to propose a satisfying compromise based on consignment policy to resolve the revenue-sharing conflict in Model 2 due to the additional revenue. An example is provided to illustrate the two models and the proposed coordination scheme, along with managerial insights on the models’ benefits. The impacts of several parameters on the scheme are also presented and discussed.

The newsvendor problem under multiplicative background risk

This note studies the single-period newsvendor problem when the newsvendor faces a multiplicative neutral independent background risk in an expected utility framework. It is shown that multiplicative risk vulnerability is a sufficient condition to guarantee a decrease in the optimal order. A weaker sufficient condition which has more interpretability is also provided and discussed. This result sheds light on situations where exchange, tax or inflation rates risks, which apply multiplicatively to the final wealth, are at work.

The Newsvendor Problem Under Multiplicative Background Risk

This note studies the single-period newsvendor problem when the newsvendor faces a multiplicative neutral independent background risk in an expected utility framework. It is shown that multiplicative risk vulnerability is a sufficient condition to guarantee a decrease in the optimal order. A weaker sufficient condition which has more interpretability is also provided and discussed. This result sheds light on situations where exchange, tax or inflation rates risks, which apply multiplicatively to the final wealth, are at work.

Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models

In this paper, we consider two fundamental inventory models, the single-period newsvendor problem and its multiperiod extension, but under the assumption that the explicit demand distributions are not known and that the only information available is a set of independent samples drawn from the true distributions. Under the assumption that the demand distributions are given explicitly, these models are well studied and relatively straightforward to solve. However, in most real-life scenarios, the true demand distributions are not available, or they are too complex to work with. Thus, a sampling-driven algorithmic framework is very attractive, both in practice and in theory. We shall describe how to compute sampling-based policies, that is, policies that are computed based only on observed samples of the demands without any access to, or assumptions on, the true demand distributions. Moreover, we establish bounds on the number of samples required to guarantee that, with high probability, the expected cost of the sampling-based policies is arbitrarily close (i.e., with arbitrarily small relative error) compared to the expected cost of the optimal policies, which have full access to the demand distributions. The bounds that we develop are general, easy to compute, and do not depend at all on the specific demand distributions.

Newsvendor solutions via conditional value-at-risk minimization

In this paper, we consider the minimization of the conditional value-at-risk (CVaR), a most preferable risk measure in financial risk management, in the context of the well-known single-period newsvendor problem, which is originally formulated as the maximization of the expected profit or the minimization of the expected cost. We show that downside risk measures including the CVaR are tractable in the problem due to their convexity, and consequently, under mild assumptions on the probability distribution of products’ demand, we provide analytical solutions or linear programming (LP) formulation of the minimization of the CVaR measures defined with two different loss functions. Numerical examples are also exhibited, clarifying the difference among the models analyzed in this paper, and demonstrating the efficiency of the LP solutions.

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.