Chapter 12 Stochastic inventory theory

Porteus, Evan L.

doi:10.1016/s0927-0507(05)80176-8

Cited by 303 publications

(241 citation statements)

References 81 publications

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“…Our setting is related to the newsvendor problem which has been extensively studied in the literature (see, e.g., Zipkin (2000), Porteus (1990), Winston (1994) and the references therein). An interesting extension that is even more related to this research is the price-setting newsvendor (see Petruzzi and Dada (1999) and Yao et al (2006)).…”

Section: Literature Reviewmentioning

confidence: 99%

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

2016

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This paper studies government subsidies for green technology adoption while considering the manufacturing industry's response. Government subsidies offered directly to consumers impact the supplier's production and pricing decisions. Our analysis expands the current understanding of the price-setting newsvendor model, incorporating the external influence from the government who is now an additional player in the system. We quantify how demand uncertainty impacts the various players (government, industry and consumers) when designing policies. We further show that for convex demand functions, an increase in demand uncertainty leads to higher production quantities and lower prices, resulting in lower profits for the supplier. With this in mind, one could expect consumer surplus to increase with uncertainty. In fact, we show this is not always the case and the uncertainty impact on consumer surplus depends on the trade-off between lower prices and the possibility of under-serving customers with high valuations. We also show that when policy makers such as governments ignore demand uncertainty when designing consumer subsidies, they can significantly miss the desired adoption target level. From a coordination perspective, we demonstrate that the decentralized decisions are also optimal for a central planner managing jointly the supplier and the government. As a result, subsidies provide a coordination mechanism.

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Section: Literature Reviewmentioning

confidence: 99%

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

2016

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“…Porteus (1990) presents a thorough review of various newsvendor models. Veinott (1965) considers the dynamic version of the multi-product inventory models in a multiperiod setting, with general assumptions in demand process, cost parameters and lead times.…”

Section: Introductionmentioning

confidence: 99%

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

Choi,

Ruszczyński

2011

European Journal of Operational Research

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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.

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“…It is well known that for a given distribution F, the optimal solution of the newsvendor problem is given by Q which satisfies inf{ : is the optimal stock-out ratio (Porteus, 2002). Hence the min-max optimal solution for a given class of distributions M is sup * inf{ :…”

Section: The Newsvendor Problemmentioning

confidence: 99%

“…The first one is the newsvendor problem pioneered by Arrow et al (1951). The newsvendor problem is considered as one of the most important one in the inventory control theory, see Porteus (2002). A good review on the problem can be found in Khouja (1999) and Qin et al (2011).…”

Section: Introductionmentioning

confidence: 99%

Min-Max Stochastic Optimization with Applications to the Single-Period Inventory Control Problem

Park¹

2015

Management Science and Financial Engineering

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Min-max stochastic optimization is an approach to address the distribution ambiguity of the underlying random variable. We present a unified approach to the problem which utilizes the theory of convex order on the random variables. First, we consider a general framework for the problem and give a condition under which the convex order can be utilized to transform the min-max optimization problem into a simple minimization problem. Then extremal distributions are presented for some interesting classes of distributions. Finally, applications to the single-period inventory control problems are given.

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Chapter 12 Stochastic inventory theory

Cited by 303 publications

References 81 publications

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

The Impact of Demand Uncertainty on Consumer Subsidies for Green Technology Adoption

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

Min-Max Stochastic Optimization with Applications to the Single-Period Inventory Control Problem

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