Continuous inventory control with stochastic and non-stationary Markovian demand

Nasr, Walid W.; Elshar, Ibrahim J.

doi:10.1016/j.ejor.2018.03.023

Cited by 18 publications

(2 citation statements)

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“…• Network/peer effects: A wide range of products are influenced by network or peer effects (Seiler et al 2017, Goolsbee and Klenow 2002, Bailey et al 2019, Nasr and Elshar 2018. Baardman et al (2020) show that demand prediction can be improved by incorporating such effects.…”

Section: Modeling Issuesmentioning

confidence: 99%

On Dynamic Pricing with Covariates

Wang¹,

Talluri²,

Li³

2021

Preprint

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We consider the dynamic pricing problem with covariates under a generalized linear demand model: a seller can dynamically adjust the price of a product over a horizon of T time periods, and at each time period t, the demand of the product is jointly determined by the price and an observable covariate vector xt ∈ R d through an unknown generalized linear model. Most of the existing literature assumes the covariate vectors xt's are independently and identically distributed (i.i.d.); the few papers that relax this assumption either sacrifice model generality or yield sub-optimal regret bounds. In this paper we show that a simple pricing algorithm has an O(d √ T log T ) regret upper bound without assuming any statistical structure on the covariates xt (which can even be arbitrarily chosen). The upper bound on the regret matches the lower bound (even under the i.i.d. assumption) up to logarithmic factors. Our paper thus shows that (i) the i.i.d. assumption is not necessary for obtaining low regret, and (ii) the regret bound can be independent of the (inverse) minimum eigenvalue of the covariance matrix of the xt's, a quantity present in previous bounds. Furthermore, we discuss a condition under which a better regret is achievable and how a Thompson sampling algorithm can be applied to give an efficient computation of the prices.

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Section: Modeling Issuesmentioning

confidence: 99%

On Dynamic Pricing with Covariates

Wang¹,

Talluri²,

Li³

2021

Preprint

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“…On the other hand, studies on a probabilistic model whose state shows discontinuous variation have been also reported so far such as Markov chain models (for example, Nasr andElshar 2018 andSchlosser 2016). Further, discussions on inventory problems having such an intermediate structure from a viewpoint of mechanical engineering have been recently reported, for instance, studies on supply chain management (Fatrias andShimizu 2010, Grewal andRogers 2015).…”

Section: Introductionmentioning

confidence: 98%

Optimal control in an inventory management problem considering replenishment lead time based upon a non-diffusive stochastic differential equation

Kanekiyo

Agata

2019

JAMDSM

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An inventory management problem is theoretically discussed for a factory having effects of lead times in replenishing the inventory, where it stocks materials used for its products. It is assumed that the factory can dynamically control the size of ordering materials. By applying the stochastic control theory, the optimal control of the ordering size is derived, in which the expected total cost up to an expiration time is minimized. First, a new stochastic model is constructed for describing an inventory fluctuation of the factory by the use of a non-diffusive stochastic differential equation, where an analytic time is introduced so that the inventory process can be a Markov process even though it is affected by lead times. Next, an optimal control is formulated by introducing an evaluation function quantifying total costs. Based upon them, the Hamilton-Jacobi-Bellman (HJB) equation is derived, whose solution gives the optimal control. Finally, the optimal control is quantitatively examined through numerical solutions of the HJB equation. Numerical results indicate that if time up to an expiration time is short then the optimal control is affected by it, otherwise, the optimal control does not depend on it. 1

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