A practical inventory control policy using operational statistics

Liyanage, Liwan; Shanthikumar, J. George

doi:10.1016/j.orl.2004.08.003

Cited by 177 publications

(108 citation statements)

References 10 publications

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“…Scarf (1959) proposed a Bayesian procedure that updates the belief regarding the uncertainty of the parameter based on observations that are collected over time. Liyanage and Shanthikumar (2005) introduced operational statistics which, unlike the Bayesian approach, does not assume any prior knowledge on the parameter values. Instead it performs optimization and estimation simultaneously.…”

Section: Literature Reviewmentioning

confidence: 99%

The Data-Driven Newsvendor Problem: New Bounds and Insights

Levi

Perakis

Uichanco

2015

Operations Research

183

117

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Consider the newsvendor model, but under the assumption that the underlying demand distribution is not known as part of the input. Instead, the only information available is a random, independent sample drawn from the demand distribution. This paper analyzes the sample average approximation (SAA) approach for the data-driven newsvendor problem. We obtain a new analytical bound on the probability that the relative regret of the SAA solution exceeds a threshold. This bound is significantly tighter than existing bounds, and it matches the empirical accuracy of the SAA solution observed in extensive computational experiments.This bound reveals that the demand distribution's weighted mean spread (WMS) affects the accuracy of the SAA heuristic.

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Section: Literature Reviewmentioning

confidence: 99%

The Data-Driven Newsvendor Problem: New Bounds and Insights

Levi

Perakis

Uichanco

2015

Operations Research

183

117

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“…In the case where the manager knows the distribution family to which demand belongs, but does not know either its parameters or its priors, Liyanage and Shanthikumar [26] propose an approach called operational statistics, which integrates the tasks of parameter estimation and expected profit optimization. They consider the stationary models with perishable inventory.…”

Section: Literature Review and Our Contributions Classical Inventorymentioning

confidence: 99%

A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

2009

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We study stochastic inventory planning with lost sales and instantaneous replenishment, where contrary to the classical inventory theory, the knowledge of the demand distribution is not available. Furthermore, we observe only the sales quantity in each period, and lost sales are unobservable, that is, demand data are censored. The manager must make an ordering decision in each period based only on historical sales data. Excess inventory is either perishable or carried over to the next period. In this setting, we propose non-parametric adaptive policies that generate ordering decisions over time. We show that the T -period average expected cost of our policy differs from the benchmark newsvendor cost -the minimum expected cost that would have incurred if the manager had known the underlying demand distribution -by at most O(1/ √ T ). IntroductionThe problem of inventory control and planning has received much interest from practitioners and academics from the early years of operations research. The early literature in this area modeled demand as deterministic and having known quantities, but it soon became apparent that deterministic modeling was often inadequate, and uncertainty needed to be incorporated in modeling future demand. As a result, a majority of the papers on inventory theory during the past fifty years employ stochastic demand models. In these models, future demand is given by a specific exogenous random variable, and the inventory decisions are made with full knowledge of the future demand distribution. In many applications, however, the demand distribution is not known a priori. Even when past data have been collected, the selection of the most appropriate distribution and its parameters remains ambiguous. In the case when excess demand is lost, the information available to the inventory manager is further limited since she does not observe the realized demand but only observes the sales quantity (often referred to as censored demand), which is the smaller of the stocking level and the realized demand. Motivated by these realistic constraints, we develop a non-parametric approach to stochastic inventory planning in the presence of lost sales and censored demand.

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“…The idea is to first assign a probability distribution to the uncertain demand and, then, to solve the problem by looking for a solution of minimum expected cost. Unfortunately, as pointed out in [LS05], even when the distribution is estimated within sufficient precision from historical data, such methods can yield solutions which, when implemented with the demand that realizes in practice, can be substantially more costly than those that were predicted with the stochastic approach. Moreover, and regardless of the accuracy of the estimation, these techniques are, in many cases, intrinsically doomed to suffer from the curse of dimensionality [BT06], as they usually require a computing time which is, at least, linear in the size of the (discrete) probability space, which is typically exponential in the size of the instance.…”

Section: Uncertain Casementioning

confidence: 99%

On Robust Lot Sizing Problems with Storage Deterioration, with Applications to Heat and Power Cogeneration

Coniglio

Koster

Spiekermann

2016

Lecture Notes in Computer Science

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Abstract. We consider a variant of the single item lot sizing problem where the product, when stored, suffers from a proportional loss, and in which the product demand is affected by uncertainty. This setting is particularly relevant in the energy sector, where the demands must be satisfied in a timely manner and storage losses are, often, unavoidable. We propose a two-stage robust optimization approach to tackle the problem with second stage storage variables. We first show that, in the case of uncertain demands, the robust problem can be solved as an instance of the deterministic one. We then address an application of robust lot sizing arising in the context of heat and power cogeneration and show that, even in this case, we can solve the problem as an instance of the deterministic lot sizing problem. Computational experiments are reported and illustrated.

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A practical inventory control policy using operational statistics

Cited by 177 publications

References 10 publications

The Data-Driven Newsvendor Problem: New Bounds and Insights

The Data-Driven Newsvendor Problem: New Bounds and Insights

A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

On Robust Lot Sizing Problems with Storage Deterioration, with Applications to Heat and Power Cogeneration

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