Optimal Centralized Ordering Policies in Multi-Echelon Inventory Systems with Correlated Demands

Erkip, Nesim; Hausman, Warren H.; Nahmias, Steven

doi:10.1287/mnsc.36.3.381

Cited by 154 publications

(69 citation statements)

References 7 publications

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“…Johnson and Thompson (1975) are among the first to study correlated demand in a single item and a single location setting. Erkip et al (1990) consider a multi-echelon inventory system where demand is a first-order autoregressive process and is correlated across sites and time. These authors solve for the optimal safety stock level and show the impact of demand correlation over time.…”

Section: Literature Reviewmentioning

confidence: 99%

A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems

Atamtürk

Berenguer

Shen

2012

Operations Research

124

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We study several joint facility location and inventory management problems with stochastic retailer demand. In particular, we consider cases with uncapacitated facilities, capacitated facilities, correlated retailer demand, stochastic lead times, and multicommodities. We show how to formulate these problems as conic quadratic mixed-integer problems. Valid inequalities, including extended polymatroid and extended cover cuts, are added to strengthen the formulations and improve the computational results. Compared to the existing modeling and solution methods, the new conic integer programming approach not only provides a more general modeling framework but also leads to fast solution times in general.

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Section: Literature Reviewmentioning

confidence: 99%

A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems

Atamtürk

Berenguer

Shen

2012

Operations Research

124

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“…This problem arises in many domains and has many practical applications (see for example [8,14]). We consider two classical models, the periodic-review stochastic inventory control problem and the stochastic lot-sizing problem with correlated and non-stationary demands.…”

Section: Introductionmentioning

confidence: 99%

Approximation Algorithms for Stochastic Inventory Control Models

et al. 2007

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We consider two classical stochastic inventory control models, the periodic-review stochastic inventory control problem and the stochastic lot-sizing problem. The goal is to coordinate a sequence of orders of a single commodity, aiming to supply stochastic demands over a discrete, finite horizon with minimum expected overall ordering, holding and backlogging costs. In this paper, we address the important problem of finding computationally efficient and provably good inventory control policies for these models in the presence of correlated and non-stationary (time-dependent) stochastic demands. This problem arises in many domains and has many practical applications in supply chain management.Our approach is based on a new marginal cost accounting scheme for stochastic inventory control models combined with novel cost-balancing techniques. Specifically, in each period, we balance the expected cost of over ordering (i.e, costs incurred by excess inventory) against the expected cost of under ordering (i.e., costs incurred by not satisfying demand on time). This leads to what we believe to be the first computationally efficient policies with constant worst-case performance guarantees for a general class of important stochastic inventory models. That is, there exists a constant C such that, for any instance of the problem, the expected cost of the policy is at most C times the expected cost of an optimal policy. In particular, we provide worst-case guarantee of 2 for the periodic-review stochastic inventory control problem and a worst-case guarantee of 3 for the stochastic lot-sizing problem. Our results are valid for all of the currently known approaches in the literature to model correlation and non-stationarity of demands over time.

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“…Erkip, Hausman, and Nahmias (1990) find that the autocorrelation in monthly demand can reach up to 0.70 in a consumer products company. Lee, Padmanabhan, and Whang (1997) report dependence between demand realizations over time -especially positive autocorrelation -in high-tech and grocery industries.…”

Section: Introductionmentioning

confidence: 91%

Near optimality guarantees for data-driven newsvendor with temporally dependent demand: A Monte Carlo approach

Akçay¹,

Biller²,

Tayur³

2013

2013 Winter Simulations Conference (WSC)

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We consider a newsvendor problem with stationary and temporally dependent demand in the absence of complete information about the demand process. The objective is to compute a probabilistic guarantee such that the expected cost of an inventory-target estimate is arbitrarily close to the expected cost of the optimal critical-fractile solution. We do this by sampling dependent uniform random variates matching the underlying dependence structure of the demand process -rather than sampling the actual demand which requires the specification of a marginal distribution function -and by approximating a lower bound on the probability of the so-called near optimality. Our analysis sheds light on the role of temporal dependence in the resulting probabilistic guarantee, which has been only investigated for independent and identically distributed demand in the inventory management literature.

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Optimal Centralized Ordering Policies in Multi-Echelon Inventory Systems with Correlated Demands

Cited by 154 publications

References 7 publications

A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems

A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems

Approximation Algorithms for Stochastic Inventory Control Models

Near optimality guarantees for data-driven newsvendor with temporally dependent demand: A Monte Carlo approach

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