Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes

Johnson, Gordon; Thompson, Howard E.

doi:10.1287/mnsc.21.11.1303

Cited by 139 publications

(62 citation statements)

References 2 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.…”

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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“…For the reasons mentioned above, some authors have studied inventory models with time-correlated demand, including AR models (Aviv, 2002;Reyman, 1989;Johnson and Thompson, 1975), compound Poisson processes (Shang and Song, 2003), martingale models of forecast evolution (Dong and Lee, 2003;Lu et al, 2006;Wang et al, 2012), factor models (See and Sim, 2010) or estimation via Kalman filter (Aviv, 2003). Most of these papers either assume perfect knowledge of the distribution function (Levi et al, 2008;Aviv, 2003Aviv, , 2002Shang and Song, 2003;Wang et al, 2012;Reyman, 1989) or are focused in calculating and optimizing bounds of the objective function.…”

Section: Introductionmentioning

confidence: 99%

Robust newsvendor problem with autoregressive demand

Carrizosa

Olivares-Nadal

Ramírez‐Cobo

2016

Computers & Operations Research

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This paper explores the classic single-item newsvendor problem under a novel setting which combines temporal dependence and tractable robust optimization. First, the demand is modeled as a time series which follows an autoregressive process AR(p), p ≥ 1. Second, a robust approach to maximize the worst-case revenue is proposed: a robust distribution-free autoregressive forecasting method, which copes with non-stationary time series, is formulated. A closed-form expression for the optimal solution is found for the problem for p = 1; for the remaining values of p, the problem is expressed as a nonlinear convex optimization program, to be solved numerically. The optimal solution under the robust method is compared with those obtained under two versions of the classic approach, in which either the demand distribution is unknown, and assumed to have no autocorrelation, or it is assumed to follow an AR(p) process with normal error terms. Numerical experiments show that our proposal usually outperforms the previous benchmarks, not only with regard to robustness, but also in terms of the average revenue.

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“…Karaesmen et al (1999) developed a dynamic programming formulation of a discretized, Markovian version of the Buzacott-Shanthikumar model with unit demand and productions in each period, and showed computationally that the value of advance information decreases with system utilization. There is also a stream of literature that ignores the capacitated nature of the production environment and uses alternative models to incorporate forecasts of stationary demand in inventory management decisions (e.g., Veinott 1965, Johnson and Thompson 1975, Miller 1986, Badinelli 1990, Lovejoy 1992, Drezner et al 1996, Chen et al 1997, Aviv 1998). To our knowledge, this paper contains the first analysis of a capacitated production-inventory model facing a general stationary stochastic demand process and dynamic forecast updates.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Forecasting-Production-Inventory System with Stationary Demand

Toktay

Wein²

2001

Management Science

128

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We consider a production stage that produces a single item in a make-to-stock manner. Demand for finished goods is stationary. In each time period, an updated vector of demand forecasts over the forecast horizon becomes available for use in production decisions. We model the sequence of forecast update vectors using the Martingale Model of Forecast Evolution developed by Graves et al. (1986Graves et al. ( , 1998 and Heath and Jackson (1994). The production stage is modeled as a single-server discrete-time continuous-state queue. We focus on the stationary version of a class of policies that is shown to be optimal in the finite time horizon, deterministic-capacity case, and use an approximate analysis rooted in heavy traffic theory and random walk theory to obtain a closed-form expression for the (forecast-corrected) base-stock level that minimizes the expected steady-state inventory holding and backorder costs. This:expression, which is shown to be accurate under certain conditions in a simulation study, sheds some light on the interrelationships among safety stock, stochastic correlated demand, inaccurate forecasts, and random and capacitated production in forecasting-production-inventory systems.

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Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes

Cited by 139 publications

References 2 publications

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

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

Robust newsvendor problem with autoregressive demand

Analysis of a Forecasting-Production-Inventory System with Stationary Demand

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