A Multiordering Newsvendor Model with Dynamic Forecast Evolution

Abstract

W e consider a newsvendor who dynamically updates her forecast of the market demand over a finite planning horizon. The forecast evolves according to the martingale model of forecast evolution (MMFE). The newsvendor can place multiple orders with increasing ordering cost over time to satisfy demand that realizes at the end of the planning horizon. In this context, we explore the trade-off between improving demand forecast and increasing ordering cost. We show that the optimal ordering policy is a state-dependent base-stock policy and analytically characterize that the base-stock level depends on the information state in a linear (loglinear) fashion for additive (multiplicative) MMFE. We also study a benchmark model where the newsvendor is restricted to order only once. By comparing the multiordering and single-ordering models, we quantify the impact of the multiordering strategy on the newsvendor's expected profit and risk exposure.

Robust newsvendor problem with autoregressive demand

“…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.…”

“…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. In some cases, as See and Sim (2010); Lu et al (2006); Dong and Lee (2003), those bounds are distribution-free, but no optimal solutions are obtained.…”

Initial Shipment Decisions for New Products at Zara

“…269-286, © 2015 INFORMS inventory management problems with demand learning in a single location (e.g., Bitran et al 1986, Eppen and Iyer 1997, Kaminsky and Swaminathan 2001, Fisher et al 2001, Gallego and Özer 2001, Wang et al 2012, few papers explore the impact of learning on inventory distribution to multiple destinations. Exceptions include Özer (2003), who models learning of location-specific demands through advance orders, Erkip et al (1990), who examine the impact of demand correlation over time through an autoregressive process, and Agrawal and Smith (2013), who consider the allocation of stock to nonidentical stores over two periods.…”

Energy procurement strategies in the presence of intermittent sources

“…Interestingly, it is typical to assume in analytical work that forecast errors are Gaussian [17,37,28] (leading to the conclusion of Theorem 5), whereas empirical work on wind power generation suggests that a truncated version of a heavy-tailed Weibull distribution may be a more accurate description [18,5] (potentially leading to the conclusion of Theorem 4).…”

“…Informally, if the estimation error is, in a sense, light-tailed (e.g., Gaussian), then the addition of an intermediate market reduces procurement of conventional generation (Theorem 5); but if the error has a heavy-tail (e.g., power-law, heavy-tailed Weibull), then the addition of an intermediate market can have the opposite effect (Theorem 4). Interestingly, it is typical to assume in analytical work that forecast errors are Gaussian [17,37,28], whereas empirical work on wind power generation suggests that a Weibull distribution may be a more accurate description [18,5].…”