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We consider a finite-horizon, periodic-review inventory model with demand forecasting updates following the martingale model of forecast evolution (MMFE). The optimal policy is a state-dependent base-stock policy, which, however, is computationally intractable to obtain. We develop tractable bounds on the optimal base-stock levels and use them to devise a general class of heuristic solutions. Through this analysis, we identify a necessary and sufficient condition for the myopic policy to be optimal. Finally, to assess the effectiveness of the heuristic policies, we develop upper bounds on their value loss relative to optimal cost. These solution bounds and cost error bounds also work for general dynamic inventory models with nonstationary and autocorrelated demands. Numerical results are presented to illustrate the results.

Due to their mobile character, ground vehicles and unmanned aerial vehicles (UAVs) are currently being considered as sensing devices that can collect data in the Internet of Things (IoT). Building and enhancing trust and security environments in data collection processes are fundamental and essential requirements. Here, we proposed a novel scheme named “Trust Data Collections via Vehicles joint with UAVs in the Smart Internet of Things” (T‐SIoTs scheme), which targets to establish a trust‐based environment for data collections by utilizing both trust vehicles and UAVs. First, to optimize security aspect, data center (DC) selected trust‐based vehicles as mobile data collectors via analyzing and digging historical datasets. To promise coverage regions of data collections, several static stations are established, which can be utilized as static data collectors. Second, UAVs are arranged by the DC to collect data stored by both trust‐based vehicles and static data collectors. In the T‐SIoTs scheme, trajectories of UAVs are designed according to shortest‐distance‐first routing scheme. Comprehensive theoretical analyses and experiments have been provided to evaluate and support the T‐SIoTs scheme. Compared with the previous studies, the T‐SIoTs scheme can improve the security ratio by 46.133% to 54.60% approximately. And with the routing scheme, the energy consumptions of UAVs can be reduced by 46.93% approximately.

We consider a multiperiod inventory system of a perishable product with unobservable lost sales. Demand distribution parameters are unknown and are updated periodically using the Bayesian approach based on the censored historical sales data. We develop an explicit expression of the first-order condition for optimality that demonstrates the key trade-off of the problem. The result generalizes partial characterizations of this trade-off in the literature. It shows that the myopic solution is a lower bound on the optimal inventory level. It also enables us to quantify the expected marginal value of information. Subject classifications: stochastic inventory control; censored demand data; Bayesian models; exact analysis; sample-path approach. Area of review: Stochastic Models.

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