As more renewable, yet volatile, forms of energy like solar and wind are being incorporated into the grid, the problem of finding optimal control policies for energy storage is becoming increasingly important. These s...
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ISBN:
(纸本)9781479945528
As more renewable, yet volatile, forms of energy like solar and wind are being incorporated into the grid, the problem of finding optimal control policies for energy storage is becoming increasingly important. These sequential decision problems are often modeled as stochastic dynamic programs, but when the state space becomes large, traditional (exact) techniques such as backward induction, policy iteration, or value iteration quickly become computationally intractable. Approximate dynamicprogramming (ADP) thus becomes a natural solution technique for solving these problems to near-optimality using significantly fewer computational resources. In this paper, we compare the performance of the following: various approximation architectures with approximate policy iteration (API), approximate value iteration (AVI) with structured lookup table, and direct policy search on a benchmarked energy storage problem (i.e., the optimal solution is computable).
We study a production problem in which the cumulative consumer demand for an item follows a Brownian motion with drift, with both the drift and the variance parameters modulated by a continuous-time Markov chain that ...
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We study a production problem in which the cumulative consumer demand for an item follows a Brownian motion with drift, with both the drift and the variance parameters modulated by a continuous-time Markov chain that represents the regime. The company wants to maintain the inventory level as close as possible to a target inventory level, but there is a linear cost of production. We assume that the production rate is nonnegative. The company is penalized for deviations from the inventory target level and the cost of production, and the objective is to minimize the total discounted penalty costs. We consider two models. In the first model, there is no upper bound for the production rate, and in the second model there is an upper bound for the production rate. We solve both problems analytically and obtain the optimal production policy and the minimal total expected discounted cost. Our solutions allow us to obtain interesting managerial insights.
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