Finite鈥恏orizon approximate linear programs for capacity allocation over a rolling horizon.
Vossen, Thomas W.M.; You, Fan; Zhang, Dan. Finite鈥恏orizon approximate linear programs for capacity allocation over a rolling horizon. Production & Operations Management. May2022, Vol. 31 Issue 5, p2127-2142.听听听听
Approximate linear programs (ALPs) have been used extensively to approximately solve stochastic dynamic programs that suffer from the well鈥恔nown curse of dimensionality. Due to canonical results establishing the optimality of stationary value functions and policies for infinite鈥恏orizon dynamic programs, the literature has largely focused on approximation architectures that are stationary over time. In a departure from this literature, we apply a nonstationary approximation architecture to an infinite鈥恉imensional linear programming formulation of the stochastic dynamic programs. We solve the resulting problems using a finite鈥恏orizon approximation. Such finite鈥恏orizon approximations are common in the theoretical analysis of infinite鈥恏orizon linear programs, but have not been considered in the approximate linear programming literature. We illustrate the approach on a rolling鈥恏orizon capacity allocation problem using an affine approximation architecture. We obtain three main results. First, nonstationary approximations can substantially improve upper bounds on the optimal revenue. Second, the upper bounds from the finite鈥恏orizon approximation monotonically decrease as the horizon length increases, and converge to the upper bound from the infinite鈥恏orizon approximation. Finally, the improvement does not come at the expense of tractability, as the resulting ALPs admit compact representations and can be solved efficiently. The resulting approximations also produce strong heuristic policies and significantly reduce optimality gaps in numerical experiments.听听听听
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