Infinite Horizon Problems

Ghate, Archis

doi:10.1002/9780470400531.eorms0403

Cited by 6 publications

(3 citation statements)

References 60 publications

(64 reference statements)

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“…We solve the infinite-dimensional ALP using a so-called finite-horizon approximation, where the weights are timedependent within a chosen time horizon and are stationary afterward. The use of such finite-horizon approximations for infinite-dimensional linear programming problems is wellestablished in the literature (Chand et al, 2002;Ghate, 2010;Grinold, 1977), and we note that this approximation is similar to the finite-horizon approximations in the analysis of infinite-horizon discounted stochastic dynamic programming problems. In both settings, the key to the analysis is the vanishing difference in value functions when the horizon length is sufficiently large.…”

Section: Production and Operations Managementmentioning

confidence: 87%

Finite‐horizon approximate linear programs for capacity allocation over a rolling horizon

Vossen

You

Zhang

2022

Production and Operations Management

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Approximate linear programs (ALPs) have been used extensively to approximately solve stochastic dynamic programs that suffer from the well‐known curse of dimensionality. Due to canonical results establishing the optimality of stationary value functions and policies for infinite‐horizon 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‐dimensional linear programming formulation of the stochastic dynamic programs. We solve the resulting problems using a finite‐horizon approximation. Such finite‐horizon approximations are common in the theoretical analysis of infinite‐horizon linear programs, but have not been considered in the approximate linear programming literature. We illustrate the approach on a rolling‐horizon 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‐horizon approximation monotonically decrease as the horizon length increases, and converge to the upper bound from the infinite‐horizon 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.

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Section: Production and Operations Managementmentioning

confidence: 87%

Finite‐horizon approximate linear programs for capacity allocation over a rolling horizon

Vossen

You

Zhang

2022

Production and Operations Management

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“…Although our results hold for an arbitrary sequence satisfying our assumptions, our policy requires explicit knowledge of only the first few values of the sequence (two in the model as currently stated, but see Corollary 1 below for an extension). For a discussion of related issues with non-stationary data in infinite-horizon optimization, see, for example, Ghate (2010).…”

Section: Model Formulation and Assumptionsmentioning

confidence: 99%

Strategic health workforce planning

Lavieri

Toriello

et al. 2016

IIE Transactions

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Analysts predict impending shortages in the health care workforce, yet wages for health care workers already account for over half of U.S. health expenditures. It is thus increasingly important to adequately plan to meet health workforce demand at reasonable cost. Using infinite linear programming methodology, we propose an infinite-horizon model for health workforce planning in a large health system for a single worker class; e.g., nurses. We give a series of common-sense conditions that any system of this kind should satisfy and use them to prove the optimality of a natural lookahead policy. We then use real-world data to examine how such policies perform in more complex systems; in particular, our experiments show that a natural extension of the lookahead policy performs well when incorporating stochastic demand growth.

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“…Alternatively, a finite data set that incorporates time dependent data associated with a long finite horizon still introduces a challenging forecasting and computational task, which realistically can only reliably deliver a limited finite horizon look ahead into the future. One can then attempt a planning horizon approach by solving a sequence of ever longer horizon problems in an attempt to approximate the next best decision that one must implement now [2,4,5,14]. These successive finite horizon problems are typically solved as dynamic programs [1,3,15].…”

mentioning

confidence: 99%

Solving infinite horizon optimization problems through analysis of a one-dimensional global optimization problem

2016

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Infinite horizon optimization (IHO) problems present a number of challenges for their solution, most notably, the inclusion of an infinite data set. This hurdle is often circumvented by approximating its solution by solving increasingly longer finite horizon truncations of the original infinite horizon problem. In this paper, we adopt a novel transformation that reduces the infinite dimensional IHO problem into an equivalent one dimensional optimization problem, i.e., minimizing a Hölder continuous objective function with known parameters over a closed and bounded interval of the real line. We exploit the characteristics of the transformed problem in one dimension and introduce an algorithm with a graphical implementation for solving the underlying infinite dimensional optimization problem.

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Infinite Horizon Problems

Cited by 6 publications

References 60 publications

Finite‐horizon approximate linear programs for capacity allocation over a rolling horizon

Finite‐horizon approximate linear programs for capacity allocation over a rolling horizon

Strategic health workforce planning

Solving infinite horizon optimization problems through analysis of a one-dimensional global optimization problem

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