Nonlinear and dynamic programming models for an inventory problem in a partially observable environment

Darendeliler, Alp
In this study, a single-item periodic-review inventory system is considered in a partially observable environment with finite capacity, random yield and Markov modulated demand and supply processes for finite-horizon. The exact state of the real process, which determines the distribution of the demand and supply, is unobservable so the decisions must be made according to the limited observations called observed process. Partially Observable Markov Decision Process is used to model this problem. As an alternative to the dynamic programming model, a nonlinear programming model is developed to find optimal policies. The optimal policies of the nonlinear program is more practical to obtain and use compared to the dynamic programming model. Computational study is performed for the three data sets in order to compare the results of the two models. The results show that the optimal policies of the two models are the same.


Energy preserving methods for lattice equations
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Integral preserving methods, like the averaged vector field, discrete gradient and trapezoidal methods are to Poisson systems. Numerical experiments on the Volterra equations and integrable discretization of the nonlinear Schrodinger equation are presented.
Nonlinear Finite Element Analysis Versus Ex Vivo Strain Gauge Measurements on Immediately Loaded Implants
Eser, Atilim; AKÇA, KIVANÇ; Eckert, Steven; Cehreli, Murat Cavit (2009-05-01)
Purpose: To evaluate the level of agreement between nonlinear finite element stress analysis (NL-FEA) and ex vivo strain gauge analysis (EV-SGA) on immediately loaded implants. Materials and Methods: Four 4.1-mm-diameter, 12-mm-long implants were placed bilaterally into the lateral and first premolar regions of completely edentulous maxillae of four human cadavers. Two-element 90-degree rosette strain gauges were bonded to the labial cortical bone around the implants, and 100 N maximal load was applied over...
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Eraslan, Ahmet Nedim (2005-08-01)
A simple computational model is developed to estimate elastic, elastic-plastic, fully plastic, and residual stress states in generalized plane strain axisymmetric structures considering temperature dependent physical properties as well as nonlinear isotropic strain hardening. Using the von Mises yield criterion, total deformation theory and a Swift-type nonlinear hardening law, a single nonlinear differential equation governing thermoelastoplastic behavior is obtained. A shooting technique using Newton iter...
Pruning algorithms for partially observable markov decision processes
Özgen, Selim; Demirekler, Mübeccel; Department of Electrical and Electronics Engineering (2017)
It is possible to represent the value function in partially observable Markov decision processes as a piecewise linear function if the state, action, and observation space is discrete. Exact value iteration algorithm searches for this value function by creating an exponential number of linear functions at each step, many of which can be pruned without changing the value of the value function. The pruning procedure is made possible by the use of linear programming. This study first gives a geometric framewor...
Singularly perturbed diffusion-advection-reaction processes on extremely large three-dimensional curvilinear networks with a periodic microstructure -- efficient solution strategies based on homogenization theory
Kropat, Erik; Meyer-Nieberg, Silja; Weber, Gerhard-Wilhelm (American Institute of Mathematical Sciences (AIMS), 2016-8)
Boundary value problems on large periodic networks arise in many applications such as soil mechanics in geophysics or the analysis of photonic crystals in nanotechnology. As a model example, singularly perturbed elliptic differential equations of second order are addressed. Typically, the length of periodicity is very small compared to the size of the covered region. The overall complexity of the networks raises serious problems on the computational side. The high density of the graph, the huge number of ed...
Citation Formats
A. Darendeliler, “Nonlinear and dynamic programming models for an inventory problem in a partially observable environment,” M.S. - Master of Science, Middle East Technical University, 2016.