Joint Economic Lot Sizing Optimization in a Supplier-Buyer Inventory System When the Supplier Offers Decremental Temporary Discounts

This research discusses mathematical models of joint economic lot size optimization in a supplier-buyer inventory system in a situation when the supplier offers decremental temporary discounts during a sale period. Here, the sale period consists of n phases and the phases of discounts offered descend as much as the number of phases. The highest discount will be given when orders are placed in the first phase while the lowest one will be given when they are placed in the last phase. In this situation, the supplier attempts to attract the buyer to place orders as early as possible during the sale period. The buyers will respon these offers by ordering a special quantity in one of the phase. In this paper, we propose such a forward buying model with discount-proportionally-distributed time phases. To examine the behaviour of the proposed model, we conducted numerical experiments. We assumed that there are three phases of discounts during the sale period. We then compared the total joint costs of special order placed in each phase for two scenarios. The first scenario is the case of independent situation – there is no coordination between the buyer and the supplie-, while the second scenario is the opposite one, the coordinated model. Our results showed the coordinated model outperform the independent model in terms of producing total joint costs. We finally conducted a sensitivity analyzis to examine the other behaviour of the proposed model

A framework for joint design of pilot sequence and linear precoder

Most performance measures of pilot-assisted multiple-input multiple-output systems are functions of the linear precoder and the pilot sequence. A framework for the optimization of these two parameters is proposed, based on a matrix-valued generalization of the concept of effective signal-to-noise ratio (SNR) introduced in the famous work by Hassibi and Hochwald. Our framework aims to extend the work of Hassibi and Hochwald by allowing for transmit-side fading correlations, and by considering a class of utility functions of said effective SNR matrix, most notably including the well-known capacity lower bound used by Hassibi and Hochwald. We tackle the joint optimization problem by recasting the optimization of the precoder (resp. pilot sequence) subject to a fixed pilot sequence (resp. precoder) into a convex problem. Furthermore, we prove that joint optimality requires that the eigenbases of the precoder and pilot sequence be both aligned along the eigenbasis of the channel correlation matrix. We finally describe how to wrap all studied subproblems into an iteration that converges to a local optimum of the joint optimization.Peer ReviewedPostprint (author's final draft

Confidence-aware Levenberg-Marquardt optimization for joint motion estimation and super-resolution

Motion estimation across low-resolution frames and the reconstruction of high-resolution images are two coupled subproblems of multi-frame super-resolution. This paper introduces a new joint optimization approach for motion estimation and image reconstruction to address this interdependence. Our method is formulated via non-linear least squares optimization and combines two principles of robust super-resolution. First, to enhance the robustness of the joint estimation, we propose a confidence-aware energy minimization framework augmented with sparse regularization. Second, we develop a tailor-made Levenberg-Marquardt iteration scheme to jointly estimate motion parameters and the high-resolution image along with the corresponding model confidence parameters. Our experiments on simulated and real images confirm that the proposed approach outperforms decoupled motion estimation and image reconstruction as well as related state-of-the-art joint estimation algorithms.Comment: accepted for ICIP 201