Necessary Condition For Feasibility Research Articles

Framework for produced water discharge management with flow-weighted mean concentration based economic model predictive control

Offshore discharges of produced water (PW) is heavily regulated by government authorities through flow-weighted mean concentration (FWMC). To cope with regulations, treatment facilities are commissioned to reduce the oil content in water. However, disturbances may affect their performance, leading to regulation infringement. Produced water re-injection (PWRI) facilities can affect the FWMC by reducing oil discharge, and increasing re-injection. This strategy can aid the offshore facility in achieving the regulation requirements. Nevertheless, if improperly done, energy consumption can significantly increase, and regulations might still be violated. Therefore, we developed a framework for an Economical Model Predictive Control (EMPC) based on FWMC. It comprises an EMPC to which FWMCs are added as constraints; and a logic algorithm to maintain the necessary conditions for feasibility of the environmental constraint. Closed-loop results show that this strategy complies with environmental regulation, and adapts discharges of PW and pumping energy consumption based on facilities’ historical data.

Integrating Empirical Estimation and Assortment Personalization for E-Commerce: A Consider-Then-Choose Model

We develop a new approach that integrates empirical estimation and assortment optimization to achieve display personalization for e-commerce platforms. We propose a two-stage Multinomial Logit (MNL) based consider-then-choose model, which accurately captures the two stages of a consumer's decision-making process -- consideration set formation and purchase decision given a consideration set. To calibrate our model, we develop an empirical estimation method using views and sales data at the aggregate level. The accurate predictions of both view counts and sales numbers provide a solid basis for our assortment optimization. To maximize the expected revenue, we compute the optimal target assortment set based on each consumer’s taste. Then we adjust the display of items to induce this consumer to form her consideration set that coincides with the target assortment set. We formulate this consideration set induction process as a nonconvex optimization, for which we provide the sufficient and necessary condition for feasibility. This condition reveals that a consumer is willing to consider at most K(C) items given the viewing cost C incurred by considering and evaluating an item, which is intrinsic to consumers’ online shopping behavior. As such, we argue that the assortment capacity should not be imposed by the platform, but rather comes from the consumers due to limited time and cognitive capacity. We provide a simple closed-form relationship between the viewing cost and the number of items a consumer is willing to consider. To mitigate computational difficulties associated with nonconvexity, we develop an efficient heuristic to induce the optimal consideration set. We test the heuristic and show that it yields near-optimal solutions. Given accurate taste information, our approach can increase the revenue by up to 35%. Under noisy predictions of consumer taste, the revenue can still be increased by 1% to 2%. Our approach does not require a designated space within a webpage, and can be applied to virtually all webpages thereby generating site-wise revenue improvement.

Anti-windup-based dynamic controller synthesis for nonlinear systems under input saturation

This paper describes the design of dynamic controller and static anti-windup compensator (AWC) for Lipschitz nonlinear systems under input saturation. Global and local AWC-based control schemes for stabilization of the nonlinear systems are proposed, and necessary conditions for feasibility of the control approaches are investigated. A one-step approach for simultaneous design of H∞ controller and AWC by means of linear matrix inequalities (LMIs) is presented herein, which supports multi-objective synthesis to attain stabilization or tracking, robustness against disturbance and noise, and penalization of large and high frequency control signals. This multi-objective synthesis can be accomplished by incorporating design weights, as commonly used in the standard H∞ control theory, to design a performance-oriented anti-windup-based control scheme. LMIs for the global control of the nonlinear systems subject to input saturation are derived by application of a quadratic Lyapunov function, the Lipschitz condition, the global sector condition, L2 gain reduction, substantial matrix algebra and variable transformation. In order to cope with unstable and oscillatory nonlinear systems, LMI-based local results are established using a local sector condition. Additional conditions are derived, by incorporating properties of the saturation function, to ensure well-posedness of the controller. Two simulation examples are provided to show the effectiveness of the proposed control schemes for control of stable and chaotic nonlinear systems under input saturation.

On the Feasibility of Wireless Shadowing Correlation Models

There is emerging interest in more detailed models for wireless shadowing, which may include nonconstant shadowing variance, non-lognormal shadowing, and, most importantly, correlation between paths; we focus on this last aspect. This paper offers a structured synthesis of the existing literature on autocorrelation and cross-correlation in wireless shadowing and attempts to fill existing gaps in the analysis of correlation models. We make a survey of these models and argue, as has previously been observed, that certain models are not mathematically feasible, which may lead to problems in simulations or analysis. We then state some theorems that test whether the models are positive semidefinite, which is the central necessary condition for feasibility, and evaluate the existing models accordingly. Additionally, we evaluate the models according to their physical plausibility, which leads us to choose one model among many as arguably the best one in existence so far. This paper should be useful as a guide on how to implement shadowing correlation in one's work, how to choose an appropriate correlation model, and how to modify existing models or create new models so that they fulfill mathematical feasibility.

Feasibility of the Mixed Postman Problem with Restrictions on the Edges

Abstract The mixed postman problem consists of finding a minimum cost tour of a connected mixed graph traversing all its vertices, edges, and arcs at least once. We consider the variant of the mixed postman problem where all edges must be traversed exactly once. The feasibility version of this problem is NP-complete. We introduce an infinite class of necessary conditions for feasibility, which we conjecture are also sufficient. We prove that no finite subset of these conditions is sufficient.

Generalized Pinwheel Problem

This paper studies a non-preemptive infinite-horizon scheduling problem with a single server and a fixed set of recurring jobs. Each job is characterized by two given positive numbers: job duration and maximum allowable time between the job completion and its next start. We show that for a feasible problem there exists a periodic schedule. We also provide necessary conditions for the feasibility, formulate an algorithm based on dynamic programming, and, since this problem is NP-hard, formulate and study heuristic algorithms. In particular, by applying the theory of Markov Decision Process, we establish natural necessary conditions for feasibility and develop heuristics, called frequency based algorithms, that outperform standard scheduling heuristics.

An interaction/prediction approach to hierarchical production planning and control with delay interaction

The paper proposes an interaction/prediction approach to interaction-delay-based hierarchical production planning and control in flexible automation workshops (FAWs). A mathematical model with delay interaction equations is built up to solve the problem of hierarchical production planning (HPP) in FAWs. An interaction/prediction algorithm for HPP is then deduced in detail and its properties and necessary condition for feasibility are proved. The algorithm has been adopted to develop the software package named as interaction/prediction algorithm with interaction-delay (IPAD), by means of which, examples of HPP in FAWs have been studied. In this paper, the application of the algorithm is introduced in detail through one of those examples. As compared with the existing HPP approaches, the present algorithm is more suitable for decomposing optimally mediumterm plans (assigned to an FAW by CIMS/MRP II) into short-term plans (to be executed by FMSs in the FAW), especially for the case that workpieces are transported between FMSs through a shop storage with a delay of a step.

The Two-Product, Single-Machine, Static Demand, Infinite Horizon Lot Scheduling Problem

In this paper, we deal with the two-product, single-machine, static demand, infinite horizon lot scheduling problem. After a quick review of the literature, the necessary and sufficient conditions for feasibility are derived without imposing any preliminary requirements. Then, an optimal solution algorithm is presented. Finally, we show that a necessary condition for the feasibility of N-product schedules is that each cycle time be an integer multiple of some basic cycle time.