Optimal control of production with improvement

2018 ◽  
Vol 232 (6) ◽  
pp. 777-785
Author(s):  
Nobuyuki Tamura
Keyword(s):  
Optimal Control ◽  
State Space Model ◽  
Sufficient Conditions ◽  
Control Policy ◽  
Quality Characteristic ◽  
Process Mean ◽  
Initial Value ◽  
Target Value ◽  
The Relationship ◽  
Asymmetric Function

This article considers a process that produces items and in which the process mean is observed periodically. We use a state-space model to describe the relationship between the process mean and the quality characteristic of the items. At each observation, one of the following actions can be taken: production, repair, replacement, or improvement. When production is chosen, some number of items are produced. The quality characteristic of the items has a target value, and the quality loss is expressed by an asymmetric function of the deviation of the quality characteristic from the target value. Replacement resets the process mean to an initial value. When improvement is selected, the process mean is returned to the same initial value as in replacement. When improvement is repeated, it becomes less likely that the process mean will increase. There are several kinds of repairs, and each repair returns the process mean to some value greater than the initial value. For this model, we obtain a total expected discount cost for an unbounded horizon, and we show that under several reasonable assumptions, a control-limit policy is optimal. Furthermore, we derive the sufficient conditions to ensure that the optimal control policy has monotonic structures.

scholarly journals Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Lingling Zhang ◽  
Noriaki Yamazaki ◽  
Rui Guo
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Control Problem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Initial Value ◽  
Mixed Monotone Operator

We consider positive solutions and optimal control problem for a second order impulsive differential equation with mixed monotone terms. Firstly, by using a fixed point theorem of mixed monotone operator, we study positive solutions of the boundary value problem for impulsive differential equations with mixed monotone terms, and sufficient conditions for existence and uniqueness of positive solutions will be established. Also, we study positive solutions of the initial value problem for our system. Moreover, we investigate the control problem of positive solutions to our equations, and then, we prove the existence of an optimal control and its stability. In addition, related examples will be given for illustrations.

scholarly journals Linearity extensions of the market model: a case of the top 10 cryptocurrency prices during the pre-COVID-19 and COVID-19 periods

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Serdar Neslihanoglu
Keyword(s):  
State Space Model ◽  
Additive Model ◽  
Market Model ◽  
Time Varying ◽  
Daily Data ◽  
Forecasting Performance ◽  
Modeling And Forecasting ◽  
Crypto Currency ◽  
Beta Risk ◽  
The Relationship

AbstractThis research investigates the appropriateness of the linear specification of the market model for modeling and forecasting the cryptocurrency prices during the pre-COVID-19 and COVID-19 periods. Two extensions are offered to compare the performance of the linear specification of the market model (LMM), which allows for the measurement of the cryptocurrency price beta risk. The first is the generalized additive model, which permits flexibility in the rigid shape of the linearity of the LMM. The second is the time-varying linearity specification of the LMM (Tv-LMM), which is based on the state space model form via the Kalman filter, allowing for the measurement of the time-varying beta risk of the cryptocurrency price. The analysis is performed using daily data from both time periods on the top 10 cryptocurrencies by adjusted market capitalization, using the Crypto Currency Index 30 (CCI30) as a market proxy and 1-day and 7-day forward predictions. Such a comparison of cryptocurrency prices has yet to be undertaken in the literature. The empirical findings favor the Tv-LMM, which outperforms the others in terms of modeling and forecasting performance. This result suggests that the relationship between each cryptocurrency price and the CCI30 index should be locally instead of globally linear, especially during the COVID-19 period.

scholarly journals Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1781
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Soft Sets ◽  
New Concepts ◽  
Bitopological Spaces ◽  
The Relationship ◽  
Soft Topological Space

In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

Some Sufficiency Conditions for Pareto-Optimal Control

1973 ◽  
Vol 95 (4) ◽  
pp. 356-361 ◽  
Author(s):  
G. Leitmann ◽  
W. Schmitendorf
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pareto Optimality ◽  
Optimal Control Theory ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Vector Valued ◽  
Sufficiency Conditions

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

The Maxslope Taxometric Procedure: Mathematical Derivation, Parameter Estimation, Consistency Tests

2004 ◽  
Vol 95 (2) ◽  
pp. 517-550 ◽  
Author(s):  
William M. Grove
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Regression ◽  
Classification Accuracy ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Indicator Variable ◽  
Regression Slope ◽  
The Relationship ◽  
Mathematical Derivation ◽  
Made In

This article first explains concepts in taxometrics, including the meaning of “taxon” in relation to taxometric procedures. It then mathematically develops the MAXSLOPE procedure of Grove and Meehl which relies on nonlinear regression of one taxometric indicator variable on another. Sufficient conditions for MAXSLOPE's validity are set forth. The relationship between the point of maximum regression slope (MAXSLOPE point) and the HITMAX cut, i.e., the point on a variable which, if used as a diagnostic cut-off score, yields maximum classification accuracy, is analyzed. A sufficient condition is given for the MAXSLOPE point to equal the HITMAX cut; however, most distributions have different MAXSLOPE and HITMAX points. Equations and an algorithm are spelled out for making a graphical test for the existence of a taxon, estimating taxometric parameters, and conducting consistency tests; the latter serve as stringent checks on the validity of a taxonic conjecture. The plausibility of assumptions made, in deriving MAXSLOPE equations, is discussed, and the qualitative effects of violations of these assumptions are explained.

Regional vascular resistance vs. conductance: which index for baroreflex responses?

1991 ◽  
Vol 260 (2) ◽  
pp. H632-H637 ◽  
Author(s):  
D. S. O'Leary
Keyword(s):  
Blood Pressure ◽  
Cardiac Output ◽  
Arterial Pressure ◽  
Pressure Regulation ◽  
Differential Analysis ◽  
Initial Value ◽  
Baseline Effect ◽  
Regional Vascular Resistance ◽  
Vascular Beds ◽  
The Relationship

When large changes in baseline blood flow occur in regional vascular beds (i.e., in skeletal muscle between rest and dynamic exercise or in skin between normothermia and hyperthermia) opposite conclusions are often drawn regarding the magnitude of a given vasomotor response (such as baroreflex vasoconstriction during hypotension) using regional resistance versus conductance. This report analyzes the relationship between changes in regional resistance or conductance and the contribution of the responses in the maintenance of blood pressure. The main supposition is that the appropriate index of baroreflex responses should reflect the importance of the response in the maintenance of blood pressure. Through differential analysis of the relationship between changes in resistance and conductance on arterial pressure, it can be seen that in terms of resistance, the effect of a given change in resistance on arterial pressure is greatly dependent on the baseline level of resistance. For conductance, while a modest baseline effect exists when cardiac output changes markedly, at a constant cardiac output, the same change in regional conductance always causes the same change in arterial pressure regardless of the initial value of conductance. Conclusions drawn are that while neither resistance nor conductance is a perfect index of vasomotor responses, changes in conductance far better reflect the importance of the response in pressure regulation than do changes in regional resistance.

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