In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formula...In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.展开更多
This paper studies the price decisions in a dual-channel closed-loop supply chain with a risk-averse retailer and a risk-neutral manufacturer by modeling and analyzing three cases:(1)the retailer does not have fairnes...This paper studies the price decisions in a dual-channel closed-loop supply chain with a risk-averse retailer and a risk-neutral manufacturer by modeling and analyzing three cases:(1)the retailer does not have fairness concerns;(2)the retailer has fairness concerns and the manufacturer considers it;and(3)the retailer has fairness concerns and the manufacturer does not consider it.The effects of risk aversion and fairness concerns on the pricing decisions,profits and demand are examined in differing scenarios.展开更多
基金the Educational Department Foundation of Tianjin of Science and Technology (No.20042120).
文摘In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.
基金the National Social Science Fund of China(No.18BJY009)the Natural Sciences and Engineering Research Council of Canada(No.06446)the National Natural Science Foundation of China(Nos.11771386 and 11728104).
文摘This paper studies the price decisions in a dual-channel closed-loop supply chain with a risk-averse retailer and a risk-neutral manufacturer by modeling and analyzing three cases:(1)the retailer does not have fairness concerns;(2)the retailer has fairness concerns and the manufacturer considers it;and(3)the retailer has fairness concerns and the manufacturer does not consider it.The effects of risk aversion and fairness concerns on the pricing decisions,profits and demand are examined in differing scenarios.
