Renewing warranty can provide customers with better service,and thus help manufacturers to gain market opportunities.In engineering practice,the cost for replacement is usually higher than the cost for maintenance,hen...Renewing warranty can provide customers with better service,and thus help manufacturers to gain market opportunities.In engineering practice,the cost for replacement is usually higher than the cost for maintenance,hence manufacturers often face huge challenge to reduce the warranty service cost.With consideration of the warranty deadline,we propose a two-stage optimization model for renewing warranty.In the first stage,a renewing warranty with deadline(RWD)policy is implemented,where the deadline represents the cumulative uptime threshold.When the cumulative uptime exceeds the deadline,the product will be minimally repaired and kept to the residual warranty period.When RWD is expired,the replacement warranty with limited repairs(RWLR)policy is applied.Under the free replacement and pro-rata warranty policy,the corresponding two-stage cost optimization model is established from the manufacturer’s perspective,the aim is to minimize the cost rate and obtain the optimal warranty period.A numerical example is provided to illustrate the validity of the proposed model,and the sensitivity analysis is also carried out.展开更多
In this paper, we construct a continuous positive periodic function p(t) such that the corresponding superlinear Duffing equation x′′+ a(x)^(x2n+1)+p(t)x^(2m+1)= 0, n + 2≤2 m+1<2n+1 possesses a solution which es...In this paper, we construct a continuous positive periodic function p(t) such that the corresponding superlinear Duffing equation x′′+ a(x)^(x2n+1)+p(t)x^(2m+1)= 0, n + 2≤2 m+1<2n+1 possesses a solution which escapes to infinity in some finite time, and also has infinitely many subharmonic and quasi-periodic solutions, where the coefficient a(x) is an arbitrary positive smooth periodic function defined in the whole real axis.展开更多
基金Project(71671035) supported by the National Natural Science Foundation of China
文摘Renewing warranty can provide customers with better service,and thus help manufacturers to gain market opportunities.In engineering practice,the cost for replacement is usually higher than the cost for maintenance,hence manufacturers often face huge challenge to reduce the warranty service cost.With consideration of the warranty deadline,we propose a two-stage optimization model for renewing warranty.In the first stage,a renewing warranty with deadline(RWD)policy is implemented,where the deadline represents the cumulative uptime threshold.When the cumulative uptime exceeds the deadline,the product will be minimally repaired and kept to the residual warranty period.When RWD is expired,the replacement warranty with limited repairs(RWLR)policy is applied.Under the free replacement and pro-rata warranty policy,the corresponding two-stage cost optimization model is established from the manufacturer’s perspective,the aim is to minimize the cost rate and obtain the optimal warranty period.A numerical example is provided to illustrate the validity of the proposed model,and the sensitivity analysis is also carried out.
基金supported by National Natural Science Foundation of China (Grant No.11571041)the Fundamental Research Funds for the Central Universities
文摘In this paper, we construct a continuous positive periodic function p(t) such that the corresponding superlinear Duffing equation x′′+ a(x)^(x2n+1)+p(t)x^(2m+1)= 0, n + 2≤2 m+1<2n+1 possesses a solution which escapes to infinity in some finite time, and also has infinitely many subharmonic and quasi-periodic solutions, where the coefficient a(x) is an arbitrary positive smooth periodic function defined in the whole real axis.
