In a multi-stage manufacturing system,defective components are generated due to deteriorating machine parts and failure to install the feed load.In these circumstances,the system requires inspection counters to distin...In a multi-stage manufacturing system,defective components are generated due to deteriorating machine parts and failure to install the feed load.In these circumstances,the system requires inspection counters to distinguish imperfect items and takes a few discreet decisions to produce impeccable items.Whereas the prioritisation of employee appreciation and working on reward is one of the important policies to improve productivity.Here we look at the multistage manufacturing system as an M/PH/1 queue model and rewards are given for using certain inspection strategies to produce the quality items.A matrix analytical method is proposed to explain a continuous-time Markov process in which the reward points are given to the strategy of inspection in each state of the system.By constructing the value functions of this dynamic programming model,we derive the optimal policy and the optimal average reward of the entire system in the long run.In addition,we obtain the percentage of time spent on each system state for the probability of conformity and non-conformity of the product over the long term.The results of our computational experiments and case study suggest that the average reward increases due to the actions are taken at each decision epoch for rework and disposal of the non-conformity items.展开更多
Let B be a Banach space, {T_(s,t), 0≤s≤t≤∞} be a two-parameter contraction semigroup on B, and {R_(λ,s),λ>0, s≥0} be the right resolvent. Definition Let D such
Let B be a Banach space. The definitions on the strong convergence, continuation, derivative and integral (namely Bochner integral) are the same as Ref. [1]. Definition 1. Let {T_(s,t)0<s<t<∞} be a semigroup...Let B be a Banach space. The definitions on the strong convergence, continuation, derivative and integral (namely Bochner integral) are the same as Ref. [1]. Definition 1. Let {T_(s,t)0<s<t<∞} be a semigroup for two parameters on B(See[2]). If T_(s,s+t+τ)=T_(s,s+t)·T_(s,s+τ),(0<s,t,τ<∞), then{T_(s,t),0<s<t<∞} is said to be a hypo-homogeneous semigroup for two parameters.展开更多
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our constru...We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.展开更多
文摘In a multi-stage manufacturing system,defective components are generated due to deteriorating machine parts and failure to install the feed load.In these circumstances,the system requires inspection counters to distinguish imperfect items and takes a few discreet decisions to produce impeccable items.Whereas the prioritisation of employee appreciation and working on reward is one of the important policies to improve productivity.Here we look at the multistage manufacturing system as an M/PH/1 queue model and rewards are given for using certain inspection strategies to produce the quality items.A matrix analytical method is proposed to explain a continuous-time Markov process in which the reward points are given to the strategy of inspection in each state of the system.By constructing the value functions of this dynamic programming model,we derive the optimal policy and the optimal average reward of the entire system in the long run.In addition,we obtain the percentage of time spent on each system state for the probability of conformity and non-conformity of the product over the long term.The results of our computational experiments and case study suggest that the average reward increases due to the actions are taken at each decision epoch for rework and disposal of the non-conformity items.
文摘Let B be a Banach space, {T_(s,t), 0≤s≤t≤∞} be a two-parameter contraction semigroup on B, and {R_(λ,s),λ>0, s≥0} be the right resolvent. Definition Let D such
文摘Let B be a Banach space. The definitions on the strong convergence, continuation, derivative and integral (namely Bochner integral) are the same as Ref. [1]. Definition 1. Let {T_(s,t)0<s<t<∞} be a semigroup for two parameters on B(See[2]). If T_(s,s+t+τ)=T_(s,s+t)·T_(s,s+τ),(0<s,t,τ<∞), then{T_(s,t),0<s<t<∞} is said to be a hypo-homogeneous semigroup for two parameters.
基金supported by the Scientific Research Fund of Education Department of Heilongjiang Province of China (Grant No. 11551020)
文摘We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
