Study On Scheduling Problems With Resources,Learning Effects And Deterioration Effects

This paper consists of the following six sections.We firstly introduce scheduling problems,giving some backgrounds,development,the three parameters representation of the scheduling problems and related notations.In chapter 2,we study the problem P2|res...G,p_1j?p₁,p_2j?p₂|C_max,discussing two cases:?1?)p₁=1,p₂=k?k?Z⁺?;?2?p₁=2,p₂=k?k?Z⁺? Zkkpp,respectively.In case?2?,we further discuss the preemptive case:P2|prmp,res...,G,p_1j?2,p_2j?k|C_max.In chapter 3,we discuss the scheduling problem that 1|p_j=b_j-a_ju_j^l,agreeable0,0?u_j????_j,?u_j????|C_max,a class of single-machine scheduling problems where the processing time depends on resources with some agreeable parameters.We point out an important property?Property 3.10?of its optimal solution,getting a sufficient condition?Theorem 3.11?of the existence of the only optimal solution and giving the solving method to the optimal solution.In chapter 4,we mainly discuss a class of single-machine scheduling problems where the processing time has learning effect and deterioration effect.Then we study the problem of makespan,the total completion time,the total square of completion time and the maximum lateness,respectively.In chapter 5,we research the single-machine group scheduling problems with the setup time where the processing time have learning effect and deterioration effect.We study the problem of makespan for the setup time only having learning effect and the setup time with learning effect and deterioration effect,respectively.We give the polynomialalgorithm for the above two scheduling problems,respectively.The summary of the paper and further discussions are given in chapter 6.