1. A computer-implemented method for scheduling a cluster tool, the cluster tool comprising a single-arm robot for wafer handling, a loadlock for wafer cassette loading and unloading, n process modules each for performing a wafer-processing step with a wafer residency time constraint where the ith process module, i ∈ {1, 2,. .. , n}, is used for performing Step i of the n wafer-processing steps for each wafer, and a specialized processor configured to control the robot, the loadlock, and the process modules through execution of the method, the method comprising: when max ≦ iU and ψ 1 ≦ iU , i=1, 2,. .. , n, determining, by the specialized processor, values of ω 0 , ω 1 ,. .. , ω d for each of plural system states M sd , d=0, 1,. .. n−1, of the cluster tool, where M st , 1≦i≦n−1 denotes that i instances of a wafer unloading from the robot to any one of the n process modules have occurred since system start-up, and ω j , j ∈{0, 1,. .. d}, is a robot waiting time used in the state M sd for the robot to wait before unloading a wafer in Step j from the robot to the (j+1)th process module; wherein the determining of ω 0 , ω 1 ,. .. , ω d for each of the system states M sd , d=0, 1,. .. , n−1, comprises: setting, by the specialized processor, ω 0 =0 and ω 1 =a 1 for the states M s0 and M s1 ); where: 
 max =max{ iL , i ∈ N n }; 
 ψ 1 =2( n+ 1)μ+(2 n+ 1 )α+α 0 
 iU =a i +4α+3μ+δ i , i ∈ N n {1}; 
 1U =a i +3α+α 0 +3μ+δ 1 ; 
 1L =a i +4α+μ, i ∈ N n {1}; 
 1L =a 1 +3α+α 0 +3μ; a i , i ∈ N n , is a time that a wafer is processed in the ith process module; δ i is the wafer residency time constraint of Step i, given by a pre-determined longest time for which a wafer in the ith process module is allowed to stay therein after this wafer is processed; α is a time of loading a wafer to or unloading the wafer to the robot in Step i; μ is a time of the robot moving from one wafer-processing step to another; α 0 is a time of the robot unloading a wafer from the loadlock and aligning the same; and N m ={1 ,2,. .. ,} for a positive integer m.