@Frank Kampas, Can you please elaborate on undefined parameters? I have only one parameter that is defined with constraints. 

They are variables defined as Vf=100 and Kj=150

@ Bill Simpson, I did some debuging and realized that the forum software messed up the code at 3 palces. I fixed it. I believe the error you got were due to the errors in the code. Will you please look at this updated code?

@Bill, I apologize for the confusion. Let me clarify things.
The original objective function I want to evaluate has several variables and has a very large solution space. However, to check that Nminimize works properly, I am testing with a smaller solution space with fewer variables and modified parameters (shown in the above code).  
For the above "test parameter set", I know that the optimal happens at a=10. you can check it with instead of the Nminimize function.

However, as your would notice, the NMinimize method is giving a=3 as the minimizer. That is the problem.

I do not think constantArray mean it will never change. I have checked it on the hep. I was using "Clear" to make sure the variables are cleared during every iteration. Thanks to your comment, I realize that it is absolete.   Can you please be more specific about what parts of my code are complicated? The "Plus@@" simply adds all the values of the array. Thanks for your attempts to answer my question. 

Comment: "It is not clear to me whether some parts of your code are quickly simplified versions of much more complicated code from your real problem or whether they are written in a style that is not usual for Mathematica or whether they are written in a style that is not as simple and understandable as possible. Your Module depending on a mixture of internally calculated values and global variables is one example. Your RM function which ignores the parameters it is given is another. "
Response: This code is basically a simulation of traffic flow on a network. I load the network with vehicles for "m" timeperiods and then then let the network empty. The objective is to find the optimal control variables (here "a") that minimize the output, NtwrkTT, that is dependent on the control value used. The simulation depends on some global traffic flow parameters such as freeflow speed, capacity, etc. to calculate the traffic densities from which the NetworkTT is calulated.  Thus, the simulation depends on both global parameters and calculated values. I am not sure what you mean by "RM function ignores the parameters". RM function is supposed to be 100 times the "a" as mentioned in the code. 

This is the actual code. I did not simplify the code; only used fewer variables for the objective function and smaller parameter values. 

Comment: There is no way of knowing whether this applies to your actual problem, but for your simplified example this shows that your present use of NMinimize is going to be a horrible way of finding what you want. Clearly NMinimize in the way you are using it was never intended to minimize a list of discrete values.

Response: That is what bothers me.  What I have found is if I donot print the function value (f) during every iteration using the EvaluationMonitor, NMinimize runs 1000s of iterations extremely quickly without running the simulation (because if it runs simulations, it will need few seconds for each simulation run and can not do 1000s of simulations in no time). NMinimize only outputs a bunch of possible values for "a". However, when I include "f" in the evaluation monitor, NMinimize runs the simulation disconnected to the optimization process (I suspect NMinimize barely runs the simulation for every value of "a" it outputs). I found that NMinimize does not converge even after 1000s of iterations, when there are only 10 possible values "a" can take.
Comment:There also appears to be yet more problems, because you said above that you know the optimal value happen at a=10, but we can see from this list that the minimum value of f[ a ] happens at a=7. I cannot know what that problem is.
Response:  I apologize for the software issue where I entered  "RMLocation = Round[(2/3) p];" and it showed "RMLocation = Round[(2/13) p];". with my numbers, you should see that the minimum happens at a=10.

Yes. My objective function is complex with multiple variables. therefore, I need to use RM[ i dx, j dt ] instead of RM = 100 a. kr is supposed to be nested tables. So it needs to be kr = Table[Table[0, {i1, 1, p}], {i2, 1, n}] and not kr = ConstantArray[ 0, { p, n } ]. 
I list some variables inside the Module and others outside the Module because the ones outside are global and does not change with changing control, They only need to be defined once and need not be defined every iteration. Hoever, as per your suggestion, I moved everything inside the Module, but it still does not help. 
The code I posted above is the final version of the code and we can use that for debugging. May be we can talk on phone or Gtalk/Skype call, if you think it will help.

I found the solution on another website "http://eternaldisturbanceincosmos.wordpress.com/2011/04/27/nminimize-in-mathematica-could-drive-you-insane/" which says "It turns out that NMinimize does not hold its arguments. This means that as the list of arguments is read from left to right, each argument is evaluated and replaced by the result of the evaluation". So I used `Hold[]` in the `NMinimize` function that fixed the problem.I found the solution on another website "http://eternaldisturbanceincosmos.wordpress.com/2011/04/27/nminimize-in-mathematica-could-drive-you-insane/" which says "It turns out that NMinimize does not hold its arguments. This means that as the list of arguments is read from left to right, each argument is evaluated and replaced by the result of the evaluation". So I used `Hold[]` in the `NMinimize` function that fixed the problem.