Hi,

Although everyone one might know, but still I want to clarify the concept of Sensitivity analysis. Suppose we have an objective function Z in which we have two variables X & Y and two parameters a and b. So in sensitivity analysis, we systematically change the values of parameters ( for eg. changing value of "a" by 20%, then 40%, then 60%, similiarly for parameter "b"). At a time, we only change the value of one parameter and the values of other parameters remain fixed to their original value. Then we would again solve the model ( ie. objective function Z) and calculate the new values of objective function and variables.  Then we try to see the impact of parameter change on the value of objective function Z and on variables X & Y.

The formula for sensitivity analysis for parameter a is  for objective function Z =

 (new values of objective function  - old value of objective function)*100 / (old value of objective function)

Here new value of objective function Z denotes when we use changed value of paramter a (keeping other parameter values fixed to their original value) and old value of objective function denotes value of Z with all parameters (including parameter a) at their original value

Although I can do it by a for loop but it is not an efficient procedure and also time consuming. Can anybody suggest whether any package suitable for sensitivity analysis is available in maple.

Thanks for your attentive reading of problem.

Thanks and Regards,

Nilesh

Hi, 

Can we tell maple to give output in a form which contain any specific term or expression. For example- Can I tell maple to give output which contain (x^2+2*x+3) expression in the output. I used various combinations in collect command but it doesn't work. It is shown in enclosed maple worksheet.

I have some questions about output produced by maple. I have attached a maple worksheet in which I asked the questions in comments. Please help mein in this problem because it become very tedious to type each expression by hand in desired form. If maple produce it by some means it would be great help.

desired_form_in_output.mw

Thanks and Regards,

Nilesh

Hi,

I have two objective function which I want to prove concave with respect to four independent variables jointly (simultaneously).

`TP1 is the first objective function which is defined  in sol1 equation. TP2 is the second objective function which is defined  in sol3 equation. I want to maximize both function. There are four decision variables (independent variables) in both the objective function expression- T,E,W,p. Ten  parameters used in both the equations are- alpha, beta, c, h, m, o, s, u, a, b.

1) My first question is - How can I prove both the function as a concave function with respect to four decision variables jointly. Can I specify some range of parameters in which both these function would behave like a concave function. The feasible range of these parameters are-

`[alpha>0, 0<= beta<1, c>0, h>0, 0<= m<=1, o>0, s>0, u>0, a>0] [ b>0 for objective function TP1 and b>1 for objective function TP2].

Some other restriction on parameters and variables are-  p>c  ,  T<=m , T>=0, E>=0, W>=0, W>=E.

2) My second question is if I simplify my first question and specify some specific values of parameters as I done for both objective function, then I got two new objective function in sol2 and sol4 equation. Now can I prove these two objective function (sol2 & sol4) as concave with respect to four decision variables T,E,W,p jointly. I want to prove concavity for these two objective function because if it is proved concave then The first order optimality solution would give me the global optimal solution. 

Maple worksheet is enclosed.

concavity_proof_question.mw

Thanks and Regards,

Nilesh

Hi,

I have three simultaneous equations  with three unknown variables (E, W, T). When I solve these  simultaneous equations with fsolve command without specifying any range for variables, I don't get desirable root ( equation sol4 in maple worksheet- {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}). For this problem, I know the correct root {E = 2843.916504, T = .2782913990, W = 5344.844134} beforehand which maximize the objective function TP (equation sol8 in maple worksheet) and when I specify the narrow range of variables around the already known correct root in the fsolve command, then I get correct root ( equation sol5 in maple worksheet). If I don't know the actual answer (correct roots of the simultaneous equation) beforehand, How  could I get the correct root with fsolve command because it is very tedious work to specify different range in fsolve command repetitively to solve it by trial and error.

I also tried Direct Search method as suggested in this forum  but DirectSearch is also not able to provide the correct root (equation sol6 in maple worksheet). If I specify the narrow range around known root in direct search method ( equation sol6a in maple worksheet), then it would provide close to optimal root but if I don't know the correct root beforehand, then I couldn't specify the narrow range of variables, then how can I get correct root through direct search command.

Equation sol10 in maple worksheet  (objective function value at correct root) confirms that {E = 2843.916504, T = .2782913990, W = 5344.844134} is the correct root because it provide the value of objective function (TP) equal to 78285.85621 as opposed to negative value (TP value -12.53348074 in equation sol9)  produced by incorrect root  {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}).

Is there any method which would provide all the roots of these simultaneous equations which also include correct root. Maple worksheet is attached.

I am trying fsolve and direct search method with known root so that I could get the proper procedure to get the correct root which I can apply to another problem (set of similar simultaneous equations) for which I don't know correct root beforehand.

Thanks for your anticipated help.fsolve_question.mw

Hi, I am trying to solve two nonlinear simultaneous equations with two unknown variables T & W. The Range of one variable T is from 0 to 0.4

When I use fsolve command to solve it, it gives me a solution in which T value is more than the specified range so it is an invalid solution for me. When I specify the range of T from 0 to 0.4 in fsolve, it doesn't give any solution.

Solve command in maple also doesn't give any solution and just shows evaluating.

My question is how can I get all the roots of unknown variables (T & W), which can solve these two simultaneous equations.

The maple worksheet is attached. 

.maple_simul.equation.mw