Simplification with Power Set

[Shawn]

Greetings,

Is there an efficient way to simplify the following expression using powersets in AMPL?

Specifically, I defined one powerset for p and the other one for Qmax where p represent failure probabilities of suppliers and Qmax represent capacity (p and Qmax values are set in .dat file).

I do not know how to combine these two power sets correctly.

 

p[1]*(1-p[2])*(1-p[3])*min(D[p,t],Qmax[p,2,t]+Qmax[p,3,t])+

p[2]*(1-p[1])*(1-p[3])*min(D[p,t],Qmax[p,1,t]+Qmax[p,3,t])+

p[3]*(1-p[1])*(1-p[2])*min(D[p,t],Qmax[p,1,t]+Qmax[p,2,t])+

p[1]*p[2]*(1-p[3])*min(D[p,t],Qmax[p,3,t])+

p[1]*p[3]*(1-p[2])*min(D[p,t],Qmax[p,2,t])+

p[2]*p[3]*(1-p[1])*min(D[p,t],Qmax[p,1,t])+

p[1]*p[2]*p[3]);

Any guide is highly appreciated.

Thank you

[AMPL Google Group]

I need to be clear about a couple of things before working in your problem. One thing that surprise me is Qmax[p,2,t]. You have been accessing p[1] that means p should be indexed. How are you using 'p' without any index in Qmax[p,2,t]? Can you successfully compile your code in AMPL? You said you defined power set for 'p', but you are accessing p[1]..p[3] as if 'p' is a param. Refer to following documents about how to define power set in AMPL https://ampl.com/faqs/how-can-i-get-ampl-to-index-over-the-power-set-consisting-of-all-subsets-of-a-set/. I have copied the small portion below:

param n:=3 integer > 0;
set S := 0 .. n - 1;
set SS := 0 .. 2**n - 1;
set POW {k in SS} := {i in S: (k div 2**i) mod 2 = 1};

The POW[i] corresponds to the ith set in the power set. Are you trying to create all subset of a set?

--
Dr. Paras Tiwari
am...@googlegroups.com

{#HS:656434708-22123#}

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