Formulation (Core)

MPL

INDEX I = 1..7;

DECISION

h[I,T] ;

b[I,T];

d[I,T];

c[T] ;

DATA

C0 = 50000; ! Initial amount of cash

U = 10; ! Coupon

G = 0.005; ! Transaction cost rate

V = 0.15; ! Diversification limit

MODEL

obj = max SUM(T=4: c[T]);

SUBJECT TO

BAL[T,I] WHERE (Tɜ) AND (Iɟ):

H[I,T] = H[I+1,T-1] + B[I,T] - S[I,T] ;

BAL[T,I] WHERE (Tɜ) AND (I=7) :

H[I,T] = B[I,T] ;

BAL[T,I] WHERE (T=4) AND (Iɟ) :

H[I,T] = H[I+1,T-1] ;

….

AMPL

set I:= 1 .. 7;

var h{i in I, t in T} >=0;

var b{i in I, t in T} >=0;

var d{i in I, t in T} >=0;

var c{t in T} >=0;

param C0:= 50000; # Initial amount of cash

param U = 10; # Coupon

param G = 0.005; # Transaction cost rate

param V = 0.15; # Diversification limit

maximize obj: sum {t inT: t=4} c[t];

subject to bal{t in T: t< 4,i in I: i ɟ}:

h[i,t] =h[i+1, t-1]+ b[i,t] - d[i,t];

subject to bal {t in T: t< 4,i in I: i = 7}:

h[i,t] = b[i,t];

subject to bal{t in T: t=4,i in I: iɟ}:

h[i,t] = h[i+1,t-1];

….

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