#define BKS 4		 // number of breakpoints at which 
				 // investments can be made
#define NUM 3		// number of different kinds of CDs
#define NA 0.0			// not applicable
#define SC 3			// number of scenarios

double infd, lq;
double r[SC][NUM][BKS];
int mtrs[NUM][1+BKS], prchsbl[NUM][BKS], prob[SC], ttm[NUM];

data()
{
	mtrs = {		// CD i matures at breakpoint j if entry is 1
			0, 1, 1, 1, 1,
		 	0, 0, 1, 1, 1,
			0, 0, 0, 0, 1
	 };

	prchsbl = { 	// CD i can be purchased at 
		      		// breakpoint j if entry is 1
			1, 1, 1, 1,
			1, 1, 1, 0,
			1, 0, 0, 0
	 };

	ttm = { 1, 2, 4 };	 // time to maturity in breakpoints 

	r = { 		// return in scenarios on CD i at breakpoint j
		1.02,   1.01785, 1.01625, 1.015,
		1.0425, 1.040,   1.03875, NA,
		1.09,   NA,      NA,      NA,

		1.02,   1.02,   1.02,   1.02, 
		1.0425, 1.0425, 1.0425, NA,
		1.09,   NA,     NA,     NA,

		1.02,   1.0225, 1.02375, 1.03,
		1.0425, 1.045,  1.04625, NA,
		1.09,   NA,     NA,      NA 
	};
	
	prob = { .25, .35, .4 }; 	// probabilities of scenarios
}

2lp_main()
{
continuous Cd[SC][NUM][BKS],CashFlow[SC][BKS+1];
int type[NUM];                // for I/O

	infd = 100000;	
	lq = 75000;

	data();
	type = { 3, 6, 12 };      // duration of CDs

	and(int s=0;s<SC;s++)
		scenario(CashFlow[s],Cd[s],r[s]);

	alias_first_stage_variables(Cd);

	max: sigma(int s=0;s<SC;s++) prob[s]*CashFlow[s][BKS];

	output_stage1(Cd[0],type);

	and(int s=0;s<SC;s++)
		later_stages(s,CashFlow[s],Cd[s],type);

}

output_stage1(continuous Cd[][BKS],int type[]) 
{
	printf("\nAt stage 1 the plan is:\n\n");
	and(int i=0;i<NUM;i++)
		printf("Invest %.2f in a %d month CD now\n",	Cd[i][0],type[i]);
}

later_stages(int s,continuous Flo[],Cd[][BKS],int type[])
{
	printf("\nThe plan in scenario %d is then:\n\n",s);
	and(int j=1;j<BKS;j++)
		and(int i=0;i<NUM;i++) {
			printf("Invest %.2f ",Cd[i][j]);
			printf("in a %d month CD in %d months\n", type[i],3*j);
		}
	printf("The fund will be worth %.2f\n",Flo[BKS]);
}

alias_first_stage_variables(continuous Cd[][NUM][BKS])
{
	and(int s=1;s<SC;s++)  
		and(int i=0;i<NUM;i++) 
			Cd[s][i][0] == Cd[s-1][i][0];	
}

scenario(continuous CashFlow[],Cd[][BKS],double r[][BKS])
{
	CashFlow[0] == infd;       // initial fund

	and(int j=0;j<BKS;j++)     // cash going out
	   CashFlow[j] == 
	     sigma(int i=0;i<NUM;i++) prchsbl[i][j]*Cd[i][j];

	and(int j=1;j<=BKS;j++)   // cash coming in
	   CashFlow[j] == 
            sigma(int i=0;i<NUM;i++)
		    mtrs[i][j]*r[i][j-ttm[i]]*Cd[i][j-ttm[i]];

	and(int j=0;j<=BKS;j++)   // liquidity constraints
		CashFlow[j] >= lq;
	
	and(int i=0;i<NUM;i++)    // good programming practice
		and(int j=0;j<BKS;j++) 
			if prchsbl[i][j] == 0;
			then Cd[i][j] == 0.0;
 
	max:CashFlow[BKS];       // optimize worth

	printf("The fund will be worth %.2f\n",
						CashFlow[BKS]);
}
 