$title Stochastic Two-stage program $ontext Coordinating Pre- and Post-Disaster Investments at Multiple Locations $offtext Sets i 'potential affected locations' / PAL1, PAL2 / j 'main distribution centers' / MDC1, MDC2 /; Parameters Alpha(i) 'Unit cost of pre-disaster preparedness' / PAL1 10, PAL2 10 / Beta(j) 'Unit cost of pre-disaster preparedness at main distribution center' / MDC1 10, MDC2 10 / Gamma(i) 'relief at the potential affected location' / PAL1 10, PAL2 10 / lamda(i) 'Coeeffcient of the damage function' / PAL1 10, PAL2 10 / v(i) 'Coeefficient of the damage function' / PAL1 10, PAL2 10 / Ecl(i) 'Local preparedness effectiveness at potential affected location' /PAL1 10, PAL2 10/ Ecd(j) 'Preparedness effectiveness at main distribution center' /MDC1 10, MDC2 10/ Er(i) 'Local relief at potential affected location' /PAL1 10, PAL2 10/ Ecr(i) 'Joint effectiveness of local preparedness and relief at PAL' /PAL1 10, PAL2 10/ Ecdr(i) 'Joint effectiveness of the preparedness at MDC and relief at PAL' /PAL1 10, PAL2 10/ ; scalars P12 'Conditional Probability of disaster magnitude at location 2 given that disaster has occurred at location 1' / 0.01/ P1 'Probability of disaster magnitude at location 1' / 0.01/ P2 'Probability of disaster magnitude at location 2' / 0.01/ m1m 'Disaster magnitude at location 1' / 10 / m2m 'Disaster magnitude at location 2' / 10 / budget /10000/ ; positive variables cd(j) 'pre-disaster preparedness effort main distribution center MDC', r(i) 'post-disaster relief effort at PAL', cl(i) 'pre-disaster preparedness effort at PAL', y(i,j)'whether PAL location i seeks post disaster relief from MDC j'; variables z 'loss minimized'; Equations obj budgetlimit ; *(gamma(1)*r(1) + v(1)*(1-exp**(-lamda(1)*m1m))*exp**(cl(1)-cd(1)*y(1,1)-r(1) -cl(1)*r(1) - cd(1)*r(1)*y(1,1)-cd(2)*r(2)*y(1,2)))*P12*P2 + (gamma(2)*r(2) + v(2)*(1-exp**(-lamda(2)*m2m))*exp**(cl(2)-cd(2)*y(2,1)-r(1) -cl(2)*r(1) - cd(1)*r(2)*y(2,1)-cd(2)*r(2)*y(2,2)))*P12*P2 obj.. z =e= sum(i,Alpha(i)*cl(i)) + sum(j,Beta(j)*cd(j)) + (sum(i,Gamma(i)*r(i))+ sum(i,v(i)*(1-exp(-lamda(i)*m1m))*exp(-Ecl(i)*cl(i)-sum(j,Ecd(j)*cd(j)* y(i,j)-Er(i)*r(i)-Ecr(i)*cl(i)*r(i))-sum(j,Ecdr(i)*cd(j)*r(i)*y(i,j)))))*(P12*P2) +(sum(i,Gamma(i)*r(i))+ sum(i,v(i)*(1-exp(-lamda(i)*m2m))*exp(-Ecl(i)*cl(i)-sum(j,Ecd(j)*cd(j)*y(i,j)-Er(i)*r(i)-Ecr(i)*cl(i)*r(i))-sum(j,Ecdr(i)*cd(j)*r(i)* y(i,j)))))*(P12*P2) + (P1*(1-P12*P2/P1))*sum(i,Gamma(i)*r(i)) + (sum(i,Gamma(i)*r(i))+ sum(i,v(i)*(1-exp(-lamda(i)*m1m))*exp(-Ecl(i)*cl(i)-sum(j,Ecd(j)*cd(j)* y(i,j)-Er(i)*r(i)-Ecr(i)*cl(i)*r(i))-sum(j,Ecdr(i)*cd(j)*r(i)*y(i,j)))))*(P1*(1-P12*P2/P1)) + ((1-P12)*P2)*sum(i,Gamma(i)*r(i))+(sum(i,Gamma(i)*r(i))+ sum(i,v(i)*(1-exp(-lamda(i)*m2m))*exp(-Ecl(i)*cl(i)-sum(j,Ecd(j)*cd(j)* y(i,j)-Er(i)*r(i)-Ecr(i)*cl(i)*r(i))-sum(j,Ecdr(i)*cd(j)*r(i)*y(i,j)))))*((1-P12)*P2) + sum(i,Gamma(i)*r(i))*(1-P1-P2+P12*P2) + sum(i,Gamma(i)*r(i))*(1-P1-P2+P12*P2); budgetlimit.. sum(i,Alpha(i)*cl(i)) + sum(j,Beta(j)*cd(j)) + sum(i,Gamma(i)*r(i)) =l= budget; Model StochasticTwostage /All/ ; solve StochasticTwostage minimizing z usin nlp; display z.l, cd.l, r.l, cl.l, y.l;