$Title A Stochastic Transportation Problem (TRANSSP,SEQ=94) $Ontext This model is a stochastic extension of the TRNSPORT model from the GAMS model library. Here the demand at each market is uncertain. This is modeled with a random variable df (demand factor) which gets multiplied with the demand. It has a discrete distribution. A recourse variable u (unsatisfied demand) was added. Contributor: Lutz Westermann $Offtext Sets i canning plants / seattle, san-diego / j markets / new-york, chicago, topeka / ; Parameters a(i) capacity of plant i in cases / seattle 350 san-diego 600 / b(j) demand at market j in cases / new-york 325 chicago 300 topeka 275 / ; Table d(i,j) distance in thousands of miles new-york chicago topeka seattle 2.5 1.7 1.8 san-diego 2.5 1.8 1.4 ; Scalar f freight in dollars per case per thousand miles /90 / p penalty for unsatisfied demand / 1 / bf demand factor / 1 /; Parameter c(i,j) transport cost in thousands of dollars per case ; c(i,j) = f * d(i,j) / 1000 ; display c; Variables x(i,j) shipment quantities in cases u(j) unsatisfied demand (recourse variable) z total transportation costs in thousands of dollars ; Positive Variable x,u ; Equations cost define objective function supply(i) observe supply limit at plant i demand(j) satisfy demand at market j ; cost .. z =e= sum((i,j), c(i,j)*x(i,j)) + p*sum(j,u(j)); supply(i) .. sum(j, x(i,j)) =l= a(i) ; demand(j) .. sum(i, x(i,j)) =g= bf*b(j) - u(j) ; Model transport /all/ ; file emp / '%emp.info%' /; put emp '* problem %gams.i%'/; $onput randvar bf discrete 0.3 0.95 0.5 1.00 0.2 1.05 stage 2 bf u demand $offput putclose emp; Set scen scenarios / l,m,h /; Parameter s_bf(scen) demand factor realization by scenario s_u(scen,j) s_x(scen,i,j) shipment per scenario s_s(scen) ; Set dict / scen .scenario.'' bf .randvar .s_bf u .level .s_u x .level .s_x /; Solve transport using emp minimizing z scenario dict; Display s_bf, s_x, s_u;