senstran.gms : Sensitivity analysis using LOOPS

**Description**

This problem performs sensitivity analysis on the TRNSPORT problem. The basic model is taken from the GAMS model library. A separate model is solved for each variation of the transport cost matrix. The transport cost on each link is raised and lowered by 30 percent and the shipment patterns are either saved in a GAMS data table or written to file for further analysis by a statistical system.

**Reference**

- Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963.

**Small Model of Type :** LP

**Category :** GAMS Model library

**Main file :** senstran.gms

$Title Sensitivity analysis using LOOPS (SENSTRAN,SEQ=106) $Ontext This problem performs sensitivity analysis on the TRNSPORT problem. The basic model is taken from the GAMS model library. A separate model is solved for each variation of the transport cost matrix. The transport cost on each link is raised and lowered by 30 percent and the shipment patterns are either saved in a GAMS data table or written to file for further analysis by a statistical system. Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963. $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/ ; Parameter c(i,j) transport cost in thousands of dollars per case ; c(i,j) = f * d(i,j) / 1000 ; Variables x(i,j) shipment quantities in cases z total transportation costs in thousands of dollars ; Positive Variable x ; 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)) ; supply(i) .. sum(j, x(i,j)) =l= a(i) ; demand(j) .. sum(i, x(i,j)) =g= b(j) ; Model transport /all/ ; $Stitle sensitivity part for trnsport $Eolcom ! Alias (i,ip),(j,jp); Scalar sens sensitivity value / .3 / pors put or save option save=0 put=1 / 0 / counter maximum number of problems / 2 / Parameter report(*,ip,jp,i,j) summary results ; File repdat sensitivity data report file ; Option limcol=0,limrow=0,solprint=off; pors = 1; ! write file counter = 2; ! set to inf to run all problems If(pors, repdat.nw = 5; repdat.nd = 0; repdat.lw=11; Put repdat "low/high i j x(i,j)" /); counter = 10; Loop((ip,jp)$counter, counter = counter-1; c(ip,jp) = c(ip,jp)*(1-sens); ! reduce cell Solve transport using lp minimizing z ; ! solve model If(pors, Put / "low ",ip.tl,jp.tl; ! write Loop((i,j), ! solution Put x.l(i,j) ); ! one solve per line Else report("low",ip,jp,i,j) = x.l(i,j)); ! save results c(ip,jp) = c(ip,jp)/(1-sens)*(1+sens); ! increase cell Solve transport using lp minimizing z ; ! solve model c(ip,jp) = c(ip,jp)/(1+sens); ! reset cell If(pors, Put / "high ",ip.tl,jp.tl; ! write Loop((i,j), ! solution Put x.l(i,j) ); ! one solve per line Else report("high",ip,jp,i,j) = x.l(i,j)) );! save results If(not pors, Option report:3:3:2; Display report );