gams:schrage_s_snow_removal_problem_stochastic_programming

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Contributed by Richard E. Rosenthal: At the risk of boring many of the list members, I will attach a very simple stochastic program implemented in gams. It is Linus Schrage’s snow removal example, which I have found to be a nice teaching example. The exact reference to Schrage’s book is included.

$TITLE STOCHASTIC PROGRAMMING: SCHRAGE’S SNOW REMOVAL PROBLEM $offupper offsymxref offsymlist onlisting inlinecom { } $ontext Two-Stage Stochastic Programming Problem with Recourse Source: Linus Schrage, LINDO, 3rd ed., p.140-145 By: Richard E. Rosenthal (Oct 91) $offtext SETS R consumable resources / FUEL, SALT / A activities / PLOWING, SALTING / S states of nature / WARM, COLD / E durable resources / TRUCK-DAYS / ; PARAMETER C1(R) cost of buying resources in Stage 1 / FUEL 70 SALT 20 / ; TABLE C2(S,R) cost of buying resources in Stage 2 FUEL SALT WARM 73 30 COLD 73 32 ; PARAMETER SALV(R) salvage value of resources after Stage 2 / FUEL 65 SALT 15 / ; TABLE OPCOST(S,A) operating cost in Stage 2 PLOWING SALTING WARM 110 110 COLD 120 120 ; TABLE EFF(S,A) efficiency factor for snow removal activity PLOWING SALTING WARM 1.0 1.2 COLD 1.0 1.1 ; TABLE CON(R,A) consumption rates for snow removal activity PLOWING SALTING FUEL 1.0 1.0 SALT 0.0 1.0 ; PARAMETER DEM(S) demand for snow removal / WARM 3500 COLD 5100 / ; PARAMETER PROB(S) probability of Stage 2 states of nature / WARM 0.4 COLD 0.6 / ; PARAMETER SUP(E) equipment supply / TRUCK-DAYS 5000 / ; POSITIVE VARIABLES X1(R) Stage 1 resource purchases X2(S,R) Stage 2 resource purchases under SON s Y2(S,A) Stage 2 activities under SON s W2(S,R) Stage 2 salvages under SON s ; FREE VARIABLE Z total expected cost ; EQUATIONS BAL(S,R) Stage 2 resource balance under SON s EQUIP(S,E) Stage 2 equipment supply under SON s DEMAND(S) Stage 2 snow removal demand under SON s OBJDEF; BAL(S,R).. X1(R) + X2(S,R) =E= W2(S,R) + SUM(A, CON(R,A) * Y2(S,A)) ; * Purchases = Salvage + Consumption EQUIP(S,E).. SUM(A, Y2(S,A) ) =L= SUP(E) ; DEMAND(S).. SUM(A, EFF(S,A) * Y2(S,A) ) =G= DEM(S) ; OBJDEF.. SUM( R, C1(R) * X1(R) ) + SUM( (S,R), PROB(S) * C2(S,R) * X2(S,R) ) + SUM( (S,A), PROB(S) * OPCOST(S,A) * Y2(S,A) ) - SUM( (S,R), PROB(S) * SALV(R) * W2(S,R) ) =E= Z ; OPTION LIMROW=10, LIMCOL=0, SOLPRINT=ON MODEL SNOW / ALL / ; SOLVE SNOW USING LP MINIMIZING Z;

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gams/schrage_s_snow_removal_problem_stochastic_programming.1190861531.txt.gz · Last modified: 2007/10/21 06:33 (external edit)