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!. Sets-declaration,

, Sets: Times:; Flow : fori,fdes,fpro,ftlt,fope,fcost,fitc,fsoc,fenv

(. Matft and . Flow, Times): fexp

, Supplier:sid,spro

(. Matst and . Supplier, Times): ssca,Sout

:. Warehouse, . Wtpen, and W. Wavg,

. Matwt(warehouse, Times

, Customer:cid,cpro,cunc

(. Matct and . Customer, Times): cqua

, Lexicographic

, Test:eff_tol,soc_tol,env_tol,eco_tol

. Matlt, Lexicographic):eff_cons,soc_cons,env_cons,eco_cons,eff_ind ic,soc_indic,env_indic,eco_indic,eff_init,soc_init,env_init,eco_init, Test

, Cell/1..1

!. .. Endsets,

!. .. ,

, SubModel Constraints

, ! Numbero of time periods

, NT=@SIZE(Times

, ! FlOWS CONSERVATION @for(MatFT(f,t)|t#LE#ftlt(f):Fin(f,t)=fexp(f,t

, @for(MatFT(f,t)|t#GT#ftlt(f):Fin(f,t)=fout(f,tftlt(f))+fexp(f,t))

, @for(MatFT(f,t)|t#GT#(NT-ftlt(f)):fout(f,t)=0)

, ! SUPPLIERS ! supplier balance, or flow conservation

, Sout(s,t)=@sum(MatFt(f,t)|(fori(f)#EQ#sid(s))

, #AND# (fpro(f)#EQ#spro(s)): Fout(f,t)))

, ! supply capacity constraint

, MatST(s,t):Sout(s,t)<=ssca(s,t))

!. Warehouse,

, ! warehouse balance, or flow conservation

, @for(MatWT(w,t)|t#EQ#1: wini(w)+ @sum(Flow(f)|fdes(f)#EQ#wid(w)#AND# fpro(f)#EQ#wpro(w): Fin(f,1

, Winv(w,1)+@sum(Flow(f)|(fori(f)#EQ#wid(w))

, #AND# (fpro(f)#EQ#wpro(w)):Fout(f,1)))

, @for(MatWT(w,t)|t#GT#1

, Winv(w,t-1)+@sum(Flow(f)|(fdes(f)#EQ#wid(w)

, #AND# (fpro(f)#EQ#wpro(w)):Fin(f,t))=

, Winv(w,t)+@sum(Flow(f)|(fori(f)#EQ#wid(w))

, #AND# (fpro(f)#EQ#wpro(w)):Fout(f,t)))

, ! warehouse contingency stock constraint

, @for(MatWT(w,t): Winv(w,t)-wreq(w)=Wove(w,t)-Wsto

, @for(MatWT(w,t): Winv(w,NT)=wreq(w)

!. Customers,

, ! Total needs value over the periode

, Customer(c): ctqua(c)=@sum(Times(t):cqua(c,t))*cunc(c))

, ! Total received value

, Ctrec(c)=@sum(Times(t):Cin(c,t))*cunc(c))

, ! Total stockout value over the periode

, Customer(c): ctsto(c)=@sum(Times(t):csto(c,t))*cunc(c))

, ! Customer balance @for(MatCT(c,t):Cin(c,t)= @sum(Flow(f)|(fdes(f)#EQ#cid(c))

, #AND# (fpro(f)#EQ#cpro(c))

, MatCT(c,t)|t#EQ#1:Cin(c,1)+Csto(c,1)=Cqua(c,1)+Cove(c,1))

, @for(MatCT(c,t)|t#GT#1:Cin(c,t)+Csto(c,t)=Cqua(c,t)+Cove(c,t)+Csto (c,t-1)-Cove(c

, Customer(c): Ctqua(c)=@sum(Times(t):Cin(c,t)*cunc(c)))

!. Equity-constraint,

, Customer(c)|(cpen(c)#EQ#1, vol.5

, Customer(c):Ctsto(c))/@sum(Customer(c):ctqu a(c)))+0.1)

, Customer(c)|(cpen(c)#EQ#1, vol.5

, Ctsto(c)/ctqua(c)>(@sum(Customer(c):Ctsto(c))/@sum(Customer(c):ctq


!. Effectiveness,

, !Ctpen calculation _ Penalty of the stockout par customer and product

, Ctpen(c)=@sum(Times(t):((Cpen(c)*Csto(c,t))+Cove(c,t))* cunc(c)))

, !Wtpen calculation _ Penalty of the stockout par warehouse and product

, @for(Warehouse(w):Wtpen(w)=@sum(Times(t):(Wsto(w,t)+Wove(w,t))*wunc(w)))

, EndSubModel SubModel Indicators: Effective=@sum(Customer(c):Ctqua(c)*cpen(c))-@sum(Customer(c):Ctpen(c)/NT)+@sum(Warehouse(w):Wreq(w)*wunc(w))-@sum(Warehouse(w):Wtpen(w)/NT)

, ! Maximize local suppliers volume, considering the expected commands (fin)

. Social=@sum, MatFT(f,t):(Fin(f,t)*fsoc(f)*fcost(f)))

, Environment=@sum(MatFT(f,t):(Fin(f,t)*fenv(f)))

, Economy=@sum(MatFT(f,t):(Fin(f,t)*fcost(f)))

. Endsubmodel,

, SubModel EconomyOpt: min=Economy

. Endsubmodel-!*********-5, . Environment, and . Optimization-****************,

, SubModel EnvironmentOpt: min=Environment

. Endsubmodel-!*********-6.-effectiveness and . Constraint-****************************,

, SubModel EffConstraint: Effective>=eff_cons(1,6)-(eff_cons(1,6)*eff_tol(testn))

. Endsubmodel-!*********-7 and . Social-constraint-****************************,

, SubModel SocConstraint: Social>=soc_cons(testn,ord)-(soc_cons(testn,ord)*soc_tol(testn))

. Endsubmodel-!*********-8.-economy and . Constraint-****************************,

. Endsubmodel-!*********-9 and . Environment-constraint-**************************,

, SubModel EnvConstraint: !equal or lower than the constraint

E. Submodel-vide,