haverly.gms : Haverly's pooling problem example

**Description**

Haverly's pooling problem example. This is a non-convex problem. Setting initial levels for the nonlinear variables is a good approach to find the global optimum.

**References**

- Haverly, C A, Studies of the Behavior of Recursion for the Pooling Problem. ACM SIGMAP Bull 25 (1978), 19-28.
- Adhya, N, Tawarmalani, M, and Sahinidis, N V, A Lagrangian Approach to the Pooling Problem. Industrial and Engineering Chemistry Research 38, 5 (1999), 1956-1972.

**Small Model of Type :** NLP

**Category :** GAMS Model library

**Main file :** haverly.gms

$title Haverly's pooling problem example (HAVERLY,SEQ=214) $ontext Haverly's pooling problem example. This is a non-convex problem. Setting initial levels for the nonlinear variables is a good approach to find the global optimum. Haverly, C A, Studies of the Behavior of Recursion for the Pooling Problem. ACM SIGMAP Bull 25 (1978), 29-32. Adhya, N, Tawaralani, M, and Sahinidis, N, A Lagrangian Approach to the Pooling Problem. Independent Engineering Chemical Research 38 (1999), 1956-1972. ----- crudeA ------/--- pool --| / |--- finalX ----- crudeB ----/ | |--- finalY ----- crudeC ------------------| $offtext sets s supplies (crudes) / crudeA, crudeB, crudeC / f final products / finalX, finalY / i intermediate sources for final products / Pool, CrudeC / poolin(s) crudes going into pool tank / crudeA, crudeB / table data_S(s,*) supply data summary price sulfur crudeA 6 3 crudeB 16 1 crudeC 10 2 table data_f(f,*) final product data price sulfur demand finalX 9 2.5 100 finalY 15 1.5 200 parameters sulfur_content(s) supply quality in (percent) req_sulfur(f) required max sulfur content (percentage) demand(f) final product demand; sulfur_content(s) = data_S(s,'sulfur'); req_sulfur(f) = data_F(f,'sulfur'); demand(f) = data_F(f,'demand'); equations costdef cost equation incomedef income equation blend(f) blending of final products poolbal pool tank balance crudeCbal balance for crudeC poolqualbal pool quality balance blendqualbal quality balance for blending profitdef profit equation positive variables crude(s) amount of crudes being used stream(i,f) streams q pool quality variables profit total profit cost total costs income total income final(f) amount of final products sold; profitdef.. profit =e= income - cost; costdef.. cost =e= sum(s, data_S(s,'price')*crude(s)); incomedef.. income =e= sum(f, data_F(f,'price')*final(f)); blend(f).. final(f) =e= sum(i, stream(i,f)); poolbal.. sum(poolin, crude(poolin)) =e= sum(f, stream('pool',f)); crudeCbal.. crude('crudeC') =e= sum(f, stream('crudeC',f)); poolqualbal.. q*sum(f, stream('pool', f)) =e= sum(poolin, sulfur_content(poolin)*crude(poolin)); blendqualbal(f).. q*stream('pool',f) + sulfur_content('CrudeC')*stream('CrudeC',f) =l= req_sulfur(f)*sum(i,stream(i,f)); final.up(f) = demand(f); model m /all/; * Because of the product terms, some local solver may get * trapped at 0*0, we therefore set an initial value for q. q.l=1; solve m maximizing profit using nlp;