$*************************************************************
$ Multiproduct Batch Plant Scheduling
$ Iftekhar A. Karimi
$
$ CACHE Process Design Case Studies
$ M. Morari and I.E. Grossmann
$
$ Optimal Solution:  34.8
$*************************************************************

DECLARATION {{
  INDEX {i,j,k};

  PARA N = 4;
  PARA M = 3;

  SET P = |1:4|; #products
  SET U = |1:3|; #units in the plant

#Processing Times of Products [h]
  PARA t(P,U) = {3.5, 4.3, 8.7,
                 4.0, 5.5, 3.5,
                 3.5, 7.5, 6.0,
                12.0, 3.5, 8.0};

  XVAR {C(P,U)}; #Completion time
  POSI {C(P,U)};

  XVAR {x(P,P)};
  BINA {x(P,P)};
}}

MODEL {{
  MIN:  C(N,M);

  con1(j E P): <<i E P| x(i,j) >> =e= 1;
  con2(i E P): <<j E P| x(i,j) >> =e= 1;

  con3(i E P & i>1, k E U & k<M): C(i,k) =g= C(i-1,k+1);

  con4(i E P, k E U & k>1):  C(i,k) =g= C(i,k-1) + <<j E P| x(j,i)*t(j,k)>>;

  con5(i E P & i>1): C(i,1) =g= C(i-1,1) + <<j E P| x(j,i)*t(j,1)>>;
  con6:              C(1,1) =g=            <<j E P| x(j,1)*t(j,1)>>;
}}