Batch Plant Design Problem
minco
BARON
AMPL
short
= 0, <= log(k); # log of number of parallel units at stage j
var NPU {M} >= 0, <= k; # number of parallel units at stage j
var v {j in M} >= log(VL[j]), <= log(VU[j]); # log of volume at stage j
var b {i in N} >= bLO[i], <= bUP[i]; # log of batch size of batch i
var tL{i in N} >= tLO[i], <= tUP[i]; # log of cycle time of batch i
var y {KxM} >= 0, <= 1, binary; # models number of parallel units
minimize cost: sum {j in M} ( alpha[j] * exp(npu[j] + beta[j]*v[j]) )
+ 1e-36*sum{i in K, j in M} y[i,j];
subject to
volm {i in N, j in M}: v[j] >= log(S[i,j]) + b[i];
ctim {i in N, j in M}: npu[j] + tL[i] >= log(t[i,j]);
horizon: sum {i in N} ( Q[i]*exp(tL[i] - b[i]) ) <= H;
npar {j in M}: npu[j] = sum {l in K} ( log(l) * y[l,j] );
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solve;
display _varname, _var;