batchsp.gms : Design of batch chemical plants with stochastic demand and price

**Description**

Subrahmanyam, Pekny, and Reklaitis describe the design of a batch type chemical plant to produce products for which we do not know the future demand. We present here only half of the problem. We must decide how many plants to build, of what type, when to build them, and how to operate them.

**Small Model of Type : ** SP

**Category :** GAMS EMP library

**Main file :** batchsp.gms

```
$Title Design of batch chemical plants with stochastic demand and price (BATCHSP,SEQ=89)
$ontext
Subrahmanyam, Pekny, and Reklaitis describe the design of a batch
type chemical plant to produce products for which we do not know the
future demand.
We present here only half of the problem. We must decide how many
plants to build, of what type, when to build them, and how to operate
them.
S. Subrahmanyam, J. F. Pekny, and G. V. Reklaitis. Design of batch
chemical plants under market uncertainty. Ind. Eng. Chem. Res., 33,
2688-2701, 1994.
Ariyawansa, K A, and Felt, A J, On a New Collection of Stochastic
Linear Programming Test Problems, INFORMS Journal on Computing 16(3),
291-299, 2004.
$offtext
Sets
i tasks / i1*i4 /
j equipment types / j1*j3 /
t time periods / t1*t2 /
s resources / s1*s7 /
sb(s) resources for purchase / s1,s2 /
ss(s) resources for sale / s4,s7 /
ijmap(i,j) tasks that can be performed by equipment types j;
Alias(t,tt);
Parameter
h(t) length of time period t in days / t1 80, t2 80 /
p(i,j) processing time for task i with equipment type j
m(i,j) capacity of equipment type j to perform task i (measured in units of reaction per batch)
q_s(ss,t) demand for resource s in time period t
q_b(sb,t) maximum purchase of resource s in time period t
vs(ss,t) price for sold resources ss in time period t
vb(sb,t) price for bought resources sb in time period t
budget(t) total operating budget per plant in time period t / #t 100 /
cc(i,j,t) operating expense for using equipment type j for task i in time period t / #i.#j.#t 0 /;
Table ijData(i,j,*)
procTime capacity
i1.j1 4 100
i1.j2 4 200
i2.j3 4 150
i3.j3 4 150
i4.j1 4 100
i4.j2 4 200;
p(i,j) = ijData(i,j,'procTime');
m(i,j) = ijData(i,j,'capacity');
ijmap(i,j)$p(i,j) = yes;
Table ssData(ss,t,*)
(t1*t2).demand t1.price t2.price
s4 150 58 59
s7 200 80 81;
q_s(ss,t) = ssData(ss,t,'demand');
vs(ss,t) = ssData(ss,t,'price');
Table sbData(sb,t,*)
(t1*t2).purchase t1.price t2.price
s1 200 23 24
s2 250 25 26;
q_b(sb,t) = sbData(sb,t,'purchase');
vb(sb,t) = sbData(sb,t,'price');
Table c(j,t) capital investment cost for equipment type j at stage t
t1 t2
j1 2500 2600
j2 3000 3100
j3 2800 2900;
Table f(s,i) input-output coefficients
i1 i2 i3 i4
s1 -1
s2 1 -1
s3 1 -1
s4 1
s5 1 -1
s6 1 -1
s7 1;
Variables
N(j,t) new units of type j
TOTALN(j,t) cumulative number of units of type j
Y(i,j,t) number of times task i is performed by equipment type j during time period t
A(s,t) mass of resource s in inventory at the end of time period t
B(i,j,t) amount of task i performed on type j in time period t (measured in units of reaction)
QS(s,t) mass of resource s sold in time period t
QS0(s,t) mass of resource s sold in time period t below demand
QSPLUS(s,t) mass of resource s sold in time period t above demand
QB(s,t) mass of resource s bought in time period t
Z objective function value
;
Positive variables A,QB,QS,QS0,QSPLUS,B;
Integer variable n,totalN,y;
Equations
obj objective function
procTime(j,t) processing time
opExp(t) operating expense
cumulUnits(j,t) cumulative number of units
matBal(s,t) material balance
tasklim(i,j,t) task limit
sales(ss,t) sales
salesLim(ss,t) sales limit;
obj.. Z =e= sum((t,ss), vs(ss,t)*QS0(ss,t))
- sum((t,sb), vb(sb,t)*QB(sb,t))
- sum((j,t), N(j,t)*c(j,t))
- sum((i,j,t), cc(i,j,t)*Y(i,j,t));
procTime(j,t).. sum(ijmap(i,j), p(i,j)*Y(i,j,t)) =l= h(t)*TOTALN(j,t) ;
opExp(t).. sum(ijmap(i,j), cc(i,j,t)*Y(i,j,t)) =l= budget(t)*sum(j,TOTALN(j,t)) ;
cumulUnits(j,t).. TOTALN(j,t) =e= sum(tt$(ord(tt)<=ord(t)), N(j,tt)) ;
matBal(s,t).. A(s,t) =e= A(s,t-1) + sum(ijmap(i,j), f(s,i)*B(i,j,t)) - QS(s,t)$ss(s) + QB(s,t)$sb(s) ;
taskLim(ijmap(i,j),t).. B(i,j,t) =l= m(i,j)*Y(i,j,t) ;
sales(ss,t).. QS(ss,t) =e= QS0(ss,t) + QSPLUS(ss,t) ;
salesLim(ss,t).. QS0(ss,t) =l= q_s(ss,t) ;
model chem /all/;
A.up(s,t) = 400;
QB.up(sb,t) = q_b(sb,t);
Solve chem using mip maximizing Z ;
file emp / '%emp.info%' /; put emp '* problem %gams.i%'/;
$onput
jrandvar q_s('s4','t1') q_s('s7','t1') vs('s4','t1') vs('s7','t1')
0.4 0 0 51 70
0.6 150 200 58 80
jrandvar q_s('s4','t2') q_s('s7','t2') vs('s4','t2') vs('s7','t2')
0.4 0 0 50 71
0.6 150 200 59 81
stage 2 q_s('s4','t1') q_s('s7','t1') vs('s4','t1') vs('s7','t1')
stage 3 q_s('s4','t2') q_s('s7','t2') vs('s4','t2') vs('s7','t2')
$offput
loop(t,
put / 'stage ' (ord(t)+1):0:0;
if (ord(t)<card(t), loop(j, put N(j,t+1), TOTALN(j,t+1), cumulUnits(j,t+1)));
loop(sb, put QB(sb,t));
loop(ss, put QS(ss,t), QS0(ss,t), QSPLUS(ss,t) sales(ss,t) salesLim(ss,t));
loop(s, put A(s,t) matBal(s,t));
loop(ijmap(i,j), put Y(i,j,t) B(i,j,t) taskLim(i,j,t) );
loop(j, put procTime(j,t) );
put opexp(t);
);
putclose emp;
Set scen Scenarios / sc1*sc4 /;
Parameter
sc_q_s(scen,ss,t) demand by scenario
sc_vs(scen,ss,t) price for sellable resources by scenario
sc_Y(scen,i,j,t) number of times task i is performed by equipment type j during time period t by scenario
sc_N(scen,j,t) new units of type j by scenario
sc_QS0(scen,s,t) mass of resource s sold in time period t below demand by scenario
sc_QSPLUS(scen,s,t) mass of resource s sold in time period t below demand by scenario ;
Set dict / scen .scenario.''
q_s .randvar. sc_q_s
vs .randvar. sc_vs
Y .level. sc_Y
N .level. sc_N
QS0 .level. sc_QS0
QSPLUS .level. sc_QSPLUS /;
solve chem max Z use emp scenario dict;
display sc_q_s, sc_vs, sc_Y, sc_N, sc_QS0, sc_QSPLUS;
```