Migration: Production, Inventory, Distribution (lpsol8)
/***********************************************************************/
/* */
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: lpsol8 */
/* TITLE: Migration: Production, Inventory, Distribution (lpsol8) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* KEYS: OR */
/* PROCS: OPTMODEL */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: */
/* MISC: Example 8 from the Linear Programming Solver */
/* chapter of Mathematical Programming. */
/* */
/***********************************************************************/
title 'Minimum Cost Flow Problem';
title2 'Production Planning/Inventory/Distribution';
data node0;
input _node_ $ _supdem_ ;
datalines;
fact1_1 1000
fact2_1 850
fact1_2 1000
fact2_2 1500
shop1_1 -900
shop2_1 -900
shop1_2 -900
shop2_2 -1450
;
data arc0;
input _tail_ $ _head_ $ _cost_ _capac_ _lo_
diagonal factory key_id $10. mth_made $ _name_&$17.;
datalines;
fact1_1 f1_mar_1 127.9 500 50 19 1 production March prod f1 19 mar
fact1_1 f1_apr_1 78.6 600 50 19 1 production April prod f1 19 apl
fact1_1 f1_may_1 95.1 400 50 19 1 production May .
f1_mar_1 f1_apr_1 15 50 . 19 1 storage March .
f1_apr_1 f1_may_1 12 50 . 19 1 storage April .
f1_apr_1 f1_mar_1 28 20 . 19 1 backorder April back f1 19 apl
f1_may_1 f1_apr_1 28 20 . 19 1 backorder May back f1 19 may
f1_mar_1 f2_mar_1 11 . . 19 . f1_to_2 March .
f1_apr_1 f2_apr_1 11 . . 19 . f1_to_2 April .
f1_may_1 f2_may_1 16 . . 19 . f1_to_2 May .
f1_mar_1 shop1_1 -327.65 250 . 19 1 sales March .
f1_apr_1 shop1_1 -300 250 . 19 1 sales April .
f1_may_1 shop1_1 -285 250 . 19 1 sales May .
f1_mar_1 shop2_1 -362.74 250 . 19 1 sales March .
f1_apr_1 shop2_1 -300 250 . 19 1 sales April .
f1_may_1 shop2_1 -245 250 . 19 1 sales May .
fact2_1 f2_mar_1 88.0 450 35 19 2 production March prod f2 19 mar
fact2_1 f2_apr_1 62.4 480 35 19 2 production April prod f2 19 apl
fact2_1 f2_may_1 133.8 250 35 19 2 production May .
f2_mar_1 f2_apr_1 18 30 . 19 2 storage March .
f2_apr_1 f2_may_1 20 30 . 19 2 storage April .
f2_apr_1 f2_mar_1 17 15 . 19 2 backorder April back f2 19 apl
f2_may_1 f2_apr_1 25 15 . 19 2 backorder May back f2 19 may
f2_mar_1 f1_mar_1 10 40 . 19 . f2_to_1 March .
f2_apr_1 f1_apr_1 11 40 . 19 . f2_to_1 April .
f2_may_1 f1_may_1 13 40 . 19 . f2_to_1 May .
f2_mar_1 shop1_1 -297.4 250 . 19 2 sales March .
f2_apr_1 shop1_1 -290 250 . 19 2 sales April .
f2_may_1 shop1_1 -292 250 . 19 2 sales May .
f2_mar_1 shop2_1 -272.7 250 . 19 2 sales March .
f2_apr_1 shop2_1 -312 250 . 19 2 sales April .
f2_may_1 shop2_1 -299 250 . 19 2 sales May .
fact1_2 f1_mar_2 217.9 400 40 25 1 production March prod f1 25 mar
fact1_2 f1_apr_2 174.5 550 50 25 1 production April prod f1 25 apl
fact1_2 f1_may_2 133.3 350 40 25 1 production May .
f1_mar_2 f1_apr_2 20 40 . 25 1 storage March .
f1_apr_2 f1_may_2 18 40 . 25 1 storage April .
f1_apr_2 f1_mar_2 32 30 . 25 1 backorder April back f1 25 apl
f1_may_2 f1_apr_2 41 15 . 25 1 backorder May back f1 25 may
f1_mar_2 f2_mar_2 23 . . 25 . f1_to_2 March .
f1_apr_2 f2_apr_2 23 . . 25 . f1_to_2 April .
f1_may_2 f2_may_2 26 . . 25 . f1_to_2 May .
f1_mar_2 shop1_2 -559.76 . . 25 1 sales March .
f1_apr_2 shop1_2 -524.28 . . 25 1 sales April .
f1_may_2 shop1_2 -475.02 . . 25 1 sales May .
f1_mar_2 shop2_2 -623.89 . . 25 1 sales March .
f1_apr_2 shop2_2 -549.68 . . 25 1 sales April .
f1_may_2 shop2_2 -460.00 . . 25 1 sales May .
fact2_2 f2_mar_2 182.0 650 35 25 2 production March prod f2 25 mar
fact2_2 f2_apr_2 196.7 680 35 25 2 production April prod f2 25 apl
fact2_2 f2_may_2 201.4 550 35 25 2 production May .
f2_mar_2 f2_apr_2 28 50 . 25 2 storage March .
f2_apr_2 f2_may_2 38 50 . 25 2 storage April .
f2_apr_2 f2_mar_2 31 15 . 25 2 backorder April back f2 25 apl
f2_may_2 f2_apr_2 54 15 . 25 2 backorder May back f2 25 may
f2_mar_2 f1_mar_2 20 25 . 25 . f2_to_1 March .
f2_apr_2 f1_apr_2 21 25 . 25 . f2_to_1 April .
f2_may_2 f1_may_2 43 25 . 25 . f2_to_1 May .
f2_mar_2 shop1_2 -567.83 500 . 25 2 sales March .
f2_apr_2 shop1_2 -542.19 500 . 25 2 sales April .
f2_may_2 shop1_2 -461.56 500 . 25 2 sales May .
f2_mar_2 shop2_2 -542.83 500 . 25 2 sales March .
f2_apr_2 shop2_2 -559.19 500 . 25 2 sales April .
f2_may_2 shop2_2 -489.06 500 . 25 2 sales May .
;
proc optmodel;
set <str> NODES;
num _supdem_ {NODES} init 0;
read data node0 into NODES=[_node_] _supdem_;
set <str,str> ARCS;
num _lo_ {ARCS} init 0;
num _capac_ {ARCS} init .;
num _cost_ {ARCS};
num diagonal {ARCS};
num factory {ARCS};
str key_id {ARCS};
str mth_made {ARCS};
str _name_ {ARCS};
read data arc0 nomiss into ARCS=[_tail_ _head_] _lo_ _capac_ _cost_
diagonal factory key_id mth_made _name_;
NODES = NODES union (union {<i,j> in ARCS} {i,j});
var Flow {<i,j> in ARCS} >= _lo_[i,j];
for {<i,j> in ARCS: _capac_[i,j] ne .} Flow[i,j].ub = _capac_[i,j];
min obj = sum {<i,j> in ARCS} _cost_[i,j] * Flow[i,j];
con balance {i in NODES}: sum {<(i),j> in ARCS} Flow[i,j]
- sum {<j,(i)> in ARCS} Flow[j,i] = _supdem_[i];
num infinity = min {r in {}} r;
num excess = sum {i in NODES} _supdem_[i];
if (excess > 0) then do;
/* change equality constraint to le constraint for supply nodes */
for {i in NODES: _supdem_[i] > 0} balance[i].lb = -infinity;
end;
else if (excess < 0) then do;
/* change equality constraint to ge constraint for demand nodes */
for {i in NODES: _supdem_[i] < 0} balance[i].ub = infinity;
end;
solve;
num _supply_ {<i,j> in ARCS} =
(if _supdem_[i] ne 0 then _supdem_[i] else .);
num _demand_ {<i,j> in ARCS} =
(if _supdem_[j] ne 0 then -_supdem_[j] else .);
num _fcost_ {<i,j> in ARCS} = _cost_[i,j] * Flow[i,j].sol;
create data arc1 from [_tail_ _head_]
_cost_ _capac_ _lo_ _name_ _supply_ _demand_ _flow_=Flow _fcost_
_rcost_ =
(if Flow[_tail_,_head_].rc ne 0 then Flow[_tail_,_head_].rc else .)
_status_ = Flow.status diagonal factory key_id mth_made;
create data node2 from [_node_]
_supdem_ = (if _supdem_[_node_] ne 0 then _supdem_[_node_] else .)
_dual_ = balance.dual;
quit;
options ls=80 ps=54;
proc print data=arc1 heading=h width=min;
var _tail_ _head_ _cost_ _capac_ _lo_ _name_
_supply_ _demand_ _flow_ _fcost_;
sum _fcost_;
run;
proc print data=arc1 heading=h width=min;
var _rcost_ _status_ diagonal factory key_id mth_made;
run;
proc print data=node2;
run;