lemon-project-template-glpk

comparison deps/glpk/examples/egypt.mod @ 9:33de93886c88

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Import GLPK 4.47
author Alpar Juttner <alpar@cs.elte.hu>
date Sun, 06 Nov 2011 20:59:10 +0100
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1 # EGYPT, a static model of fertilizer production
2 #
3 # References:
4 # Robert Fourer, David M. Gay and Brian W. Kernighan, "A Modeling Language
5 # for Mathematical Programming." Management Science 36 (1990) 519-554.
6
7 ### SETS ###
8
9 set center; # Locations from which final product may be shipped
10 set port within center; # Locations at which imports can be received
11 set plant within center; # Locations of plants
12
13 set region; # Demand regions
14
15 set unit; # Productive units
16 set proc; # Processes
17
18 set nutr; # Nutrients
19
20 set c_final; # Final products (fertilizers)
21 set c_inter; # Intermediate products
22 set c_ship within c_inter; # Intermediates for shipment
23 set c_raw; # Domestic raw materials and miscellaneous inputs
24
25 set commod := c_final union c_inter union c_raw;
26
27 # All commodities
28
29 ### PARAMETERS ###
30
31 param cf75 {region,c_final} >= 0;
32
33 # Consumption of fertilizer 1974-75 (1000 tpy)
34
35 param fn {c_final,nutr} >= 0;
36
37 # Nutrient content of fertilizers
38
39 param cn75 {r in region, n in nutr} := sum {c in c_final} cf75[r,c] * fn[c,n];
40
41 # Consumption of nutrients 1974-75 (1000 tpy)
42
43 param road {region,center} >= 0;
44
45 # Road distances
46
47 param rail_half {plant,plant} >= 0;
48 param rail {p1 in plant, p2 in plant} :=
49 if rail_half[p1,p2] > 0 then rail_half[p1,p2] else rail_half[p2,p1];
50
51 # Interplant rail distances (kms)
52
53 param impd_barg {plant} >= 0;
54 param impd_road {plant} >= 0;
55
56 # Import distances (kms) by barge and road
57
58 param tran_final {pl in plant, r in region} :=
59 if road[r,pl] > 0 then .5 + .0144 * road[r,pl] else 0;
60
61 param tran_import {r in region, po in port} :=
62 if road[r,po] > 0 then .5 + .0144 * road[r,po] else 0;
63
64 param tran_inter {p1 in plant, p2 in plant} :=
65 if rail[p1,p2] > 0 then 3.5 + .03 * rail[p1,p2] else 0;
66
67 param tran_raw {pl in plant} :=
68 (if impd_barg[pl] > 0 then 1.0 + .0030 * impd_barg[pl] else 0)
69 + (if impd_road[pl] > 0 then 0.5 + .0144 * impd_road[pl] else 0);
70
71 # Transport cost (le per ton) for:
72 # final products, imported final products,
73 # interplant shipment, imported raw materials
74
75 param io {commod,proc}; # Input-output coefficients
76
77 param util {unit,proc} >= 0;
78
79 # Capacity utilization coefficients
80
81 param p_imp {commod} >= 0; # Import Price (cif US$ per ton 1975)
82
83 param p_r {c_raw} >= 0;
84 param p_pr {plant,c_raw} >= 0;
85
86 param p_dom {pl in plant, c in c_raw} :=
87 if p_r[c] > 0 then p_r[c] else p_pr[pl,c];
88
89 # Domestic raw material prices
90
91 param dcap {plant,unit} >= 0;
92
93 # Design capacity of plants (t/day)
94
95 param icap {u in unit, pl in plant} := 0.33 * dcap[pl,u];
96
97 # Initial capacity of plants (t/day)
98
99 param exch := 0.4; # Exchange rate
100
101 param util_pct := 0.85; # Utilization percent for initial capacity
102
103 ### DERIVED SETS OF "POSSIBILITIES" ###
104
105 set m_pos {pl in plant} := {u in unit: icap[u,pl] > 0};
106
107 # At each plant, set of units for which there is
108 # initial capacity
109
110 set p_cap {pl in plant} :=
111 {pr in proc: forall {u in unit: util[u,pr] > 0} u in m_pos[pl] };
112
113 # At each plant, set of processes for which
114 # all necessary units have some initial capacity
115
116 set p_except {plant} within proc;
117
118 # At each plant, list of processes that are
119 # arbitrarily ruled out
120
121 set p_pos {pl in plant} := p_cap[pl] diff p_except[pl];
122
123 # At each plant, set of possible processes
124
125 set cp_pos {c in commod} := {pl in plant: sum {pr in p_pos[pl]} io[c,pr] > 0};
126
127 set cc_pos {c in commod} := {pl in plant: sum {pr in p_pos[pl]} io[c,pr] < 0};
128
129 set c_pos {c in commod} := cp_pos[c] union cc_pos[c];
130
131 # For each commodity, set of plants that can
132 # produce it (cp_pos) or consume it (cc_pos),
133 # and their union (c_pos)
134
135 ### VARIABLES ###
136
137 var Z {pl in plant, p_pos[pl]} >= 0;
138
139 # Z[pl,pr] is level of process pr at plant pl
140
141 var Xf {c in c_final, cp_pos[c], region} >= 0;
142
143 # Xf[c,pl,r] is amount of final product c
144 # shipped from plant pl to region r
145
146 var Xi {c in c_ship, cp_pos[c], cc_pos[c]} >= 0;
147
148 # Xi[c,p1,p2] is amount of intermediate c
149 # shipped from plant p1 to plant p2
150
151 var Vf {c_final,region,port} >= 0;
152
153 # Vf[c,r,po] is amount of final product c
154 # imported by region r from port po
155
156 var Vr {c in c_raw, cc_pos[c]} >= 0;
157
158 # Vr[c,pl] is amount of raw material c
159 # imported for use at plant pl
160
161 var U {c in c_raw, cc_pos[c]} >= 0;
162
163 # U[c,pl] is amount of raw material c
164 # purchased domestically for use at plant pl
165
166 var Psip; # Domestic recurrent cost
167 var Psil; # Transport cost
168 var Psii; # Import cost
169
170 ### OBJECTIVE ###
171
172 minimize Psi: Psip + Psil + Psii;
173
174 ### CONSTRAINTS ###
175
176 subject to mbd {n in nutr, r in region}:
177
178 sum {c in c_final} fn[c,n] *
179 (sum {po in port} Vf[c,r,po] +
180 sum {pl in cp_pos[c]} Xf[c,pl,r]) >= cn75[r,n];
181
182 # Total nutrients supplied to a region by all
183 # final products (sum of imports plus internal
184 # shipments from plants) must meet requirements
185
186 subject to mbdb {c in c_final, r in region: cf75[r,c] > 0}:
187
188 sum {po in port} Vf[c,r,po] +
189 sum {pl in cp_pos[c]} Xf[c,pl,r] >= cf75[r,c];
190
191 # Total of each final product supplied to each
192 # region (as in previous constraint) must meet
193 # requirements
194
195 subject to mb {c in commod, pl in plant}:
196
197 sum {pr in p_pos[pl]} io[c,pr] * Z[pl,pr]
198
199 + ( if c in c_ship then
200 ( if pl in cp_pos[c] then sum {p2 in cc_pos[c]} Xi[c,pl,p2] )
201 - ( if pl in cc_pos[c] then sum {p2 in cp_pos[c]} Xi[c,p2,pl] ))
202
203 + ( if (c in c_raw and pl in cc_pos[c]) then
204 (( if p_imp[c] > 0 then Vr[c,pl] )
205 + ( if p_dom[pl,c] > 0 then U[c,pl] )))
206
207 >= if (c in c_final and pl in cp_pos[c]) then sum {r in region} Xf[c,pl,r];
208
209 # For each commodity at each plant: sum of
210 # (1) production or consumption at plant,
211 # (2) inter-plant shipments in or out,
212 # (3) import and domestic purchases (raw only)
213 # is >= 0 for raw materials and intermediates;
214 # is >= the total shipped for final products
215
216 subject to cc {pl in plant, u in m_pos[pl]}:
217
218 sum {pr in p_pos[pl]} util[u,pr] * Z[pl,pr] <= util_pct * icap[u,pl];
219
220 # For each productive unit at each plant,
221 # total utilization by all processes
222 # may not exceed the unit's capacity
223
224 subject to ap:
225
226 Psip = sum {c in c_raw, pl in cc_pos[c]} p_dom[pl,c] * U[c,pl];
227
228 # Psip is the cost of domestic raw materials,
229 # summed over all plants that consume them
230
231 subject to al:
232
233 Psil = sum {c in c_final} (
234
235 sum {pl in cp_pos[c], r in region}
236 tran_final[pl,r] * Xf[c,pl,r]
237
238 + sum {po in port, r in region} tran_import[r,po] * Vf[c,r,po] )
239
240 + sum {c in c_ship, p1 in cp_pos[c], p2 in cc_pos[c]}
241 tran_inter[p1,p2] * Xi[c,p1,p2]
242
243 + sum {c in c_raw, pl in cc_pos[c]: p_imp[c] > 0}
244 tran_raw[pl] * Vr[c,pl];
245
246 # Total transport cost is sum of shipping costs for
247 # (1) all final products from all plants,
248 # (2) all imports of final products,
249 # (3) all intermediates shipped between plants,
250 # (4) all imports of raw materials
251
252 subject to ai:
253
254 Psii / exch = sum {c in c_final, r in region, po in port}
255 p_imp[c] * Vf[c,r,po]
256
257 + sum {c in c_raw, pl in cc_pos[c]} p_imp[c] * Vr[c,pl];
258
259 # Total import cost -- at exchange rate --
260 # is sum of import costs for final products
261 # in each region and raw materials at each plant
262
263 ### DATA ###
264
265 data;
266
267 set center := ASWAN HELWAN ASSIOUT KAFR_EL_ZT ABU_ZAABAL ABU_KIR TALKHA SUEZ ;
268
269 set port := ABU_KIR ;
270
271 set plant := ASWAN HELWAN ASSIOUT KAFR_EL_ZT ABU_ZAABAL ;
272
273 set region := ALEXANDRIA BEHERA GHARBIA KAFR_EL_SH DAKAHLIA DAMIETTA
274 SHARKIA ISMAILIA SUEZ MENOUFIA KALUBIA GIZA BENI_SUEF FAYOUM
275 MINIA ASSIOUT NEW_VALLEY SOHAG QUENA ASWAN ;
276
277 set unit := SULF_A_S SULF_A_P NITR_ACID AMM_ELEC AMM_C_GAS C_AMM_NITR
278 AMM_SULF SSP ;
279
280 set proc := SULF_A_S SULF_A_P NITR_ACID AMM_ELEC AMM_C_GAS CAN_310 CAN_335
281 AMM_SULF SSP_155 ;
282
283 set nutr := N P205 ;
284
285 set c_final := UREA CAN_260 CAN_310 CAN_335 AMM_SULF DAP SSP_155 C_250_55
286 C_300_100 ;
287
288 set c_inter := AMMONIA NITR_ACID SULF_ACID ;
289
290 set c_ship := AMMONIA SULF_ACID ;
291
292 set c_raw := EL_ASWAN COKE_GAS PHOS_ROCK LIMESTONE EL_SULFUR PYRITES
293 ELECTRIC BF_GAS WATER STEAM BAGS ;
294
295 set p_except[ASWAN] := CAN_335 ;
296 set p_except[HELWAN] := CAN_310 ;
297 set p_except[ASSIOUT] := ;
298 set p_except[KAFR_EL_ZT] := ;
299 set p_except[ABU_ZAABAL] := ;
300
301 param cf75 default 0.0 :
302
303 CAN_260 CAN_310 CAN_335 AMM_SULF UREA :=
304
305 ALEXANDRIA . . 5.0 3.0 1.0
306 ASSIOUT 1.0 20.0 26.0 1.0 27.0
307 ASWAN . 40.0 . . .
308 BEHERA 1.0 . 25.0 90.0 35.0
309 BENI_SUEF 1.0 . 15.0 1.0 20.0
310 DAKAHLIA 1.0 . 26.0 60.0 20.0
311 DAMIETTA . . 2.0 15.0 8.0
312 FAYOUM 1.0 . 20.0 6.0 20.0
313 GHARBIA . . 17.0 60.0 28.0
314 GIZA . . 40.0 6.0 2.0
315 ISMAILIA . . 4.0 6.0 2.0
316 KAFR_EL_SH 1.0 . 10.0 45.0 22.0
317 KALUBIA . . 25.0 16.0 7.0
318 MENOUFIA 1.0 . 24.0 21.0 30.0
319 MINIA 2.0 15.0 35.0 1.0 41.0
320 NEW_VALLEY . . . . 1.0
321 QUENA . 95.0 2.0 . 3.0
322 SHARKIA 1.0 . 31.0 50.0 28.0
323 SOHAG . 65.0 3.0 . 7.0
324 SUEZ . . 1.0 . .
325
326 : SSP_155 C_250_55 C_300_100 DAP :=
327
328 ALEXANDRIA 8.0 . . .
329 ASSIOUT 35.0 5.0 .1 .
330 ASWAN 8.0 . . .
331 BEHERA 64.0 1.0 .1 .1
332 BENI_SUEF 13.0 3.0 . .
333 DAKAHLIA 52.0 1.0 . .
334 DAMIETTA 5.0 . . .
335 FAYOUM 17.0 1.0 . .
336 GHARBIA 57.0 1.0 .2 .1
337 GIZA 14.0 1.0 .1 .
338 ISMAILIA 4.0 . . .
339 KAFR_EL_SH 25.0 2.0 .1 .
340 KALUBIA 22.0 1.0 . .1
341 MENOUFIA 33.0 2.0 .1 .1
342 MINIA 50.0 3.0 .2 .1
343 NEW_VALLEY 1.0 . . .
344 QUENA 8.0 . . .
345 SHARKIA 43.0 1.0 .1 .
346 SOHAG 20.0 1.0 . .
347 SUEZ 1.0 . . . ;
348
349 param fn default 0.0 : N P205 :=
350
351 AMM_SULF .206 .
352 CAN_260 .26 .
353 CAN_310 .31 .
354 CAN_335 .335 .
355 C_250_55 .25 .055
356 C_300_100 .30 .10
357 DAP .18 .46
358 SSP_155 . .15
359 UREA .46 . ;
360
361 param road default 0.0 :
362
363 ABU_KIR ABU_ZAABAL ASSIOUT ASWAN HELWAN KAFR_EL_ZT SUEZ TALKHA :=
364
365 ALEXANDRIA 16 210 607 1135 244 119 362 187
366 ASSIOUT 616 420 . 518 362 504 527 518
367 ASWAN 1134 938 518 . 880 1022 1045 1036
368 BEHERA 76 50 547 1065 184 42 288 120
369 BENI_SUEF 359 163 257 775 105 248 270 261
370 DAKAHLIA 208 138 515 1033 152 58 219 3
371 DAMIETTA 267 216 596 1114 233 131 286 66
372 FAYOUM 341 145 308 826 88 230 252 243
373 GHARBIA 150 65 485 1003 122 20 226 55
374 GIZA 287 48 372 890 .9 133 169 146
375 ISMAILIA 365 142 536 1054 173 241 89 146
376 KAFR_EL_SH 145 105 525 1043 162 20 266 35
377 KALUBIA 190 97 439 957 76 66 180 81
378 MENOUFIA 157 154 472 990 109 33 213 90
379 MINIA 384 288 132 650 230 372 394 386
380 NEW_VALLEY 815 619 199 519 561 703 726 717
381 QUENA 858 662 242 276 604 746 769 760
382 SHARKIA 240 60 473 991 110 78 214 58
383 SOHAG 715 519 99 419 461 603 626 617
384 SUEZ 370 224 541 1059 178 246 . 298 ;
385
386 param rail_half default 0 :
387
388 KAFR_EL_ZT ABU_ZAABAL HELWAN ASSIOUT :=
389
390 ABU_ZAABAL 85 . . .
391 HELWAN 142 57 . .
392 ASSIOUT 504 420 362 .
393 ASWAN 1022 938 880 518 ;
394
395 param : impd_barg impd_road :=
396
397 ABU_ZAABAL 210 .1
398 ASSIOUT 583 0
399 ASWAN 1087 10
400 HELWAN 183 0
401 KAFR_EL_ZT 104 6 ;
402
403 param io default 0.0 :=
404
405 [*,AMM_C_GAS] AMMONIA 1.0
406 BF_GAS -609.
407 COKE_GAS -2.0
408 ELECTRIC -1960.
409 STEAM -4.
410 WATER -700.
411
412 [*,AMM_ELEC] AMMONIA 1.0
413 EL_ASWAN -12.0
414
415 [*,AMM_SULF] AMMONIA -.26
416 AMM_SULF 1.0
417 BAGS -22.
418 ELECTRIC -19.
419 SULF_ACID -.76
420 WATER -17.
421
422 [*,CAN_310] AMMONIA -.20
423 BAGS -23.
424 CAN_310 1.0
425 LIMESTONE -.12
426 NITR_ACID -.71
427 STEAM -.4
428 WATER -49.
429
430 [*,CAN_335] AMMONIA -.21
431 BAGS -23.
432 CAN_335 1.0
433 LIMESTONE -.04
434 NITR_ACID -.76
435 STEAM -.4
436 WATER -49.
437
438 [*,NITR_ACID] AMMONIA -.292
439 ELECTRIC -231.
440 NITR_ACID 1.0
441 WATER -.6
442
443 [*,SSP_155] BAGS -22.
444 ELECTRIC -14.
445 PHOS_ROCK -.62
446 SSP_155 1.0
447 SULF_ACID -.41
448 WATER -6.
449
450 [*,SULF_A_P] ELECTRIC -75.
451 PYRITES -.826
452 SULF_ACID 1.0
453 WATER -60.
454
455 [*,SULF_A_S] ELECTRIC -50.
456 EL_SULFUR -.334
457 SULF_ACID 1.0
458 WATER -20. ;
459
460 param util default 0 :=
461
462 [*,*] SULF_A_S SULF_A_S 1 SULF_A_P SULF_A_P 1
463 NITR_ACID NITR_ACID 1 AMM_ELEC AMM_ELEC 1
464 AMM_C_GAS AMM_C_GAS 1 SSP SSP_155 1
465 C_AMM_NITR CAN_310 1 C_AMM_NITR CAN_335 1
466 AMM_SULF AMM_SULF 1 ;
467
468 param p_imp default 0.0 :=
469
470 PYRITES 17.5 AMM_SULF 75.
471 EL_SULFUR 55. DAP 175.
472 UREA 150. SSP_155 80.
473 CAN_260 75. C_250_55 100.
474 CAN_310 90. C_300_100 130.
475 CAN_335 100. ;
476
477 param p_r default 0.0 :=
478
479 ELECTRIC .007
480 BF_GAS .007
481 WATER .031
482 STEAM 1.25
483 BAGS .28 ;
484
485 param p_pr default 0.0 :=
486
487 [HELWAN,COKE_GAS] 16.0
488 [ASWAN,EL_ASWAN] 1.0
489
490 [*,LIMESTONE] ASWAN 1.2
491 HELWAN 1.2
492
493 [*,PHOS_ROCK] ABU_ZAABAL 4.0
494 ASSIOUT 3.5
495 KAFR_EL_ZT 5.0 ;
496
497 param dcap default 0.0 :=
498
499 [ABU_ZAABAL,*] SSP 600
500 SULF_A_P 227
501 SULF_A_S 242
502
503 [ASSIOUT,*] SSP 600
504 SULF_A_S 250
505
506 [ASWAN,*] AMM_ELEC 450
507 C_AMM_NITR 1100
508 NITR_ACID 800
509
510 [HELWAN,*] AMM_C_GAS 172
511 AMM_SULF 24
512 C_AMM_NITR 364
513 NITR_ACID 282
514
515 [KAFR_EL_ZT,*] SSP 600
516 SULF_A_P 50
517 SULF_A_S 200 ;
518
519 end;