lemon-project-template-glpk
diff deps/glpk/examples/egypt.mod @ 9:33de93886c88
Import GLPK 4.47
| author | Alpar Juttner <alpar@cs.elte.hu> |
|---|---|
| date | Sun, 06 Nov 2011 20:59:10 +0100 |
| parents | |
| children |
line diff
1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000 1.2 +++ b/deps/glpk/examples/egypt.mod Sun Nov 06 20:59:10 2011 +0100 1.3 @@ -0,0 +1,519 @@ 1.4 +# EGYPT, a static model of fertilizer production 1.5 +# 1.6 +# References: 1.7 +# Robert Fourer, David M. Gay and Brian W. Kernighan, "A Modeling Language 1.8 +# for Mathematical Programming." Management Science 36 (1990) 519-554. 1.9 + 1.10 +### SETS ### 1.11 + 1.12 +set center; # Locations from which final product may be shipped 1.13 +set port within center; # Locations at which imports can be received 1.14 +set plant within center; # Locations of plants 1.15 + 1.16 +set region; # Demand regions 1.17 + 1.18 +set unit; # Productive units 1.19 +set proc; # Processes 1.20 + 1.21 +set nutr; # Nutrients 1.22 + 1.23 +set c_final; # Final products (fertilizers) 1.24 +set c_inter; # Intermediate products 1.25 +set c_ship within c_inter; # Intermediates for shipment 1.26 +set c_raw; # Domestic raw materials and miscellaneous inputs 1.27 + 1.28 +set commod := c_final union c_inter union c_raw; 1.29 + 1.30 + # All commodities 1.31 + 1.32 +### PARAMETERS ### 1.33 + 1.34 +param cf75 {region,c_final} >= 0; 1.35 + 1.36 + # Consumption of fertilizer 1974-75 (1000 tpy) 1.37 + 1.38 +param fn {c_final,nutr} >= 0; 1.39 + 1.40 + # Nutrient content of fertilizers 1.41 + 1.42 +param cn75 {r in region, n in nutr} := sum {c in c_final} cf75[r,c] * fn[c,n]; 1.43 + 1.44 + # Consumption of nutrients 1974-75 (1000 tpy) 1.45 + 1.46 +param road {region,center} >= 0; 1.47 + 1.48 + # Road distances 1.49 + 1.50 +param rail_half {plant,plant} >= 0; 1.51 +param rail {p1 in plant, p2 in plant} := 1.52 + if rail_half[p1,p2] > 0 then rail_half[p1,p2] else rail_half[p2,p1]; 1.53 + 1.54 + # Interplant rail distances (kms) 1.55 + 1.56 +param impd_barg {plant} >= 0; 1.57 +param impd_road {plant} >= 0; 1.58 + 1.59 + # Import distances (kms) by barge and road 1.60 + 1.61 +param tran_final {pl in plant, r in region} := 1.62 + if road[r,pl] > 0 then .5 + .0144 * road[r,pl] else 0; 1.63 + 1.64 +param tran_import {r in region, po in port} := 1.65 + if road[r,po] > 0 then .5 + .0144 * road[r,po] else 0; 1.66 + 1.67 +param tran_inter {p1 in plant, p2 in plant} := 1.68 + if rail[p1,p2] > 0 then 3.5 + .03 * rail[p1,p2] else 0; 1.69 + 1.70 +param tran_raw {pl in plant} := 1.71 + (if impd_barg[pl] > 0 then 1.0 + .0030 * impd_barg[pl] else 0) 1.72 + + (if impd_road[pl] > 0 then 0.5 + .0144 * impd_road[pl] else 0); 1.73 + 1.74 + # Transport cost (le per ton) for: 1.75 + # final products, imported final products, 1.76 + # interplant shipment, imported raw materials 1.77 + 1.78 +param io {commod,proc}; # Input-output coefficients 1.79 + 1.80 +param util {unit,proc} >= 0; 1.81 + 1.82 + # Capacity utilization coefficients 1.83 + 1.84 +param p_imp {commod} >= 0; # Import Price (cif US$ per ton 1975) 1.85 + 1.86 +param p_r {c_raw} >= 0; 1.87 +param p_pr {plant,c_raw} >= 0; 1.88 + 1.89 +param p_dom {pl in plant, c in c_raw} := 1.90 + if p_r[c] > 0 then p_r[c] else p_pr[pl,c]; 1.91 + 1.92 + # Domestic raw material prices 1.93 + 1.94 +param dcap {plant,unit} >= 0; 1.95 + 1.96 + # Design capacity of plants (t/day) 1.97 + 1.98 +param icap {u in unit, pl in plant} := 0.33 * dcap[pl,u]; 1.99 + 1.100 + # Initial capacity of plants (t/day) 1.101 + 1.102 +param exch := 0.4; # Exchange rate 1.103 + 1.104 +param util_pct := 0.85; # Utilization percent for initial capacity 1.105 + 1.106 +### DERIVED SETS OF "POSSIBILITIES" ### 1.107 + 1.108 +set m_pos {pl in plant} := {u in unit: icap[u,pl] > 0}; 1.109 + 1.110 + # At each plant, set of units for which there is 1.111 + # initial capacity 1.112 + 1.113 +set p_cap {pl in plant} := 1.114 + {pr in proc: forall {u in unit: util[u,pr] > 0} u in m_pos[pl] }; 1.115 + 1.116 + # At each plant, set of processes for which 1.117 + # all necessary units have some initial capacity 1.118 + 1.119 +set p_except {plant} within proc; 1.120 + 1.121 + # At each plant, list of processes that are 1.122 + # arbitrarily ruled out 1.123 + 1.124 +set p_pos {pl in plant} := p_cap[pl] diff p_except[pl]; 1.125 + 1.126 + # At each plant, set of possible processes 1.127 + 1.128 +set cp_pos {c in commod} := {pl in plant: sum {pr in p_pos[pl]} io[c,pr] > 0}; 1.129 + 1.130 +set cc_pos {c in commod} := {pl in plant: sum {pr in p_pos[pl]} io[c,pr] < 0}; 1.131 + 1.132 +set c_pos {c in commod} := cp_pos[c] union cc_pos[c]; 1.133 + 1.134 + # For each commodity, set of plants that can 1.135 + # produce it (cp_pos) or consume it (cc_pos), 1.136 + # and their union (c_pos) 1.137 + 1.138 +### VARIABLES ### 1.139 + 1.140 +var Z {pl in plant, p_pos[pl]} >= 0; 1.141 + 1.142 + # Z[pl,pr] is level of process pr at plant pl 1.143 + 1.144 +var Xf {c in c_final, cp_pos[c], region} >= 0; 1.145 + 1.146 + # Xf[c,pl,r] is amount of final product c 1.147 + # shipped from plant pl to region r 1.148 + 1.149 +var Xi {c in c_ship, cp_pos[c], cc_pos[c]} >= 0; 1.150 + 1.151 + # Xi[c,p1,p2] is amount of intermediate c 1.152 + # shipped from plant p1 to plant p2 1.153 + 1.154 +var Vf {c_final,region,port} >= 0; 1.155 + 1.156 + # Vf[c,r,po] is amount of final product c 1.157 + # imported by region r from port po 1.158 + 1.159 +var Vr {c in c_raw, cc_pos[c]} >= 0; 1.160 + 1.161 + # Vr[c,pl] is amount of raw material c 1.162 + # imported for use at plant pl 1.163 + 1.164 +var U {c in c_raw, cc_pos[c]} >= 0; 1.165 + 1.166 + # U[c,pl] is amount of raw material c 1.167 + # purchased domestically for use at plant pl 1.168 + 1.169 +var Psip; # Domestic recurrent cost 1.170 +var Psil; # Transport cost 1.171 +var Psii; # Import cost 1.172 + 1.173 +### OBJECTIVE ### 1.174 + 1.175 +minimize Psi: Psip + Psil + Psii; 1.176 + 1.177 +### CONSTRAINTS ### 1.178 + 1.179 +subject to mbd {n in nutr, r in region}: 1.180 + 1.181 + sum {c in c_final} fn[c,n] * 1.182 + (sum {po in port} Vf[c,r,po] + 1.183 + sum {pl in cp_pos[c]} Xf[c,pl,r]) >= cn75[r,n]; 1.184 + 1.185 + # Total nutrients supplied to a region by all 1.186 + # final products (sum of imports plus internal 1.187 + # shipments from plants) must meet requirements 1.188 + 1.189 +subject to mbdb {c in c_final, r in region: cf75[r,c] > 0}: 1.190 + 1.191 + sum {po in port} Vf[c,r,po] + 1.192 + sum {pl in cp_pos[c]} Xf[c,pl,r] >= cf75[r,c]; 1.193 + 1.194 + # Total of each final product supplied to each 1.195 + # region (as in previous constraint) must meet 1.196 + # requirements 1.197 + 1.198 +subject to mb {c in commod, pl in plant}: 1.199 + 1.200 + sum {pr in p_pos[pl]} io[c,pr] * Z[pl,pr] 1.201 + 1.202 + + ( if c in c_ship then 1.203 + ( if pl in cp_pos[c] then sum {p2 in cc_pos[c]} Xi[c,pl,p2] ) 1.204 + - ( if pl in cc_pos[c] then sum {p2 in cp_pos[c]} Xi[c,p2,pl] )) 1.205 + 1.206 + + ( if (c in c_raw and pl in cc_pos[c]) then 1.207 + (( if p_imp[c] > 0 then Vr[c,pl] ) 1.208 + + ( if p_dom[pl,c] > 0 then U[c,pl] ))) 1.209 + 1.210 + >= if (c in c_final and pl in cp_pos[c]) then sum {r in region} Xf[c,pl,r]; 1.211 + 1.212 + # For each commodity at each plant: sum of 1.213 + # (1) production or consumption at plant, 1.214 + # (2) inter-plant shipments in or out, 1.215 + # (3) import and domestic purchases (raw only) 1.216 + # is >= 0 for raw materials and intermediates; 1.217 + # is >= the total shipped for final products 1.218 + 1.219 +subject to cc {pl in plant, u in m_pos[pl]}: 1.220 + 1.221 + sum {pr in p_pos[pl]} util[u,pr] * Z[pl,pr] <= util_pct * icap[u,pl]; 1.222 + 1.223 + # For each productive unit at each plant, 1.224 + # total utilization by all processes 1.225 + # may not exceed the unit's capacity 1.226 + 1.227 +subject to ap: 1.228 + 1.229 + Psip = sum {c in c_raw, pl in cc_pos[c]} p_dom[pl,c] * U[c,pl]; 1.230 + 1.231 + # Psip is the cost of domestic raw materials, 1.232 + # summed over all plants that consume them 1.233 + 1.234 +subject to al: 1.235 + 1.236 + Psil = sum {c in c_final} ( 1.237 + 1.238 + sum {pl in cp_pos[c], r in region} 1.239 + tran_final[pl,r] * Xf[c,pl,r] 1.240 + 1.241 + + sum {po in port, r in region} tran_import[r,po] * Vf[c,r,po] ) 1.242 + 1.243 + + sum {c in c_ship, p1 in cp_pos[c], p2 in cc_pos[c]} 1.244 + tran_inter[p1,p2] * Xi[c,p1,p2] 1.245 + 1.246 + + sum {c in c_raw, pl in cc_pos[c]: p_imp[c] > 0} 1.247 + tran_raw[pl] * Vr[c,pl]; 1.248 + 1.249 + # Total transport cost is sum of shipping costs for 1.250 + # (1) all final products from all plants, 1.251 + # (2) all imports of final products, 1.252 + # (3) all intermediates shipped between plants, 1.253 + # (4) all imports of raw materials 1.254 + 1.255 +subject to ai: 1.256 + 1.257 + Psii / exch = sum {c in c_final, r in region, po in port} 1.258 + p_imp[c] * Vf[c,r,po] 1.259 + 1.260 + + sum {c in c_raw, pl in cc_pos[c]} p_imp[c] * Vr[c,pl]; 1.261 + 1.262 + # Total import cost -- at exchange rate -- 1.263 + # is sum of import costs for final products 1.264 + # in each region and raw materials at each plant 1.265 + 1.266 +### DATA ### 1.267 + 1.268 +data; 1.269 + 1.270 +set center := ASWAN HELWAN ASSIOUT KAFR_EL_ZT ABU_ZAABAL ABU_KIR TALKHA SUEZ ; 1.271 + 1.272 +set port := ABU_KIR ; 1.273 + 1.274 +set plant := ASWAN HELWAN ASSIOUT KAFR_EL_ZT ABU_ZAABAL ; 1.275 + 1.276 +set region := ALEXANDRIA BEHERA GHARBIA KAFR_EL_SH DAKAHLIA DAMIETTA 1.277 + SHARKIA ISMAILIA SUEZ MENOUFIA KALUBIA GIZA BENI_SUEF FAYOUM 1.278 + MINIA ASSIOUT NEW_VALLEY SOHAG QUENA ASWAN ; 1.279 + 1.280 +set unit := SULF_A_S SULF_A_P NITR_ACID AMM_ELEC AMM_C_GAS C_AMM_NITR 1.281 + AMM_SULF SSP ; 1.282 + 1.283 +set proc := SULF_A_S SULF_A_P NITR_ACID AMM_ELEC AMM_C_GAS CAN_310 CAN_335 1.284 + AMM_SULF SSP_155 ; 1.285 + 1.286 +set nutr := N P205 ; 1.287 + 1.288 +set c_final := UREA CAN_260 CAN_310 CAN_335 AMM_SULF DAP SSP_155 C_250_55 1.289 + C_300_100 ; 1.290 + 1.291 +set c_inter := AMMONIA NITR_ACID SULF_ACID ; 1.292 + 1.293 +set c_ship := AMMONIA SULF_ACID ; 1.294 + 1.295 +set c_raw := EL_ASWAN COKE_GAS PHOS_ROCK LIMESTONE EL_SULFUR PYRITES 1.296 + ELECTRIC BF_GAS WATER STEAM BAGS ; 1.297 + 1.298 +set p_except[ASWAN] := CAN_335 ; 1.299 +set p_except[HELWAN] := CAN_310 ; 1.300 +set p_except[ASSIOUT] := ; 1.301 +set p_except[KAFR_EL_ZT] := ; 1.302 +set p_except[ABU_ZAABAL] := ; 1.303 + 1.304 +param cf75 default 0.0 : 1.305 + 1.306 + CAN_260 CAN_310 CAN_335 AMM_SULF UREA := 1.307 + 1.308 +ALEXANDRIA . . 5.0 3.0 1.0 1.309 +ASSIOUT 1.0 20.0 26.0 1.0 27.0 1.310 +ASWAN . 40.0 . . . 1.311 +BEHERA 1.0 . 25.0 90.0 35.0 1.312 +BENI_SUEF 1.0 . 15.0 1.0 20.0 1.313 +DAKAHLIA 1.0 . 26.0 60.0 20.0 1.314 +DAMIETTA . . 2.0 15.0 8.0 1.315 +FAYOUM 1.0 . 20.0 6.0 20.0 1.316 +GHARBIA . . 17.0 60.0 28.0 1.317 +GIZA . . 40.0 6.0 2.0 1.318 +ISMAILIA . . 4.0 6.0 2.0 1.319 +KAFR_EL_SH 1.0 . 10.0 45.0 22.0 1.320 +KALUBIA . . 25.0 16.0 7.0 1.321 +MENOUFIA 1.0 . 24.0 21.0 30.0 1.322 +MINIA 2.0 15.0 35.0 1.0 41.0 1.323 +NEW_VALLEY . . . . 1.0 1.324 +QUENA . 95.0 2.0 . 3.0 1.325 +SHARKIA 1.0 . 31.0 50.0 28.0 1.326 +SOHAG . 65.0 3.0 . 7.0 1.327 +SUEZ . . 1.0 . . 1.328 + 1.329 + : SSP_155 C_250_55 C_300_100 DAP := 1.330 + 1.331 +ALEXANDRIA 8.0 . . . 1.332 +ASSIOUT 35.0 5.0 .1 . 1.333 +ASWAN 8.0 . . . 1.334 +BEHERA 64.0 1.0 .1 .1 1.335 +BENI_SUEF 13.0 3.0 . . 1.336 +DAKAHLIA 52.0 1.0 . . 1.337 +DAMIETTA 5.0 . . . 1.338 +FAYOUM 17.0 1.0 . . 1.339 +GHARBIA 57.0 1.0 .2 .1 1.340 +GIZA 14.0 1.0 .1 . 1.341 +ISMAILIA 4.0 . . . 1.342 +KAFR_EL_SH 25.0 2.0 .1 . 1.343 +KALUBIA 22.0 1.0 . .1 1.344 +MENOUFIA 33.0 2.0 .1 .1 1.345 +MINIA 50.0 3.0 .2 .1 1.346 +NEW_VALLEY 1.0 . . . 1.347 +QUENA 8.0 . . . 1.348 +SHARKIA 43.0 1.0 .1 . 1.349 +SOHAG 20.0 1.0 . . 1.350 +SUEZ 1.0 . . . ; 1.351 + 1.352 +param fn default 0.0 : N P205 := 1.353 + 1.354 + AMM_SULF .206 . 1.355 + CAN_260 .26 . 1.356 + CAN_310 .31 . 1.357 + CAN_335 .335 . 1.358 + C_250_55 .25 .055 1.359 + C_300_100 .30 .10 1.360 + DAP .18 .46 1.361 + SSP_155 . .15 1.362 + UREA .46 . ; 1.363 + 1.364 +param road default 0.0 : 1.365 + 1.366 + ABU_KIR ABU_ZAABAL ASSIOUT ASWAN HELWAN KAFR_EL_ZT SUEZ TALKHA := 1.367 + 1.368 +ALEXANDRIA 16 210 607 1135 244 119 362 187 1.369 +ASSIOUT 616 420 . 518 362 504 527 518 1.370 +ASWAN 1134 938 518 . 880 1022 1045 1036 1.371 +BEHERA 76 50 547 1065 184 42 288 120 1.372 +BENI_SUEF 359 163 257 775 105 248 270 261 1.373 +DAKAHLIA 208 138 515 1033 152 58 219 3 1.374 +DAMIETTA 267 216 596 1114 233 131 286 66 1.375 +FAYOUM 341 145 308 826 88 230 252 243 1.376 +GHARBIA 150 65 485 1003 122 20 226 55 1.377 +GIZA 287 48 372 890 .9 133 169 146 1.378 +ISMAILIA 365 142 536 1054 173 241 89 146 1.379 +KAFR_EL_SH 145 105 525 1043 162 20 266 35 1.380 +KALUBIA 190 97 439 957 76 66 180 81 1.381 +MENOUFIA 157 154 472 990 109 33 213 90 1.382 +MINIA 384 288 132 650 230 372 394 386 1.383 +NEW_VALLEY 815 619 199 519 561 703 726 717 1.384 +QUENA 858 662 242 276 604 746 769 760 1.385 +SHARKIA 240 60 473 991 110 78 214 58 1.386 +SOHAG 715 519 99 419 461 603 626 617 1.387 +SUEZ 370 224 541 1059 178 246 . 298 ; 1.388 + 1.389 +param rail_half default 0 : 1.390 + 1.391 + KAFR_EL_ZT ABU_ZAABAL HELWAN ASSIOUT := 1.392 + 1.393 +ABU_ZAABAL 85 . . . 1.394 +HELWAN 142 57 . . 1.395 +ASSIOUT 504 420 362 . 1.396 +ASWAN 1022 938 880 518 ; 1.397 + 1.398 +param : impd_barg impd_road := 1.399 + 1.400 +ABU_ZAABAL 210 .1 1.401 +ASSIOUT 583 0 1.402 +ASWAN 1087 10 1.403 +HELWAN 183 0 1.404 +KAFR_EL_ZT 104 6 ; 1.405 + 1.406 +param io default 0.0 := 1.407 + 1.408 + [*,AMM_C_GAS] AMMONIA 1.0 1.409 + BF_GAS -609. 1.410 + COKE_GAS -2.0 1.411 + ELECTRIC -1960. 1.412 + STEAM -4. 1.413 + WATER -700. 1.414 + 1.415 + [*,AMM_ELEC] AMMONIA 1.0 1.416 + EL_ASWAN -12.0 1.417 + 1.418 + [*,AMM_SULF] AMMONIA -.26 1.419 + AMM_SULF 1.0 1.420 + BAGS -22. 1.421 + ELECTRIC -19. 1.422 + SULF_ACID -.76 1.423 + WATER -17. 1.424 + 1.425 + [*,CAN_310] AMMONIA -.20 1.426 + BAGS -23. 1.427 + CAN_310 1.0 1.428 + LIMESTONE -.12 1.429 + NITR_ACID -.71 1.430 + STEAM -.4 1.431 + WATER -49. 1.432 + 1.433 + [*,CAN_335] AMMONIA -.21 1.434 + BAGS -23. 1.435 + CAN_335 1.0 1.436 + LIMESTONE -.04 1.437 + NITR_ACID -.76 1.438 + STEAM -.4 1.439 + WATER -49. 1.440 + 1.441 + [*,NITR_ACID] AMMONIA -.292 1.442 + ELECTRIC -231. 1.443 + NITR_ACID 1.0 1.444 + WATER -.6 1.445 + 1.446 + [*,SSP_155] BAGS -22. 1.447 + ELECTRIC -14. 1.448 + PHOS_ROCK -.62 1.449 + SSP_155 1.0 1.450 + SULF_ACID -.41 1.451 + WATER -6. 1.452 + 1.453 + [*,SULF_A_P] ELECTRIC -75. 1.454 + PYRITES -.826 1.455 + SULF_ACID 1.0 1.456 + WATER -60. 1.457 + 1.458 + [*,SULF_A_S] ELECTRIC -50. 1.459 + EL_SULFUR -.334 1.460 + SULF_ACID 1.0 1.461 + WATER -20. ; 1.462 + 1.463 +param util default 0 := 1.464 + 1.465 + [*,*] SULF_A_S SULF_A_S 1 SULF_A_P SULF_A_P 1 1.466 + NITR_ACID NITR_ACID 1 AMM_ELEC AMM_ELEC 1 1.467 + AMM_C_GAS AMM_C_GAS 1 SSP SSP_155 1 1.468 + C_AMM_NITR CAN_310 1 C_AMM_NITR CAN_335 1 1.469 + AMM_SULF AMM_SULF 1 ; 1.470 + 1.471 +param p_imp default 0.0 := 1.472 + 1.473 + PYRITES 17.5 AMM_SULF 75. 1.474 + EL_SULFUR 55. DAP 175. 1.475 + UREA 150. SSP_155 80. 1.476 + CAN_260 75. C_250_55 100. 1.477 + CAN_310 90. C_300_100 130. 1.478 + CAN_335 100. ; 1.479 + 1.480 +param p_r default 0.0 := 1.481 + 1.482 + ELECTRIC .007 1.483 + BF_GAS .007 1.484 + WATER .031 1.485 + STEAM 1.25 1.486 + BAGS .28 ; 1.487 + 1.488 +param p_pr default 0.0 := 1.489 + 1.490 + [HELWAN,COKE_GAS] 16.0 1.491 + [ASWAN,EL_ASWAN] 1.0 1.492 + 1.493 + [*,LIMESTONE] ASWAN 1.2 1.494 + HELWAN 1.2 1.495 + 1.496 + [*,PHOS_ROCK] ABU_ZAABAL 4.0 1.497 + ASSIOUT 3.5 1.498 + KAFR_EL_ZT 5.0 ; 1.499 + 1.500 +param dcap default 0.0 := 1.501 + 1.502 + [ABU_ZAABAL,*] SSP 600 1.503 + SULF_A_P 227 1.504 + SULF_A_S 242 1.505 + 1.506 + [ASSIOUT,*] SSP 600 1.507 + SULF_A_S 250 1.508 + 1.509 + [ASWAN,*] AMM_ELEC 450 1.510 + C_AMM_NITR 1100 1.511 + NITR_ACID 800 1.512 + 1.513 + [HELWAN,*] AMM_C_GAS 172 1.514 + AMM_SULF 24 1.515 + C_AMM_NITR 364 1.516 + NITR_ACID 282 1.517 + 1.518 + [KAFR_EL_ZT,*] SSP 600 1.519 + SULF_A_P 50 1.520 + SULF_A_S 200 ; 1.521 + 1.522 +end;