lemon-project-template-glpk

annotate deps/glpk/examples/prod.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
parents
children
rev   line source
alpar@9 1 # PROD, a multiperiod production model
alpar@9 2 #
alpar@9 3 # References:
alpar@9 4 # Robert Fourer, David M. Gay and Brian W. Kernighan, "A Modeling Language
alpar@9 5 # for Mathematical Programming." Management Science 36 (1990) 519-554.
alpar@9 6
alpar@9 7 ### PRODUCTION SETS AND PARAMETERS ###
alpar@9 8
alpar@9 9 set prd 'products'; # Members of the product group
alpar@9 10
alpar@9 11 param pt 'production time' {prd} > 0;
alpar@9 12
alpar@9 13 # Crew-hours to produce 1000 units
alpar@9 14
alpar@9 15 param pc 'production cost' {prd} > 0;
alpar@9 16
alpar@9 17 # Nominal production cost per 1000, used
alpar@9 18 # to compute inventory and shortage costs
alpar@9 19
alpar@9 20 ### TIME PERIOD SETS AND PARAMETERS ###
alpar@9 21
alpar@9 22 param first > 0 integer;
alpar@9 23 # Index of first production period to be modeled
alpar@9 24
alpar@9 25 param last > first integer;
alpar@9 26
alpar@9 27 # Index of last production period to be modeled
alpar@9 28
alpar@9 29 set time 'planning horizon' := first..last;
alpar@9 30
alpar@9 31 ### EMPLOYMENT PARAMETERS ###
alpar@9 32
alpar@9 33 param cs 'crew size' > 0 integer;
alpar@9 34
alpar@9 35 # Workers per crew
alpar@9 36
alpar@9 37 param sl 'shift length' > 0;
alpar@9 38
alpar@9 39 # Regular-time hours per shift
alpar@9 40
alpar@9 41 param rtr 'regular time rate' > 0;
alpar@9 42
alpar@9 43 # Wage per hour for regular-time labor
alpar@9 44
alpar@9 45 param otr 'overtime rate' > rtr;
alpar@9 46
alpar@9 47 # Wage per hour for overtime labor
alpar@9 48
alpar@9 49 param iw 'initial workforce' >= 0 integer;
alpar@9 50
alpar@9 51 # Crews employed at start of first period
alpar@9 52
alpar@9 53 param dpp 'days per period' {time} > 0;
alpar@9 54
alpar@9 55 # Regular working days in a production period
alpar@9 56
alpar@9 57 param ol 'overtime limit' {time} >= 0;
alpar@9 58
alpar@9 59 # Maximum crew-hours of overtime in a period
alpar@9 60
alpar@9 61 param cmin 'crew minimum' {time} >= 0;
alpar@9 62
alpar@9 63 # Lower limit on average employment in a period
alpar@9 64
alpar@9 65 param cmax 'crew maximum' {t in time} >= cmin[t];
alpar@9 66
alpar@9 67 # Upper limit on average employment in a period
alpar@9 68
alpar@9 69 param hc 'hiring cost' {time} >= 0;
alpar@9 70
alpar@9 71 # Penalty cost of hiring a crew
alpar@9 72
alpar@9 73 param lc 'layoff cost' {time} >= 0;
alpar@9 74
alpar@9 75 # Penalty cost of laying off a crew
alpar@9 76
alpar@9 77 ### DEMAND PARAMETERS ###
alpar@9 78
alpar@9 79 param dem 'demand' {prd,first..last+1} >= 0;
alpar@9 80
alpar@9 81 # Requirements (in 1000s)
alpar@9 82 # to be met from current production and inventory
alpar@9 83
alpar@9 84 param pro 'promoted' {prd,first..last+1} logical;
alpar@9 85
alpar@9 86 # true if product will be the subject
alpar@9 87 # of a special promotion in the period
alpar@9 88
alpar@9 89 ### INVENTORY AND SHORTAGE PARAMETERS ###
alpar@9 90
alpar@9 91 param rir 'regular inventory ratio' >= 0;
alpar@9 92
alpar@9 93 # Proportion of non-promoted demand
alpar@9 94 # that must be in inventory the previous period
alpar@9 95
alpar@9 96 param pir 'promotional inventory ratio' >= 0;
alpar@9 97
alpar@9 98 # Proportion of promoted demand
alpar@9 99 # that must be in inventory the previous period
alpar@9 100
alpar@9 101 param life 'inventory lifetime' > 0 integer;
alpar@9 102
alpar@9 103 # Upper limit on number of periods that
alpar@9 104 # any product may sit in inventory
alpar@9 105
alpar@9 106 param cri 'inventory cost ratio' {prd} > 0;
alpar@9 107
alpar@9 108 # Inventory cost per 1000 units is
alpar@9 109 # cri times nominal production cost
alpar@9 110
alpar@9 111 param crs 'shortage cost ratio' {prd} > 0;
alpar@9 112
alpar@9 113 # Shortage cost per 1000 units is
alpar@9 114 # crs times nominal production cost
alpar@9 115
alpar@9 116 param iinv 'initial inventory' {prd} >= 0;
alpar@9 117
alpar@9 118 # Inventory at start of first period; age unknown
alpar@9 119
alpar@9 120 param iil 'initial inventory left' {p in prd, t in time}
alpar@9 121 := iinv[p] less sum {v in first..t} dem[p,v];
alpar@9 122
alpar@9 123 # Initial inventory still available for allocation
alpar@9 124 # at end of period t
alpar@9 125
alpar@9 126 param minv 'minimum inventory' {p in prd, t in time}
alpar@9 127 := dem[p,t+1] * (if pro[p,t+1] then pir else rir);
alpar@9 128
alpar@9 129 # Lower limit on inventory at end of period t
alpar@9 130
alpar@9 131 ### VARIABLES ###
alpar@9 132
alpar@9 133 var Crews{first-1..last} >= 0;
alpar@9 134
alpar@9 135 # Average number of crews employed in each period
alpar@9 136
alpar@9 137 var Hire{time} >= 0; # Crews hired from previous to current period
alpar@9 138
alpar@9 139 var Layoff{time} >= 0; # Crews laid off from previous to current period
alpar@9 140
alpar@9 141 var Rprd 'regular production' {prd,time} >= 0;
alpar@9 142
alpar@9 143 # Production using regular-time labor, in 1000s
alpar@9 144
alpar@9 145 var Oprd 'overtime production' {prd,time} >= 0;
alpar@9 146
alpar@9 147 # Production using overtime labor, in 1000s
alpar@9 148
alpar@9 149 var Inv 'inventory' {prd,time,1..life} >= 0;
alpar@9 150
alpar@9 151 # Inv[p,t,a] is the amount of product p that is
alpar@9 152 # a periods old -- produced in period (t+1)-a --
alpar@9 153 # and still in storage at the end of period t
alpar@9 154
alpar@9 155 var Short 'shortage' {prd,time} >= 0;
alpar@9 156
alpar@9 157 # Accumulated unsatisfied demand at the end of period t
alpar@9 158
alpar@9 159 ### OBJECTIVE ###
alpar@9 160
alpar@9 161 minimize cost:
alpar@9 162
alpar@9 163 sum {t in time} rtr * sl * dpp[t] * cs * Crews[t] +
alpar@9 164 sum {t in time} hc[t] * Hire[t] +
alpar@9 165 sum {t in time} lc[t] * Layoff[t] +
alpar@9 166 sum {t in time, p in prd} otr * cs * pt[p] * Oprd[p,t] +
alpar@9 167 sum {t in time, p in prd, a in 1..life} cri[p] * pc[p] * Inv[p,t,a] +
alpar@9 168 sum {t in time, p in prd} crs[p] * pc[p] * Short[p,t];
alpar@9 169
alpar@9 170 # Full regular wages for all crews employed, plus
alpar@9 171 # penalties for hiring and layoffs, plus
alpar@9 172 # wages for any overtime worked, plus
alpar@9 173 # inventory and shortage costs
alpar@9 174
alpar@9 175 # (All other production costs are assumed
alpar@9 176 # to depend on initial inventory and on demands,
alpar@9 177 # and so are not included explicitly.)
alpar@9 178
alpar@9 179 ### CONSTRAINTS ###
alpar@9 180
alpar@9 181 rlim 'regular-time limit' {t in time}:
alpar@9 182
alpar@9 183 sum {p in prd} pt[p] * Rprd[p,t] <= sl * dpp[t] * Crews[t];
alpar@9 184
alpar@9 185 # Hours needed to accomplish all regular-time
alpar@9 186 # production in a period must not exceed
alpar@9 187 # hours available on all shifts
alpar@9 188
alpar@9 189 olim 'overtime limit' {t in time}:
alpar@9 190
alpar@9 191 sum {p in prd} pt[p] * Oprd[p,t] <= ol[t];
alpar@9 192
alpar@9 193 # Hours needed to accomplish all overtime
alpar@9 194 # production in a period must not exceed
alpar@9 195 # the specified overtime limit
alpar@9 196
alpar@9 197 empl0 'initial crew level': Crews[first-1] = iw;
alpar@9 198
alpar@9 199 # Use given initial workforce
alpar@9 200
alpar@9 201 empl 'crew levels' {t in time}: Crews[t] = Crews[t-1] + Hire[t] - Layoff[t];
alpar@9 202
alpar@9 203 # Workforce changes by hiring or layoffs
alpar@9 204
alpar@9 205 emplbnd 'crew limits' {t in time}: cmin[t] <= Crews[t] <= cmax[t];
alpar@9 206
alpar@9 207 # Workforce must remain within specified bounds
alpar@9 208
alpar@9 209 dreq1 'first demand requirement' {p in prd}:
alpar@9 210
alpar@9 211 Rprd[p,first] + Oprd[p,first] + Short[p,first]
alpar@9 212 - Inv[p,first,1] = dem[p,first] less iinv[p];
alpar@9 213
alpar@9 214 dreq 'demand requirements' {p in prd, t in first+1..last}:
alpar@9 215
alpar@9 216 Rprd[p,t] + Oprd[p,t] + Short[p,t] - Short[p,t-1]
alpar@9 217 + sum {a in 1..life} (Inv[p,t-1,a] - Inv[p,t,a])
alpar@9 218 = dem[p,t] less iil[p,t-1];
alpar@9 219
alpar@9 220 # Production plus increase in shortage plus
alpar@9 221 # decrease in inventory must equal demand
alpar@9 222
alpar@9 223 ireq 'inventory requirements' {p in prd, t in time}:
alpar@9 224
alpar@9 225 sum {a in 1..life} Inv[p,t,a] + iil[p,t] >= minv[p,t];
alpar@9 226
alpar@9 227 # Inventory in storage at end of period t
alpar@9 228 # must meet specified minimum
alpar@9 229
alpar@9 230 izero 'impossible inventories' {p in prd, v in 1..life-1, a in v+1..life}:
alpar@9 231
alpar@9 232 Inv[p,first+v-1,a] = 0;
alpar@9 233
alpar@9 234 # In the vth period (starting from first)
alpar@9 235 # no inventory may be more than v periods old
alpar@9 236 # (initial inventories are handled separately)
alpar@9 237
alpar@9 238 ilim1 'new-inventory limits' {p in prd, t in time}:
alpar@9 239
alpar@9 240 Inv[p,t,1] <= Rprd[p,t] + Oprd[p,t];
alpar@9 241
alpar@9 242 # New inventory cannot exceed
alpar@9 243 # production in the most recent period
alpar@9 244
alpar@9 245 ilim 'inventory limits' {p in prd, t in first+1..last, a in 2..life}:
alpar@9 246
alpar@9 247 Inv[p,t,a] <= Inv[p,t-1,a-1];
alpar@9 248
alpar@9 249 # Inventory left from period (t+1)-p
alpar@9 250 # can only decrease as time goes on
alpar@9 251
alpar@9 252 ### DATA ###
alpar@9 253
alpar@9 254 data;
alpar@9 255
alpar@9 256 set prd := 18REG 24REG 24PRO ;
alpar@9 257
alpar@9 258 param first := 1 ;
alpar@9 259 param last := 13 ;
alpar@9 260 param life := 2 ;
alpar@9 261
alpar@9 262 param cs := 18 ;
alpar@9 263 param sl := 8 ;
alpar@9 264 param iw := 8 ;
alpar@9 265
alpar@9 266 param rtr := 16.00 ;
alpar@9 267 param otr := 43.85 ;
alpar@9 268 param rir := 0.75 ;
alpar@9 269 param pir := 0.80 ;
alpar@9 270
alpar@9 271 param : pt pc cri crs iinv :=
alpar@9 272
alpar@9 273 18REG 1.194 2304. 0.015 1.100 82.0
alpar@9 274 24REG 1.509 2920. 0.015 1.100 792.2
alpar@9 275 24PRO 1.509 2910. 0.015 1.100 0.0 ;
alpar@9 276
alpar@9 277 param : dpp ol cmin cmax hc lc :=
alpar@9 278
alpar@9 279 1 19.5 96.0 0.0 8.0 7500 7500
alpar@9 280 2 19.0 96.0 0.0 8.0 7500 7500
alpar@9 281 3 20.0 96.0 0.0 8.0 7500 7500
alpar@9 282 4 19.0 96.0 0.0 8.0 7500 7500
alpar@9 283 5 19.5 96.0 0.0 8.0 15000 15000
alpar@9 284 6 19.0 96.0 0.0 8.0 15000 15000
alpar@9 285 7 19.0 96.0 0.0 8.0 15000 15000
alpar@9 286 8 20.0 96.0 0.0 8.0 15000 15000
alpar@9 287 9 19.0 96.0 0.0 8.0 15000 15000
alpar@9 288 10 20.0 96.0 0.0 8.0 15000 15000
alpar@9 289 11 20.0 96.0 0.0 8.0 7500 7500
alpar@9 290 12 18.0 96.0 0.0 8.0 7500 7500
alpar@9 291 13 18.0 96.0 0.0 8.0 7500 7500 ;
alpar@9 292
alpar@9 293 param dem (tr) :
alpar@9 294
alpar@9 295 18REG 24REG 24PRO :=
alpar@9 296
alpar@9 297 1 63.8 1212.0 0.0
alpar@9 298 2 76.0 306.2 0.0
alpar@9 299 3 88.4 319.0 0.0
alpar@9 300 4 913.8 208.4 0.0
alpar@9 301 5 115.0 298.0 0.0
alpar@9 302 6 133.8 328.2 0.0
alpar@9 303 7 79.6 959.6 0.0
alpar@9 304 8 111.0 257.6 0.0
alpar@9 305 9 121.6 335.6 0.0
alpar@9 306 10 470.0 118.0 1102.0
alpar@9 307 11 78.4 284.8 0.0
alpar@9 308 12 99.4 970.0 0.0
alpar@9 309 13 140.4 343.8 0.0
alpar@9 310 14 63.8 1212.0 0.0 ;
alpar@9 311
alpar@9 312 param pro (tr) :
alpar@9 313
alpar@9 314 18REG 24REG 24PRO :=
alpar@9 315
alpar@9 316 1 0 1 0
alpar@9 317 2 0 0 0
alpar@9 318 3 0 0 0
alpar@9 319 4 1 0 0
alpar@9 320 5 0 0 0
alpar@9 321 6 0 0 0
alpar@9 322 7 0 1 0
alpar@9 323 8 0 0 0
alpar@9 324 9 0 0 0
alpar@9 325 10 1 0 1
alpar@9 326 11 0 0 0
alpar@9 327 12 0 0 0
alpar@9 328 13 0 1 0
alpar@9 329 14 0 1 0 ;
alpar@9 330
alpar@9 331 end;