1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/examples/prod.mod Mon Dec 06 13:09:21 2010 +0100
1.3 @@ -0,0 +1,331 @@
1.4 +# PROD, a multiperiod production model
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 +### PRODUCTION SETS AND PARAMETERS ###
1.11 +
1.12 +set prd 'products'; # Members of the product group
1.13 +
1.14 +param pt 'production time' {prd} > 0;
1.15 +
1.16 + # Crew-hours to produce 1000 units
1.17 +
1.18 +param pc 'production cost' {prd} > 0;
1.19 +
1.20 + # Nominal production cost per 1000, used
1.21 + # to compute inventory and shortage costs
1.22 +
1.23 +### TIME PERIOD SETS AND PARAMETERS ###
1.24 +
1.25 +param first > 0 integer;
1.26 + # Index of first production period to be modeled
1.27 +
1.28 +param last > first integer;
1.29 +
1.30 + # Index of last production period to be modeled
1.31 +
1.32 +set time 'planning horizon' := first..last;
1.33 +
1.34 +### EMPLOYMENT PARAMETERS ###
1.35 +
1.36 +param cs 'crew size' > 0 integer;
1.37 +
1.38 + # Workers per crew
1.39 +
1.40 +param sl 'shift length' > 0;
1.41 +
1.42 + # Regular-time hours per shift
1.43 +
1.44 +param rtr 'regular time rate' > 0;
1.45 +
1.46 + # Wage per hour for regular-time labor
1.47 +
1.48 +param otr 'overtime rate' > rtr;
1.49 +
1.50 + # Wage per hour for overtime labor
1.51 +
1.52 +param iw 'initial workforce' >= 0 integer;
1.53 +
1.54 + # Crews employed at start of first period
1.55 +
1.56 +param dpp 'days per period' {time} > 0;
1.57 +
1.58 + # Regular working days in a production period
1.59 +
1.60 +param ol 'overtime limit' {time} >= 0;
1.61 +
1.62 + # Maximum crew-hours of overtime in a period
1.63 +
1.64 +param cmin 'crew minimum' {time} >= 0;
1.65 +
1.66 + # Lower limit on average employment in a period
1.67 +
1.68 +param cmax 'crew maximum' {t in time} >= cmin[t];
1.69 +
1.70 + # Upper limit on average employment in a period
1.71 +
1.72 +param hc 'hiring cost' {time} >= 0;
1.73 +
1.74 + # Penalty cost of hiring a crew
1.75 +
1.76 +param lc 'layoff cost' {time} >= 0;
1.77 +
1.78 + # Penalty cost of laying off a crew
1.79 +
1.80 +### DEMAND PARAMETERS ###
1.81 +
1.82 +param dem 'demand' {prd,first..last+1} >= 0;
1.83 +
1.84 + # Requirements (in 1000s)
1.85 + # to be met from current production and inventory
1.86 +
1.87 +param pro 'promoted' {prd,first..last+1} logical;
1.88 +
1.89 + # true if product will be the subject
1.90 + # of a special promotion in the period
1.91 +
1.92 +### INVENTORY AND SHORTAGE PARAMETERS ###
1.93 +
1.94 +param rir 'regular inventory ratio' >= 0;
1.95 +
1.96 + # Proportion of non-promoted demand
1.97 + # that must be in inventory the previous period
1.98 +
1.99 +param pir 'promotional inventory ratio' >= 0;
1.100 +
1.101 + # Proportion of promoted demand
1.102 + # that must be in inventory the previous period
1.103 +
1.104 +param life 'inventory lifetime' > 0 integer;
1.105 +
1.106 + # Upper limit on number of periods that
1.107 + # any product may sit in inventory
1.108 +
1.109 +param cri 'inventory cost ratio' {prd} > 0;
1.110 +
1.111 + # Inventory cost per 1000 units is
1.112 + # cri times nominal production cost
1.113 +
1.114 +param crs 'shortage cost ratio' {prd} > 0;
1.115 +
1.116 + # Shortage cost per 1000 units is
1.117 + # crs times nominal production cost
1.118 +
1.119 +param iinv 'initial inventory' {prd} >= 0;
1.120 +
1.121 + # Inventory at start of first period; age unknown
1.122 +
1.123 +param iil 'initial inventory left' {p in prd, t in time}
1.124 + := iinv[p] less sum {v in first..t} dem[p,v];
1.125 +
1.126 + # Initial inventory still available for allocation
1.127 + # at end of period t
1.128 +
1.129 +param minv 'minimum inventory' {p in prd, t in time}
1.130 + := dem[p,t+1] * (if pro[p,t+1] then pir else rir);
1.131 +
1.132 + # Lower limit on inventory at end of period t
1.133 +
1.134 +### VARIABLES ###
1.135 +
1.136 +var Crews{first-1..last} >= 0;
1.137 +
1.138 + # Average number of crews employed in each period
1.139 +
1.140 +var Hire{time} >= 0; # Crews hired from previous to current period
1.141 +
1.142 +var Layoff{time} >= 0; # Crews laid off from previous to current period
1.143 +
1.144 +var Rprd 'regular production' {prd,time} >= 0;
1.145 +
1.146 + # Production using regular-time labor, in 1000s
1.147 +
1.148 +var Oprd 'overtime production' {prd,time} >= 0;
1.149 +
1.150 + # Production using overtime labor, in 1000s
1.151 +
1.152 +var Inv 'inventory' {prd,time,1..life} >= 0;
1.153 +
1.154 + # Inv[p,t,a] is the amount of product p that is
1.155 + # a periods old -- produced in period (t+1)-a --
1.156 + # and still in storage at the end of period t
1.157 +
1.158 +var Short 'shortage' {prd,time} >= 0;
1.159 +
1.160 + # Accumulated unsatisfied demand at the end of period t
1.161 +
1.162 +### OBJECTIVE ###
1.163 +
1.164 +minimize cost:
1.165 +
1.166 + sum {t in time} rtr * sl * dpp[t] * cs * Crews[t] +
1.167 + sum {t in time} hc[t] * Hire[t] +
1.168 + sum {t in time} lc[t] * Layoff[t] +
1.169 + sum {t in time, p in prd} otr * cs * pt[p] * Oprd[p,t] +
1.170 + sum {t in time, p in prd, a in 1..life} cri[p] * pc[p] * Inv[p,t,a] +
1.171 + sum {t in time, p in prd} crs[p] * pc[p] * Short[p,t];
1.172 +
1.173 + # Full regular wages for all crews employed, plus
1.174 + # penalties for hiring and layoffs, plus
1.175 + # wages for any overtime worked, plus
1.176 + # inventory and shortage costs
1.177 +
1.178 + # (All other production costs are assumed
1.179 + # to depend on initial inventory and on demands,
1.180 + # and so are not included explicitly.)
1.181 +
1.182 +### CONSTRAINTS ###
1.183 +
1.184 +rlim 'regular-time limit' {t in time}:
1.185 +
1.186 + sum {p in prd} pt[p] * Rprd[p,t] <= sl * dpp[t] * Crews[t];
1.187 +
1.188 + # Hours needed to accomplish all regular-time
1.189 + # production in a period must not exceed
1.190 + # hours available on all shifts
1.191 +
1.192 +olim 'overtime limit' {t in time}:
1.193 +
1.194 + sum {p in prd} pt[p] * Oprd[p,t] <= ol[t];
1.195 +
1.196 + # Hours needed to accomplish all overtime
1.197 + # production in a period must not exceed
1.198 + # the specified overtime limit
1.199 +
1.200 +empl0 'initial crew level': Crews[first-1] = iw;
1.201 +
1.202 + # Use given initial workforce
1.203 +
1.204 +empl 'crew levels' {t in time}: Crews[t] = Crews[t-1] + Hire[t] - Layoff[t];
1.205 +
1.206 + # Workforce changes by hiring or layoffs
1.207 +
1.208 +emplbnd 'crew limits' {t in time}: cmin[t] <= Crews[t] <= cmax[t];
1.209 +
1.210 + # Workforce must remain within specified bounds
1.211 +
1.212 +dreq1 'first demand requirement' {p in prd}:
1.213 +
1.214 + Rprd[p,first] + Oprd[p,first] + Short[p,first]
1.215 + - Inv[p,first,1] = dem[p,first] less iinv[p];
1.216 +
1.217 +dreq 'demand requirements' {p in prd, t in first+1..last}:
1.218 +
1.219 + Rprd[p,t] + Oprd[p,t] + Short[p,t] - Short[p,t-1]
1.220 + + sum {a in 1..life} (Inv[p,t-1,a] - Inv[p,t,a])
1.221 + = dem[p,t] less iil[p,t-1];
1.222 +
1.223 + # Production plus increase in shortage plus
1.224 + # decrease in inventory must equal demand
1.225 +
1.226 +ireq 'inventory requirements' {p in prd, t in time}:
1.227 +
1.228 + sum {a in 1..life} Inv[p,t,a] + iil[p,t] >= minv[p,t];
1.229 +
1.230 + # Inventory in storage at end of period t
1.231 + # must meet specified minimum
1.232 +
1.233 +izero 'impossible inventories' {p in prd, v in 1..life-1, a in v+1..life}:
1.234 +
1.235 + Inv[p,first+v-1,a] = 0;
1.236 +
1.237 + # In the vth period (starting from first)
1.238 + # no inventory may be more than v periods old
1.239 + # (initial inventories are handled separately)
1.240 +
1.241 +ilim1 'new-inventory limits' {p in prd, t in time}:
1.242 +
1.243 + Inv[p,t,1] <= Rprd[p,t] + Oprd[p,t];
1.244 +
1.245 + # New inventory cannot exceed
1.246 + # production in the most recent period
1.247 +
1.248 +ilim 'inventory limits' {p in prd, t in first+1..last, a in 2..life}:
1.249 +
1.250 + Inv[p,t,a] <= Inv[p,t-1,a-1];
1.251 +
1.252 + # Inventory left from period (t+1)-p
1.253 + # can only decrease as time goes on
1.254 +
1.255 +### DATA ###
1.256 +
1.257 +data;
1.258 +
1.259 +set prd := 18REG 24REG 24PRO ;
1.260 +
1.261 +param first := 1 ;
1.262 +param last := 13 ;
1.263 +param life := 2 ;
1.264 +
1.265 +param cs := 18 ;
1.266 +param sl := 8 ;
1.267 +param iw := 8 ;
1.268 +
1.269 +param rtr := 16.00 ;
1.270 +param otr := 43.85 ;
1.271 +param rir := 0.75 ;
1.272 +param pir := 0.80 ;
1.273 +
1.274 +param : pt pc cri crs iinv :=
1.275 +
1.276 + 18REG 1.194 2304. 0.015 1.100 82.0
1.277 + 24REG 1.509 2920. 0.015 1.100 792.2
1.278 + 24PRO 1.509 2910. 0.015 1.100 0.0 ;
1.279 +
1.280 +param : dpp ol cmin cmax hc lc :=
1.281 +
1.282 + 1 19.5 96.0 0.0 8.0 7500 7500
1.283 + 2 19.0 96.0 0.0 8.0 7500 7500
1.284 + 3 20.0 96.0 0.0 8.0 7500 7500
1.285 + 4 19.0 96.0 0.0 8.0 7500 7500
1.286 + 5 19.5 96.0 0.0 8.0 15000 15000
1.287 + 6 19.0 96.0 0.0 8.0 15000 15000
1.288 + 7 19.0 96.0 0.0 8.0 15000 15000
1.289 + 8 20.0 96.0 0.0 8.0 15000 15000
1.290 + 9 19.0 96.0 0.0 8.0 15000 15000
1.291 + 10 20.0 96.0 0.0 8.0 15000 15000
1.292 + 11 20.0 96.0 0.0 8.0 7500 7500
1.293 + 12 18.0 96.0 0.0 8.0 7500 7500
1.294 + 13 18.0 96.0 0.0 8.0 7500 7500 ;
1.295 +
1.296 +param dem (tr) :
1.297 +
1.298 + 18REG 24REG 24PRO :=
1.299 +
1.300 + 1 63.8 1212.0 0.0
1.301 + 2 76.0 306.2 0.0
1.302 + 3 88.4 319.0 0.0
1.303 + 4 913.8 208.4 0.0
1.304 + 5 115.0 298.0 0.0
1.305 + 6 133.8 328.2 0.0
1.306 + 7 79.6 959.6 0.0
1.307 + 8 111.0 257.6 0.0
1.308 + 9 121.6 335.6 0.0
1.309 + 10 470.0 118.0 1102.0
1.310 + 11 78.4 284.8 0.0
1.311 + 12 99.4 970.0 0.0
1.312 + 13 140.4 343.8 0.0
1.313 + 14 63.8 1212.0 0.0 ;
1.314 +
1.315 +param pro (tr) :
1.316 +
1.317 + 18REG 24REG 24PRO :=
1.318 +
1.319 + 1 0 1 0
1.320 + 2 0 0 0
1.321 + 3 0 0 0
1.322 + 4 1 0 0
1.323 + 5 0 0 0
1.324 + 6 0 0 0
1.325 + 7 0 1 0
1.326 + 8 0 0 0
1.327 + 9 0 0 0
1.328 + 10 1 0 1
1.329 + 11 0 0 0
1.330 + 12 0 0 0
1.331 + 13 0 1 0
1.332 + 14 0 1 0 ;
1.333 +
1.334 +end;