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diff --git a/test/monniaux/glpk-4.65/examples/prod.mod b/test/monniaux/glpk-4.65/examples/prod.mod new file mode 100644 index 00000000..aa793f76 --- /dev/null +++ b/test/monniaux/glpk-4.65/examples/prod.mod @@ -0,0 +1,331 @@ +# PROD, a multiperiod production model +# +# References: +# Robert Fourer, David M. Gay and Brian W. Kernighan, "A Modeling Language +# for Mathematical Programming." Management Science 36 (1990) 519-554. + +### PRODUCTION SETS AND PARAMETERS ### + +set prd 'products'; # Members of the product group + +param pt 'production time' {prd} > 0; + + # Crew-hours to produce 1000 units + +param pc 'production cost' {prd} > 0; + + # Nominal production cost per 1000, used + # to compute inventory and shortage costs + +### TIME PERIOD SETS AND PARAMETERS ### + +param first > 0 integer; + # Index of first production period to be modeled + +param last > first integer; + + # Index of last production period to be modeled + +set time 'planning horizon' := first..last; + +### EMPLOYMENT PARAMETERS ### + +param cs 'crew size' > 0 integer; + + # Workers per crew + +param sl 'shift length' > 0; + + # Regular-time hours per shift + +param rtr 'regular time rate' > 0; + + # Wage per hour for regular-time labor + +param otr 'overtime rate' > rtr; + + # Wage per hour for overtime labor + +param iw 'initial workforce' >= 0 integer; + + # Crews employed at start of first period + +param dpp 'days per period' {time} > 0; + + # Regular working days in a production period + +param ol 'overtime limit' {time} >= 0; + + # Maximum crew-hours of overtime in a period + +param cmin 'crew minimum' {time} >= 0; + + # Lower limit on average employment in a period + +param cmax 'crew maximum' {t in time} >= cmin[t]; + + # Upper limit on average employment in a period + +param hc 'hiring cost' {time} >= 0; + + # Penalty cost of hiring a crew + +param lc 'layoff cost' {time} >= 0; + + # Penalty cost of laying off a crew + +### DEMAND PARAMETERS ### + +param dem 'demand' {prd,first..last+1} >= 0; + + # Requirements (in 1000s) + # to be met from current production and inventory + +param pro 'promoted' {prd,first..last+1} logical; + + # true if product will be the subject + # of a special promotion in the period + +### INVENTORY AND SHORTAGE PARAMETERS ### + +param rir 'regular inventory ratio' >= 0; + + # Proportion of non-promoted demand + # that must be in inventory the previous period + +param pir 'promotional inventory ratio' >= 0; + + # Proportion of promoted demand + # that must be in inventory the previous period + +param life 'inventory lifetime' > 0 integer; + + # Upper limit on number of periods that + # any product may sit in inventory + +param cri 'inventory cost ratio' {prd} > 0; + + # Inventory cost per 1000 units is + # cri times nominal production cost + +param crs 'shortage cost ratio' {prd} > 0; + + # Shortage cost per 1000 units is + # crs times nominal production cost + +param iinv 'initial inventory' {prd} >= 0; + + # Inventory at start of first period; age unknown + +param iil 'initial inventory left' {p in prd, t in time} + := iinv[p] less sum {v in first..t} dem[p,v]; + + # Initial inventory still available for allocation + # at end of period t + +param minv 'minimum inventory' {p in prd, t in time} + := dem[p,t+1] * (if pro[p,t+1] then pir else rir); + + # Lower limit on inventory at end of period t + +### VARIABLES ### + +var Crews{first-1..last} >= 0; + + # Average number of crews employed in each period + +var Hire{time} >= 0; # Crews hired from previous to current period + +var Layoff{time} >= 0; # Crews laid off from previous to current period + +var Rprd 'regular production' {prd,time} >= 0; + + # Production using regular-time labor, in 1000s + +var Oprd 'overtime production' {prd,time} >= 0; + + # Production using overtime labor, in 1000s + +var Inv 'inventory' {prd,time,1..life} >= 0; + + # Inv[p,t,a] is the amount of product p that is + # a periods old -- produced in period (t+1)-a -- + # and still in storage at the end of period t + +var Short 'shortage' {prd,time} >= 0; + + # Accumulated unsatisfied demand at the end of period t + +### OBJECTIVE ### + +minimize cost: + + sum {t in time} rtr * sl * dpp[t] * cs * Crews[t] + + sum {t in time} hc[t] * Hire[t] + + sum {t in time} lc[t] * Layoff[t] + + sum {t in time, p in prd} otr * cs * pt[p] * Oprd[p,t] + + sum {t in time, p in prd, a in 1..life} cri[p] * pc[p] * Inv[p,t,a] + + sum {t in time, p in prd} crs[p] * pc[p] * Short[p,t]; + + # Full regular wages for all crews employed, plus + # penalties for hiring and layoffs, plus + # wages for any overtime worked, plus + # inventory and shortage costs + + # (All other production costs are assumed + # to depend on initial inventory and on demands, + # and so are not included explicitly.) + +### CONSTRAINTS ### + +rlim 'regular-time limit' {t in time}: + + sum {p in prd} pt[p] * Rprd[p,t] <= sl * dpp[t] * Crews[t]; + + # Hours needed to accomplish all regular-time + # production in a period must not exceed + # hours available on all shifts + +olim 'overtime limit' {t in time}: + + sum {p in prd} pt[p] * Oprd[p,t] <= ol[t]; + + # Hours needed to accomplish all overtime + # production in a period must not exceed + # the specified overtime limit + +empl0 'initial crew level': Crews[first-1] = iw; + + # Use given initial workforce + +empl 'crew levels' {t in time}: Crews[t] = Crews[t-1] + Hire[t] - Layoff[t]; + + # Workforce changes by hiring or layoffs + +emplbnd 'crew limits' {t in time}: cmin[t] <= Crews[t] <= cmax[t]; + + # Workforce must remain within specified bounds + +dreq1 'first demand requirement' {p in prd}: + + Rprd[p,first] + Oprd[p,first] + Short[p,first] + - Inv[p,first,1] = dem[p,first] less iinv[p]; + +dreq 'demand requirements' {p in prd, t in first+1..last}: + + Rprd[p,t] + Oprd[p,t] + Short[p,t] - Short[p,t-1] + + sum {a in 1..life} (Inv[p,t-1,a] - Inv[p,t,a]) + = dem[p,t] less iil[p,t-1]; + + # Production plus increase in shortage plus + # decrease in inventory must equal demand + +ireq 'inventory requirements' {p in prd, t in time}: + + sum {a in 1..life} Inv[p,t,a] + iil[p,t] >= minv[p,t]; + + # Inventory in storage at end of period t + # must meet specified minimum + +izero 'impossible inventories' {p in prd, v in 1..life-1, a in v+1..life}: + + Inv[p,first+v-1,a] = 0; + + # In the vth period (starting from first) + # no inventory may be more than v periods old + # (initial inventories are handled separately) + +ilim1 'new-inventory limits' {p in prd, t in time}: + + Inv[p,t,1] <= Rprd[p,t] + Oprd[p,t]; + + # New inventory cannot exceed + # production in the most recent period + +ilim 'inventory limits' {p in prd, t in first+1..last, a in 2..life}: + + Inv[p,t,a] <= Inv[p,t-1,a-1]; + + # Inventory left from period (t+1)-p + # can only decrease as time goes on + +### DATA ### + +data; + +set prd := 18REG 24REG 24PRO ; + +param first := 1 ; +param last := 13 ; +param life := 2 ; + +param cs := 18 ; +param sl := 8 ; +param iw := 8 ; + +param rtr := 16.00 ; +param otr := 43.85 ; +param rir := 0.75 ; +param pir := 0.80 ; + +param : pt pc cri crs iinv := + + 18REG 1.194 2304. 0.015 1.100 82.0 + 24REG 1.509 2920. 0.015 1.100 792.2 + 24PRO 1.509 2910. 0.015 1.100 0.0 ; + +param : dpp ol cmin cmax hc lc := + + 1 19.5 96.0 0.0 8.0 7500 7500 + 2 19.0 96.0 0.0 8.0 7500 7500 + 3 20.0 96.0 0.0 8.0 7500 7500 + 4 19.0 96.0 0.0 8.0 7500 7500 + 5 19.5 96.0 0.0 8.0 15000 15000 + 6 19.0 96.0 0.0 8.0 15000 15000 + 7 19.0 96.0 0.0 8.0 15000 15000 + 8 20.0 96.0 0.0 8.0 15000 15000 + 9 19.0 96.0 0.0 8.0 15000 15000 + 10 20.0 96.0 0.0 8.0 15000 15000 + 11 20.0 96.0 0.0 8.0 7500 7500 + 12 18.0 96.0 0.0 8.0 7500 7500 + 13 18.0 96.0 0.0 8.0 7500 7500 ; + +param dem (tr) : + + 18REG 24REG 24PRO := + + 1 63.8 1212.0 0.0 + 2 76.0 306.2 0.0 + 3 88.4 319.0 0.0 + 4 913.8 208.4 0.0 + 5 115.0 298.0 0.0 + 6 133.8 328.2 0.0 + 7 79.6 959.6 0.0 + 8 111.0 257.6 0.0 + 9 121.6 335.6 0.0 + 10 470.0 118.0 1102.0 + 11 78.4 284.8 0.0 + 12 99.4 970.0 0.0 + 13 140.4 343.8 0.0 + 14 63.8 1212.0 0.0 ; + +param pro (tr) : + + 18REG 24REG 24PRO := + + 1 0 1 0 + 2 0 0 0 + 3 0 0 0 + 4 1 0 0 + 5 0 0 0 + 6 0 0 0 + 7 0 1 0 + 8 0 0 0 + 9 0 0 0 + 10 1 0 1 + 11 0 0 0 + 12 0 0 0 + 13 0 1 0 + 14 0 1 0 ; + +end; |