Farm Planning (mpex08)
/***************************************************************/
/* */
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: mpex08 */
/* TITLE: Farm Planning (mpex08) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* PROCS: OPTMODEL */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: */
/* MISC: Example 08 from the Mathematical Programming */
/* Examples book. */
/* */
/***************************************************************/
data cow_data;
do age = 0 to 11;
init_num_cows = 10;
if age < 2 then do;
acres_needed = 2/3;
annual_loss = 0.05;
bullock_yield = 0;
heifer_yield = 0;
milk_revenue = 0;
grain_req = 0;
sugar_beet_req = 0;
labour_req = 10;
other_costs = 50;
end;
else do;
acres_needed = 1;
annual_loss = 0.02;
bullock_yield = 1.1/2;
heifer_yield = 1.1/2;
milk_revenue = 370;
grain_req = 0.6;
sugar_beet_req = 0.7;
labour_req = 42;
other_costs = 100;
end;
output;
end;
run;
data grain_data;
input group $ acres yield;
datalines;
group1 20 1.1
group2 30 0.9
group3 20 0.8
group4 10 0.65
;
%let num_years = 5;
%let num_acres = 200;
%let bullock_revenue = 30;
%let heifer_revenue = 40;
%let dairy_cow_selling_age = 12;
%let dairy_cow_selling_revenue = 120;
%let max_num_cows = 130;
%let sugar_beet_yield = 1.5;
%let grain_cost = 90;
%let grain_revenue = 75;
%let grain_labour_req = 4;
%let grain_other_costs = 15;
%let sugar_beet_cost = 70;
%let sugar_beet_revenue = 58;
%let sugar_beet_labour_req = 14;
%let sugar_beet_other_costs = 10;
%let nominal_labour_cost = 4000;
%let nominal_labour_hours = 5500;
%let excess_labour_cost = 1.2;
%let capital_outlay_unit = 200;
%let num_loan_years = 10;
%let annual_interest_rate = 0.15;
%let max_decrease_ratio = 0.50;
%let max_increase_ratio = 0.75;
proc optmodel;
set AGES;
num init_num_cows {AGES};
num acres_needed {AGES};
num annual_loss {AGES};
num bullock_yield {AGES};
num heifer_yield {AGES};
num milk_revenue {AGES};
num grain_req {AGES};
num sugar_beet_req {AGES};
num cow_labour_req {AGES};
num cow_other_costs {AGES};
read data cow_data into AGES=[age]
init_num_cows acres_needed annual_loss bullock_yield heifer_yield
milk_revenue grain_req sugar_beet_req cow_labour_req=labour_req
cow_other_costs=other_costs;
num num_years = &num_years;
set YEARS = 1..num_years;
set YEARS0 = {0} union YEARS;
var NumCows {AGES union {&dairy_cow_selling_age}, YEARS0} >= 0;
for {age in AGES} fix NumCows[age,0] = init_num_cows[age];
fix NumCows[&dairy_cow_selling_age,0] = 0;
var NumBullocksSold {YEARS} >= 0;
var NumHeifersSold {YEARS} >= 0;
set <str> GROUPS;
num acres {GROUPS};
num grain_yield {GROUPS};
var GrainAcres {GROUPS, YEARS} >= 0;
read data grain_data into GROUPS=[group]
{year in YEARS} <GrainAcres[group,year].ub=acres>
grain_yield=yield;
var GrainBought {YEARS} >= 0;
var GrainSold {YEARS} >= 0;
var SugarBeetAcres {YEARS} >= 0;
var SugarBeetBought {YEARS} >= 0;
var SugarBeetSold {YEARS} >= 0;
var NumExcessLabourHours {YEARS} >= 0;
var CapitalOutlay {YEARS} >= 0;
num yearly_loan_payment =
-finance('pmt', &annual_interest_rate, &num_loan_years,
&capital_outlay_unit);
print yearly_loan_payment;
impvar Revenue {year in YEARS} =
&bullock_revenue * NumBullocksSold[year]
+ &heifer_revenue * NumHeifersSold[year]
+ &dairy_cow_selling_revenue * NumCows[&dairy_cow_selling_age,year]
+ sum {age in AGES} milk_revenue[age] * NumCows[age,year]
+ &grain_revenue * GrainSold[year]
+ &sugar_beet_revenue * SugarBeetSold[year]
;
impvar Cost {year in YEARS} =
&grain_cost * GrainBought[year]
+ &sugar_beet_cost * SugarBeetBought[year]
+ &nominal_labour_cost
+ &excess_labour_cost * NumExcessLabourHours[year]
+ sum {age in AGES} cow_other_costs[age] * NumCows[age,year]
+ sum {group in GROUPS} &grain_other_costs * GrainAcres[group,year]
+ &sugar_beet_other_costs * SugarBeetAcres[year]
+ sum {y in YEARS: y <= year} yearly_loan_payment * CapitalOutlay[y]
;
impvar Profit {year in YEARS} = Revenue[year] - Cost[year];
max TotalProfit =
sum {year in YEARS} (Profit[year]
- yearly_loan_payment * (num_years - 1 + year) * CapitalOutlay[year]);
con Num_acres_con {year in YEARS}:
sum {age in AGES} acres_needed[age] * NumCows[age,year]
+ sum {group in GROUPS} GrainAcres[group,year]
+ SugarBeetAcres[year]
<= &num_acres;
con Aging {age in AGES diff {&dairy_cow_selling_age},
year in YEARS0 diff {num_years}}:
NumCows[age+1,year+1] = (1 - annual_loss[age]) * NumCows[age,year];
con NumBullocksSold_def {year in YEARS}:
NumBullocksSold[year]
= sum {age in AGES} bullock_yield[age] * NumCows[age,year];
con NumHeifersSold_def {year in YEARS}:
NumCows[0,year]
= sum {age in AGES} heifer_yield[age] * NumCows[age,year]
- NumHeifersSold[year];
con Max_num_cows_def {year in YEARS}:
sum {age in AGES} NumCows[age,year]
<= &max_num_cows + sum {y in YEARS: y <= year} CapitalOutlay[y];
impvar GrainGrown {group in GROUPS, year in YEARS} =
grain_yield[group] * GrainAcres[group,year];
con Grain_req_def {year in YEARS}:
sum {age in AGES} grain_req[age] * NumCows[age,year]
<= sum {group in GROUPS} GrainGrown[group,year]
+ GrainBought[year] - GrainSold[year];
impvar SugarBeetGrown {year in YEARS} =
&sugar_beet_yield * SugarBeetAcres[year];
con Sugar_beet_req_def {year in YEARS}:
sum {age in AGES} sugar_beet_req[age] * NumCows[age,year]
<= SugarBeetGrown[year] + SugarBeetBought[year] - SugarBeetSold[year];
con Labour_req_def {year in YEARS}:
sum {age in AGES} cow_labour_req[age] * NumCows[age,year]
+ sum {group in GROUPS} &grain_labour_req * GrainAcres[group,year]
+ &sugar_beet_labour_req * SugarBeetAcres[year]
<= &nominal_labour_hours + NumExcessLabourHours[year];
con Cash_flow {year in YEARS}:
Profit[year] >= 0;
con Final_dairy_cows_range:
1 - &max_decrease_ratio
<= (sum {age in AGES: age >= 2} NumCows[age,num_years])
/ (sum {age in AGES: age >= 2} init_num_cows[age])
<= 1 + &max_increase_ratio;
solve;
print NumCows NumBullocksSold NumHeifersSold CapitalOutlay
NumExcessLabourHours Revenue Cost Profit;
print GrainAcres;
print GrainGrown;
print GrainBought GrainSold SugarBeetAcres SugarBeetGrown SugarBeetBought
SugarBeetSold;
print Num_acres_con.body Max_num_cows_def.body Final_dairy_cows_range.body;
create data sol_data1 from [age]=AGES
{year in YEARS} <col('NumCows_year'||year)=NumCows[age,year].sol>;
create data sol_data2 from [group year] GrainAcres GrainGrown;
create data sol_data3 from [year]
NumBullocksSold NumHeifersSold CapitalOutlay NumExcessLabourHours
Revenue Cost Profit GrainBought GrainSold
SugarBeetAcres SugarBeetGrown SugarBeetBought SugarBeetSold;
quit;
