Agricultural Pricing (mpex21)
/***************************************************************/
/* */
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: mpex21 */
/* TITLE: Agricultural Pricing (mpex21) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* PROCS: OPTMODEL */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: */
/* MISC: Example 21 from the Mathematical Programming */
/* Examples book. */
/* */
/***************************************************************/
/* missing supply indicates unbounded */
data raw_material_data;
input raw $10. supply;
datalines;
Fat 600000
DryMatter 750000
Water .
;
data product_data;
input product $ Fat DryMatter Water prev_demand prev_price;
datalines;
Milk 4 9 87 4820000 297
Butter 80 2 18 320000 720
Cheese1 35 30 35 210000 1050
Cheese2 25 40 35 70000 815
;
data elasticity_data;
input i $ j $ elasticity;
datalines;
Milk Milk -0.4
Butter Butter -2.7
Cheese1 Cheese1 -1.1
Cheese2 Cheese2 -0.4
Cheese1 Cheese2 0.1
Cheese2 Cheese1 0.4
;
proc optmodel;
set <str> RAWS;
num supply {RAWS};
read data raw_material_data into RAWS=[raw] supply;
set <str> PRODUCTS;
num prev_demand {PRODUCTS};
num prev_price {PRODUCTS};
num percent {PRODUCTS, RAWS};
read data product_data into PRODUCTS=[product]
{raw in RAWS} <percent[product,raw]=col(raw)> prev_demand prev_price;
num elasticity {PRODUCTS, PRODUCTS} init 0;
read data elasticity_data into [i j] elasticity;
var Price {PRODUCTS} >= 0;
var Demand {PRODUCTS} >= 0;
max TotalRevenue
= sum {product in PRODUCTS} Price[product] * Demand[product];
con Demand_con {i in PRODUCTS}:
(Demand[i] - prev_demand[i]) / prev_demand[i]
= sum {j in PRODUCTS} elasticity[i,j] * (Price[j] - prev_price[j]) /
prev_price[j];
con Supply_con {raw in RAWS: supply[raw] ne .}:
sum {product in PRODUCTS} (percent[product,raw]/100) * Demand[product]
<= supply[raw];
con Price_index_con:
sum {product in PRODUCTS} prev_demand[product] * Price[product]
<= sum {product in PRODUCTS} prev_demand[product] * prev_price[product];
solve;
print Price Demand;
print Price_index_con.dual;
solve with NLP / algorithm=activeset;
print Price Demand;
print Price_index_con.dual;
quit;
proc optmodel;
set <str> RAWS;
num supply {RAWS};
read data raw_material_data into RAWS=[raw] supply;
set <str> PRODUCTS;
num prev_demand {PRODUCTS};
num prev_price {PRODUCTS};
num percent {PRODUCTS, RAWS};
read data product_data into PRODUCTS=[product]
{raw in RAWS} <percent[product,raw]=col(raw)> prev_demand prev_price;
num elasticity {PRODUCTS, PRODUCTS} init 0;
read data elasticity_data into [i j] elasticity;
var Price {PRODUCTS} >= 0;
impvar Demand {i in PRODUCTS} =
prev_demand[i] * (1 +
sum {j in PRODUCTS}
elasticity[i,j] * (Price[j] - prev_price[j]) / prev_price[j]);
max TotalRevenue
= sum {product in PRODUCTS} Price[product] * Demand[product];
con Demand_nonnegative {i in PRODUCTS}:
Demand[i] >= 0;
con Supply_con {raw in RAWS: supply[raw] ne .}:
sum {product in PRODUCTS} (percent[product,raw]/100) * Demand[product]
<= supply[raw];
con Price_index_con:
sum {product in PRODUCTS} prev_demand[product] * Price[product]
<= sum {product in PRODUCTS} prev_demand[product] * prev_price[product];
solve;
print Price Demand;
print Price_index_con.dual;
solve with NLP / soltype=0;
print Price Demand;
print Price_index_con.dual;
solve with NLP / algorithm=activeset;
print Price Demand;
print Price_index_con.dual;
quit;