## Food Manufacture 1 (mpex01)

```/***************************************************************/
/*                                                             */
/*          S A S   S A M P L E   L I B R A R Y                */
/*                                                             */
/*    NAME: mpex01                                             */
/*   TITLE: Food Manufacture 1 (mpex01)                        */
/* PRODUCT: OR                                                 */
/*  SYSTEM: ALL                                                */
/*    KEYS: OR                                                 */
/*   PROCS: OPTMODEL                                           */
/*    DATA:                                                    */
/*                                                             */
/* SUPPORT:                             UPDATE:                */
/*     REF:                                                    */
/*    MISC: Example 01 from the Mathematical Programming       */
/*          Examples book.                                     */
/*                                                             */
/***************************************************************/

data cost_data;
input veg1-veg2 oil1-oil3;
datalines;
110  120  130  110  115
130  130  110   90  115
110  140  130  100   95
120  110  120  120  125
100  120  150  110  105
90  100  140   80  135
;

data hardness_data;
input oil \$ hardness;
datalines;
veg1 8.8
veg2 6.1
oil1 2.0
oil2 4.2
oil3 5.0
;

%let revenue_per_ton = 150;
%let veg_ub = 200;
%let nonveg_ub = 250;
%let store_ub = 1000;
%let storage_cost_per_ton = 5;
%let hardness_lb = 3;
%let hardness_ub = 6;
%let init_storage = 500;

proc optmodel;
set <str> OILS;
num hardness {OILS};
read data hardness_data into OILS=[oil] hardness;
print hardness;

set PERIODS;
num cost {OILS, PERIODS};
read data cost_data into PERIODS=[_N_] {oil in OILS}
<cost[oil,_N_]=col(oil)>;
print cost;

/* tons of raw oil to buy per period */
var Buy {OILS, PERIODS} >= 0;
var Use {OILS, PERIODS} >= 0;
impvar Manufacture {period in PERIODS} = sum {oil in OILS} Use[oil,period];

num last_period = max {period in PERIODS} period;
var Store {OILS, PERIODS union {0}} >= 0 <= &store_ub;
for {oil in OILS} do;
fix Store[oil,0]           = &init_storage;
fix Store[oil,last_period] = &init_storage;
end;

set VEG = {oil in OILS: substr(oil,1,3) = 'veg'};
set NONVEG = OILS diff VEG;

impvar Revenue =
sum {period in PERIODS} &revenue_per_ton * Manufacture[period];
impvar RawCost =
sum {oil in OILS, period in PERIODS} cost[oil,period] * Buy[oil,period];
impvar StorageCost =
sum {oil in OILS, period in PERIODS}
&storage_cost_per_ton * Store[oil,period];
max Profit = Revenue - RawCost - StorageCost;

con Veg_ub_con {period in PERIODS}:
sum {oil in VEG} Use[oil,period] <= &veg_ub;

con Nonveg_ub_con {period in PERIODS}:
sum {oil in NONVEG} Use[oil,period] <= &nonveg_ub;

con Flow_balance_con {oil in OILS, period in PERIODS}:
= Use[oil,period] + Store[oil,period];

con Hardness_ub_con {period in PERIODS}:
sum {oil in OILS} hardness[oil] * Use[oil,period]
>= &hardness_lb * Manufacture[period];

con Hardness_lb_con {period in PERIODS}:
sum {oil in OILS} hardness[oil] * Use[oil,period]
<= &hardness_ub * Manufacture[period];

expand;

num hardness_sol {period in PERIODS} =
(sum {oil in OILS} hardness[oil] * Use[oil,period].sol)
/ Manufacture[period].sol;

solve;
print Buy Use Store Manufacture hardness_sol;

create data sol_data1 from [oil period] Buy Use Store;
create data sol_data2 from [period] Manufacture;

solve with lp / algorithm=ps;
print Buy Use Store Manufacture hardness_sol;
solve with lp / algorithm=ip;
print Buy Use Store Manufacture hardness_sol;
solve with lp / algorithm=ns;
print Buy Use Store Manufacture hardness_sol;
quit;

```