Presenter: Davit Stepanyan

• Positive Mathematical Programing
• Hands-on exercise in Excel
• Hands-on exercise in GAMS

Download presentation: pmp_t.pptx
Download Excel exercise: pmp.xlsx
Download Excel exercise solution pmp_solution.xlsx
Download GAMS exercise:

CAPRI doc
Heckelei
Howitt

*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*
$ontext
 
* Exercise (3): MY FARM Model with sets and sum
 
*### The objective of the exercise:
        1) Getting acquainted with the GAMS programming language.
 
*### The problem:
A farmer wants to maximize his profit using 200 ha of land and 10000 hours of
labor available. He has the option of cultivating three types of crops: wheat,
barley, rapeseed and sugarbeet. The profit received and labor hours required for producing one
ha of each crop are presented in the table below. How much of each crop does he
need to cultivate in order to maximize his profit?
 
 
Item                           Wheat Barley Rapeseed Sugarbeet
Profit in €/ha                  253   443     284      516
Required labor hours/ha          25    36      27       87
 
 
*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*
$offtext
 
 
sets
   crops /
      wheat
      barley
      rapeseed
      sugarbeet
   /
;
 
Parameters
   gm(crops)   gross margin
   lab(crops)  labour quantity
;
 
gm("wheat")      = 253;
gm("barley")     = 443;
gm("rapeseed")   = 284;
gm("sugarbeet")  = 516;
 
lab("wheat")     = 25;
lab("barley")    = 36;
lab("rapeseed")  = 27;
lab("sugarbeet") = 87;
 
 
Variables
  Z  objective function value
;
 
Positive variable
  X(crops)  land area planted with crop
;
 
 
Equations
  land   land constraint
  labour labour constraint
  obj    objective function
;
 
obj ..           Z =E= sum (crops, X(crops)*gm(crops));
 
land ..          sum (crops, X(crops)) =L= 200;
 
labour ..        sum (crops, lab(crops)*X(crops)) =L= 10000;
 
Model myfarm /all/;
 
Solve myfarm using lp maximizing Z;