Examining a model for Flaws
AGEC 641 Lab, Fall 2011
Mario Andres Fernandez
Based on material written by Gillig and McCarl. Improved upon by many previous
lab instructors.
Special thanks to Yuquan “Wolfgang” Zhang
A company uses two resources to produce three
products
Maximization
Regular Ruffles BBQ
Objt
Available("Capacity")
Available("Labor")
1.2
1.7
2
1
1
1
<=
10000
0.05
0.08
0.1
<=
0
1,
1,
1,
>=
0
SET
Process
Resource
Types of production Processes / Regular, Ruffles, BBQ /
Types of Resources
/ Capacity,Labor / ;
PARAMETERS
Price(Process) PRODUCT PRICES BY Process / Regular 1.2, Ruffles 1.7, BBQ 2 /
ProdCost(Process) COST BY Process
/ Regular 0, Ruffles 0, BBQ 0 /
ResorAvail(Resource) Resource AVAILABLITY
/ Capacity 10000, Labor 0 / ;
TABLE ResourUse(Resource,Process) Resource USAGE
Regular
Ruffles
BBQ
Capacity
1
1
1
Labor
0.05
0.08
0.10 ;
VARIABLES
Profit
TOtal Profit ;
POSITIVE VARIABLES
Production(Process)
EQUATIONS
Objt
Available(Resource)
Items Produced by Process;
Objective Function ( Profit )
Resources Available;
Objt.. Profit =E=
SUM(Process,(Price(Process)-ProdCost(Process))* Production(Process));
Available(Resource)..
SUM(Process,RESOURUSE(Resource,Process)*Production(Process))
=L= ResorAvail(Resource);
MODEL
ResAlloc /ALL/;
SOLVE
ResAlloc USING LP MAXIMIZING Profit;
Now labor has cost and limits
Maximization
Regular Ruffles BBQ
Objt
1.2
1.7
2
1
1
1
<=
10000
0.05
0.08
0.1
<=
0
Purchase Limit (“Maximum”)
8
<=
600
Purchase Limit (“Minimum”)
8
>=
320
1,
>=
0
Available("Capacity")
Available("Labor")
1,
1,
Setting up GAMS. Lets take the old resource allocation problem and expand by
adding a buying possibility for resources.
Objt..
Profit
=E=
SUM(Process,(PRICE(Process)PRODCOST(Process))* PRODUCTION(Process))
- SUM(Resource,BuyResource(Resource)*BuyTerms(Resource,“Cost”)) ;
Available(Resource)..
SUM(Process,ResourUse(Resource,Process)*PRODUCTION(Process))
=L=
RESORAVAIL(Resource)
+ BuyResource(Resource)*BuyTerms(Resource,“Amount_Per_Unit");
PurchaseLimit(Resource,MinMax)$BuyTerms(Resource,“Cost")..
Sign(MinMax)*BuyResource(Resource)*BuyTerms(Resource,"Amount_Per_Unit")
=L= Sign(MinMax)*BuyTerms(Resource,MinMax) ;
SET
Process
Types of production Processes
/ Regular, Ruffles, BBQ /
Resource
Types of Resources
/ Capacity,Labor / ;
PARAMETERS
Price(Process)
PRODUCT PRICES BY Process
/ Regular 1.2, Ruffles 1.7, BBQ 2 /
ProdCost(Process)
COST BY Process
/ Regular 0, Ruffles 0, BBQ 0 /
ResorAvail(Resource)
Resource AVAILABLITY
/ Capacity 10000, Labor 0 / ;
TABLE ResourUse(Resource,Process) Resource USAGE
Regular
Ruffles
BBQ
Capacity
1
1
1
Labor
0.05
0.08
0.10 ;
SET Terms
Resource purchase Terms
/ Cost, Amount_per_unit, Maximum, Minimum /
MinMax(Terms) Min and max subset of Terms
/ Maximum, Minimum / ;
TABLE BuyTerms(Resource,Terms) Resource purchase Terms
Cost
Amount_per_unit
Maximum
Minimum
Capacity
Labor
64
8
600
320;
PARAMETER
Sign(MinMax)
Sign to use in limit equation
/ Maximum 1, Minimum –1 / ;
VARIABLES
Profit
Total Profit ;
POSITIVE VARIABLES
Production(Process)
Items Produced by Process
BuyResource(Resource)
Resources purchased ;
EQUATIONS
Objt
Objective Function ( Profit )
Available(Resource)
Resources Available
PurchaseLimit(Resource,MinMax)
Limits on Resource for purchase;
Objt.. Profit =E=
SUM(Process,(Price(Process)-ProdCost(Process))* Production(Process))
- SUM(Resource,BuyResource(Resource)*BuyTerms(Resource,"Cost")) ;
Available(Resource)..
SUM(Process,RESOURUSE(Resource,Process)*Production(Process))
=L= ResorAvail(Resource)
+ BuyResource(Resource)*BuyTerms(Resource,"Amount_per_unit");
PurchaseLimit(Resource,MinMax)$BuyTerms(Resource,"cost")..
Sign(MinMax)*BuyResource(Resource)*BuyTerms(Resource,"Amount_per_unit")
=L= Sign(MinMax)*BuyTerms(Resource,MinMax);
MODEL
ResAlloc /ALL/;
SOLVE
ResAlloc USING LP MAXIMIZING Profit;
Dissecting Revised Resource Allocation Problem
SET Terms Resource purchase Terms /Cost, Amount_per_unit,
Maximum, Minimum /
MinMax(Terms) min max subset of Terms / Maximum, Minimum / ;
TABLE BuyTerms(Resource,Terms) Resource purchase Terms
Cost
Amount_per_unit
Maximum
Minimum
Capacity
Labor
64
8
600
320;
PARAMETER
Sign(MinMax)
Sign to use in limit equation
/ Maximum 1, Minimum –1 / ;
POSITIVE VARIABLES BuyResource(Resource)
Resources purchased ;
EQUATIONS
Objt
Objective Function (Profit)
Available(Resource)
Resources Available
PurchaseLimit(Resource,MinMax) Limits on Resource purchase;
Basics of revision
1. Add a purchase variable
2. Define a purchase limit constraint
Objt.. Profit =E= SUM(Process,(Price(Process)ProdCost(Process))* Production(Process))
- SUM(Resource,BuyResource(Resource)*BuyTerms(Resource,"Cost"));
Available(Resource)..
SUM(Process,ResourUse(Resource,Process)*Production(Process))
=L= ResorAvail(Resource)
+ BuyResource(Resource)*BuyTerms(Resource,"Amount_per_unit");
PurchaseLimit(Resource,MinMax)$BuyTerms(Resource,"cost")..
Sign(MinMax)*BuyResource(Resource)*BuyTerms(Resource,"Amount_per_u
nit") =L=
Sign(MinMax)*BuyTerms(Resource,MinMax);
Basics of Revision
3. Add term to objective function with cost
4. Add term to Resource Availability allowing purchase
5. Add terms to constrain limiting purchase imposing min and max
6. Add data giving cost, per unit amount, min and max
Dissecting Revised Resource Allocation Problem
SET Terms Resource purchase Terms
/ Cost, Amount_per_unit,
Maximum, Minimum /
MinMax(Terms) Min and max subset of Terms / Maximum, Minimum /
;
TABLE BuyTerms(Resource,Terms)
Resource purchase Terms
Cost
Amount_per_unit
Maximum
Minimum
Capacity
Labor
64
8
600
320;
PARAMETER
Sign(MinMax)
Sign to use in limit equation
/ Maximum 1, Minimum –1 / ;
POSITIVE VARIABLES BuyResource(Resource) Resources purchased ;
EQUATIONS
Objt
Objective Function ( Profit )
Available(Resource)
Resources Available
PurchaseLimit(Resource,MinMax) Limits on Resource purchase;
Tricks in revision
1. Add a conditional to the purchase limit constraint to only generate if there is a
non zero cost, don’t need this elsewhere
Objt..
Profit =E=
SUM(Process,(Price(Process)ProdCost(Process))* Production(Process))
- SUM(Resource,BuyResource(Resource)*BuyTerms(Resource,"Cost")) ;
Available(Resource)..
SUM(Process,ResourUse(Resource,Process)*Production(Process))
=L= ResorAvail(Resource)
+
BuyResource(Resource)*BuyTerms(Resource,"Amount_per_unit");
PurchaseLimit(Resource,MinMax) $BuyTerms(Resource,"cost")..
Sign(MinMax)*BuyResource(Resource)*BuyTerms(Resource,"Amount_pe
r_unit")
=L=
Sign(MinMax)*BuyTerms(Resource,MinMax);
1. Add a parameter called sign that puts a different sign on limit depending
on whether the constraint is min or max (multiplying through by –1 for
min).
Regular
Ruffles
BBQ
1.2
1.7
2
1
1
1
<=
10000
0.05
0.08
0.1
<=
0
Purchase Limit (“Maximum”)
8
<=
600
Purchase Limit (“Minimum”)
8
>=
320
1,
>=
0
Objt
Available("Capacity")
Available("Labor")
1,
1,
After setting up the LP problem, how to assure that it is transformed to a GAMS
formulation correctly?
Objt..
Profit
=E= SUM(Process,(PRICE(Process)-PRODCOST(Process))* PRODUCTION(Process))
- SUM(Resource,BuyResource(Resource)*BuyTerms(Resource,“Cost”)) ;
Available(Resource)..
SUM(Process,ResourUse(Resource,Process)*PRODUCTION(Process))
=L= RESORAVAIL(Resource)
+ BuyResource(Resource)*BuyTerms(Resource,“Amount_Per_Unit");
PurchaseLimit(Resource, MinMax)$BuyTerms(resource,"cost")..
Sign(MinMax)*BuyResource(Resource)*BuyTerms(Resource,"Amount_Per_Unit")
=L= Sign(MinMax)*BuyTerms(Resource, MinMax) ;
Two ways to look at your model structure.

LIMROW and LIMCOL options

GAMSCHK
Using LIMROW and LIMCOL options
MODEL
ResAlloc /All/ ;
OPTION
LIMROW =10;
OPTION
LIMCOL =10;
SOLVE
ResAlloc USING LP MAXIMATION Profit ;
OPTION
LIMROW = 10;
OPTION
LIMROW = 10
This non-negativity is already specified in the variable
specification step
An alternative way to check the model structure is to use
GAMSCHK for examining the model structure and
solutions.

DISPLAYCR: Listing selected equations and/or
variables

PICTURE: Generating schematics on location of
coefficients by
sign and magnitude on an
individual equation/variable
basis

BLOCKPIC: Generating a whole model summary

POSTOPT: Debugging unrealistic optimal solutions
Steps to run GAMS CHECK
Here are steps to run GAMSCHK.
Step 1:
Insert a command line
OPTION LP = GAMSCHK ;
for LP problem
or
OPTION NLP = GAMSCHK ;
for NLP problem
or
OPTION MIP = GAMSCHK ;
for MIP problem
in the model right before SOLVE
Step 2:
Create a new file with extension *.gck that has the same
corresponding name as the program file. If your program file is
called chipprob.gms, then make a new file called chipprob.gck
To create a new file, go to the FILE menu and use the NEW
option. You will then get a file called untitled with an empty
screen. Then save your program as chipprob.gck using the file
SAVE option.
As illustration let’s mess up the model. Here are two alternative
data input tables. Which one is right?
Alternative A
What is the
meaning of a
positive 64 in
the Objt?
Alternative B
What is the
meaning of a
negative 64 in
the Objt?
DISPLAYCR mirrors LIMROW and LIMCOL, but allows to select specific items
to be displayed.
A
B
A
B
A
B
PICTURE looks at
magnitude, sign and
location of coefficients.
B
Which one is right, A or B?
A
A
BLOCKPIC is used to look
at the whole model
summary.
Is there anything
wrong with this
BLOCKPIC?
B
BLOCKPIC is used to look
at the whole model
summary.
Revise maximum labor hours from 600 hours to 1200 hours
A
POSTOPT : used to debug
unrealistic solutions. Row
Summing : used to reconstruct
equation activity.
Is there any wrong with
this accounting?
A
B
Is this
accounting
reasonable?
B
A
POSTOPT : Budgeting is
use to reconstruct
reduced costs.
Is this accounting reasonable,
(SiUiAij – Cj = 0 )? Why Xij = 0?
B
Is this accounting
reasonable,
(SiUiAij – Cj = 0 )? Why
Xij = 0?