Hi,

First of all, you did not set optcr correctly. OptCr is an option not a user scalar. Here is the correct use:

…

MODEL NetProfit /ALL/ ;

option optcr=0, decimals=8;

SOLVE NetProfit USING NLP MAXIMIZING z1 ;

…

When I run the model (with correct optcr), I get clear indicators from GAMS/BARON why BARON can’t prove global optimality:

User did not provide appropriate variable bounds.

Some model expressions are unbounded.

We may not be able to guarantee globality.

and at the end of the run:

*** User did not provide appropriate variable bounds ***

*** Globality is therefore not guaranteed ***

For BARON to prove global optimality everything needs to be nicely bounded. If the variables is not bounded (and BARON can deduce bounds) this is not good. Try to set finite upper bounds (lower you set already).

After setting some upper bounds (T1.up = 1.01; T2.up = 1.01; v.up = 20; not sure if they really make sense), BARON solves to global optimality.

Hope this helps,

Michael Bussieck - GAMSWorld Coordinator

On Tuesday, February 11, 2014 5:30:02 AM UTC-5, Zohreh wrote:

Dear Mr. Bussieck,

I set optcr to zero. But I still get the status model as Locally Optimal and the answers are exactly as same as before. I would highly appreciate it if you guide me what the possible problem is.

SCALARS r1 the manufacturer capacity utilization /0.9/

r2 the supplier capacity utilization /0.8/

q deteriorating rate which is a fraction of the on-hand inventory /0.1/

F supplier setup cost per setup /200 /

A manufacturer ordering setup cost per cycle /50/

c supplier production cost per unit /5/

s the unit price charged by the supplier to the manufacturer /10/

b backorder cost /2/

h manufacturer inventory holding cost rate excluding interest charges /0.1/

j supplier inventory holding cost rate excluding interest charges /0.1/

Is supplier opportunity cost per dollar per unit time /0.02/

Ip manufacturer opportunity cost per dollar per unit time /0.06/

Ie manufacturer interest earned per dollar per unit time /0.04/

k constant in the manufacturer demand function representing his market scale /5000000/

e price elasticity of manufacturer demand rate which is alpha in the thesis /1.5/

M the manufacturer trade credit period offered by the supplier /0.166666666666667/

N the customer trade credit period offered by the manufacturer /0.0821917808219178/

g number of shipments from the supplier to the manufacturer per production run /1/ ;

VARIABLES

z1 total net profit ;

POSITIVE VARIABLES

T1 production time with backorder at manufacturer’s side

T2 production time when positive stock builds up and the stock depletes due to the demand and deterioration at manufacturers side

v the unit price charged by the manufacturer to the customers ;

T1.lo = 0.01 ;

T2.lo = 0.01 ;

v.lo = 1 ;

Equations

Profit define objective function

Constraint condition for NP1

PriceConstraint constraint for price ;

Profit … z1 =e= (1/((1/r1)*T1+T2+(1/q)*(log((1-(1/r1))*exp(-q*T2)+(1/r1)))))*((v-s)*(k*(v**(-e)))*((1/r1)**T1+(T2+((1/q)*(log((1-(1/r1))*exp(-q*T2)+(1/r1))))))-A-(sh/q)*(k*(v**(-e)))*(((1/r1)-1)**T2-((1/q)*(log((1-(1/r1))*exp(-q*T2)+(1/r1)))))-(b)((1/2)*(T1**2)*(k*(v**(-e)))*((1/r1)-1)*(1/r1))-s*(k*(v**(-e)))*((1/r1)**T2-(T2+((1/q)*(log((1-(1/r1))*exp(-q*T2)+ 1/r1)))))+(vIe)*((k*(v**(-e))/(2*r1))*((M-N)*2))-(s**Ip*(k(v*(-e)))/q)*(((1/r1)-1)**T2-((1/q)*(log((1-(1/r1))*exp(-q*T2)+(1/r1))))) -vIp*(1/2)*(k*(v**(-e)))*((N*(2*T2+2*((1/q)*(log((1-(1/r1))**exp(-q*T2)+(1/r1))))-N))+N(T1+N-M)*(1/r1))+(s-c)*((k*(v**(-e))/r1)*(T1+T2))-F/(g)- c*(j+Is)*(((k*(v**(-e)))/r1)*((1/r1)**T1+T2+(1/q)*(log((1-(1/r1))*exp(-q*T2)+(1/r1))))(T1+T2)*(r2*(1-((g)/2))+(((g)-1)/2)))-s*Is*((k*(v**(-e))/r1)*(T1+T2)*M)) ;

Constraint … M =l= T1 ;

PriceConstraint … v =g= s ;

MODEL NetProfit /ALL/ ;

scalars optcr relative gap following the GAMS formula ;

optcr=0;

option decimals=8; display optcr;

SOLVE NetProfit USING NLP MAXIMIZING z1 ;

option decimals=8;

Display z1.l;

Display T1.l, T2.l, v.l;

execute_unload

parameter ms, ss;

ms=NetProfit.modelstat;

ss=NetProfit.solvestat;

I would be looking forward to hearing your kind response.

Best regards.

On Tuesday, February 11, 2014 12:54:29 PM UTC+8, Zohreh wrote:

Dear Friends,

As far as I have found, BARON is a global optimizer. But, after solving my model, its status is locally optimal. Does it mean that the model in not concave (for maximum) and the global optimum does not exist?

I would highly appreciate it if anybody can help me understanding this issue.

I would be looking forward to hearing your kind response.

Best regards.

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