Dear friends,

I have a model for which GAMS does not present answer. The model 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/

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

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

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/ ;

VARIABLES

z6 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 ;

T1.up = 2 ;

T2.up = 2 ;

INTEGER VARIABLES

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

g.lo = 1;

g.up = 10;

Equations

Profit define objective function

Constraint1 condition1 for NP6

PriceConstraint constraint for price

ConstraintForNandT1 constraint for N and T1;

Profit … z6 =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(-qT2)+(1/r1))))))-A-(s*h/q)

*(k*(v**(-e)))

*(((1/r1)-1)*((1/2)

*T2-((1/q)*(log((1-(1/r1))*exp(-q*T2)+(1/r1)))))-(b)*(T1**2)*(k*(v**(-e)))

*((1/r1)-1)*(1/r1))-s*(k*(v**(-e)))

*((1/r1)*Ie)

*T2-(T2+((1/q)*(log((1-(1/r1))*exp(-q*T2)+ (1/r1))))))+(v*(k*(v**(-e)))

*((1/(2*r1))

*(T1**2)+(T1/r1)*(M-T1-N)+(1/2)

*(power((T2+((1/q)*(log((1-(1/r1))

*exp(-q*T2)+ (1/r1))))),2))+((T2+((1/q)

*(log((1-(1/r1))*(M-T1-T2-((1/q)

*exp(-q*T2)+(1/r1)))))*(log((1-(1/r1))*((k*(v**(-e))/r1)

*exp(-q*T2)+ (1/r1)))-N))))+(s-c)*(T1+T2))-F/(g)- c*(j+Is)

*(((k*(v**(-e)))/r1)

*((1/r1)*(T1+T2)

*T1+T2+(1/q)*(log((1-(1/r1))*exp(-q*T2)+(1/r1))))*(r2*(1-(g/2))+((g-1)/2)))-s

*Is*((k*(v**(-e))/r1)*(T1+T2)

*M)) ; ;*

Constraint1 … M =g= T1+T2+(1/q)(log((1-(1/r1))

Constraint1 … M =g= T1+T2+(1/q)

*exp(-q*T2)+(1/r1)))+N ;

PriceConstraint … v =g= s ;

ConstraintForNandT1 … N =l= T1 ;

MODEL NetProfit /ALL/ ;

SOLVE NetProfit USING MINLP MAXIMIZING z6 ;

option decimals=8;

Display z6.l;

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

execute_unload

I would highly appreciate it if anybody can help me to find the problem.

I would be waiting for your kind response.

Best regards.

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