Sets

i departments $/$cutting$,$ insulating, sewing, packaging$/$

j products $/$shirts$,$ caps, pants, gloves$/$

k weeks $/1,2,3,4/$

q $/1,2,3,4,5,6,7,8,9,10/$;

Scalars

PermanentWorkers "Number of permanent workers" $/25/$

PermanentProductionRate "Production rate of permanent worker per week" $/12/$

TemporaryProductionRate "Production rate of temporary worker per week" $/10/$

hiring$\_$cost "Cost of hiring a temporary worker" $/200/$

firing$\_$cost "Cost of firing a temporary worker" $/400/$

inventory$\_$cost "Inventory cost per item per week" $/5/$;

Parameters

capacity$($k$,$i$)$ capacity of each department in each week $/1.$cutting $1000,1.$insulating $1000,1.$sewing $1000,1.$packaging $1000$

$2.$cutting $990,2.$insulating $990,2.$sewing $990,2.$packaging $990$

$3.$cutting $980,3.$insulating $980,3.$sewing $980,3.$packaging $980$

$4.$cutting $970,4.$insulating $970,4.$sewing $970,4.$packaging $970/,$

X$\_$coeff$($i$,$j$)$ Coefficients for products produced in departments $/$cutting$.$shirts $0\mathrm{.}3,$ cutting.caps $0\mathrm{.}3,$ cutting.pants $0\mathrm{.}25,$ cutting.gloves $0\mathrm{.}15$

insulating.shirts $0\mathrm{.}25,$ insulating.caps $0\mathrm{.}35,$ insulating.pants $0\mathrm{.}3,$ insulating.gloves $0\mathrm{.}7$

sewing.shirts $0\mathrm{.}45,$ sewing.caps $0\mathrm{.}5,$ sewing.pants $0\mathrm{.}4,$ sewing.gloves $0\mathrm{.}22$

packaging.shirts $0\mathrm{.}15,$ packaging.caps $0\mathrm{.}15,$ packaging.pants $0\mathrm{.}1,$ packaging.gloves $0\mathrm{.}5/,$

demand$($k$,$j$)$ demand for each product in each week $/1.$shirts $800,1.$caps $750,1.$pants $600,1.$gloves $500$

$2.$shirts $900,2.$caps $800,2.$pants $650,2.$gloves $550$

$3.$shirts $950,3.$caps $850,3.$pants $700,3.$gloves $600$

$4.$shirts $1000,4.$caps $900,4.$pants $750,4.$gloves $650/,$

production$\_$cost$($k$,$j$)$ production cost of each product $/1.$shirts $30,1.$caps $40,1.$pants $20,1.$gloves $10$

$2.$shirts $35,2.$caps $45,2.$pants $25,2.$gloves $15$

$3.$shirts $40,3.$caps $50,3.$pants $30,3.$gloves $20$

$4.$shirts $45,4.$caps $55,4.$pants $35,4.$gloves $25/,$

penalty$\_$cost$($k$,$j$)$ penalty cost for undelivered items of each product in each week $/1.$shirts $15,1.$caps $20,1.$pants $15,1.$gloves $8$

$2.$shirts $20,2.$caps $25,2.$pants $20,2.$gloves $13$

$3.$shirts $25,3.$caps $30,3.$pants $25,3.$gloves $18$

$4.$shirts $30,4.$caps $35,4.$pants $30,4.$gloves $23/$;

Positive Variables

X$($j$,$k$)$ production of each product in each department and week

H$($k$)$ number of temporary workers hired in each week

F$($k$)$ number of temporary workers fired in each week

M$($j$,$k$)$ inventory of each product at the end of each week

P$($j$,$k$)$ undelivered items of each product at the end of each week;

Variable

total$\_$cost total cost;

Equations

obj objective function

capacity$\_$con$($k$,$i$)$ capacity constraints

total$\_$production$\_$con$($k$,$j$)$

demand$\_$con$($k$,$j$)$ demand constraints

demand$\_$con$\_1($k$,$j$)$

initial$\_$inv$($j$)$ initial inventory constraints

hiring$\_$con$($k$)$ hiring constraints

hiring$\_$con$\_1($k$)$

max$\_$workers$($k$)$ maximum temporary workers constraint;

obj.. total$\_$cost $=$e$=$

sum$(($j$,$k$),$ production$\_$cost$($k$,$j$)*$ X$($j$,$k$))$

$+$ sum$($k$,$ hiring$\_$cost $*$ H$($k$)+$ firing$\_$cost $*$ F$($k$))$

$+$ sum$(($j$,$k$),$ inventory$\_$cost $*$ M$($j$,$k$))$

$+$ sum$(($j$,$k$),$ penalty$\_$cost$($k$,$j$)*$ P$($j$,$k$))$;

capacity$\_$con$($k$,$i$)..$ sum$($j$,$ X$\_$coeff$($i$,$j$)*$ X$($j$,$k$))=$l$=$ capacity$($k$,$i$)$;

total$\_$production$\_$con$($k$,$j$)..$

X$($j$,$k$)=$e$=$ PermanentProductionRate $*$ PermanentWorkers $+$ TemporaryProductionRate $*$ sum$(($q$),($ord$($q$)$ le ord$($k$))$$$($ord$($q$)$ le ord$($k$))),$ H$($q$)-$F$($q$))$;

demand$\_$con$($k$,$j$)$$$($ord$($k$)$ gt $1)..$ X$($j$,$k$)+$ M$($j$,$k$-1)-$ M$($j$,$k$)=$e$=$ demand$($k$,$j$)-$ P$($j$,$k$)$;

demand$\_$con$\_1($k$(\text{'}1\text{'}),$ j$)..$

X$($j$,\text{'}1\text{'})-$ M$($j$,\text{'}1\text{'})=$e$=$ demand$(\text{'}1\text{'},$j$)-$ P$($j$,\text{'}1\text{'})$;

initial$\_$inv$($j$)..$ M$($j$,\text{'}1\text{'})=$e$=0$;

hiring$\_$con$($k$)$$$($ord$($k$)$ gt $1)..$ H$($k$)=$l$=$ F$($k$-1)$;

hiring$\_$con$\_1($k$(\text{'}1\text{'}))..$ H$(\text{'}1\text{'})=$e$=0$;

max$\_$workers$($k$)..25+$ H$($k$)-$ F$($k$)=$l$=50$;

Model production$\_$model $/$all$/$;

Solve production$\_$model using LP minimizing total$\_$cost; NOTE: above is my GAMS software code for my linear programming optimization model. i am facing error in code of line with name of equation $\{$total production$\_$con$\}$ plz fix this error in my code of line $.$second, fix error without changing my logic in total production$\_$con equation $.$third, i want to display my all decision variable and its objective function so plz also do it in given code and last thing plz introduce in my code that in week inventory will be zero. plz do all things in my GAMS code and share GAMS code with me $.$ i need of GAMS code. dont answer me in form of text but answer me via sharing GAMS CODE and dont put data in gdx or local file all work do on GAMS