sets

i 'canning plants' $/$ seattle, san$-$diego $/$

j 'markets' $/$ new$-$york, chicago, topeka $/$

r $\text{'}$DCs$\text{'}/1,2/$;

parameters

a$($i$)$ 'capacity of plant i in cases'

$/$ seattle $350$

san$-$diego $600/$

b$($j$)$ 'demand at market j in cases'

$/$ new$-$york $325$

chicago $300$

topeka $275/$

fixdc$($r$)$ 'fixed cost of opening DC r$\text{'}$

$/1100$

$2100/$

q$($r$)$ 'capacity of opening DC r$\text{'}$

$/11000$

$21000/$;

Table d$1($i$,$r$)$ distance btw i and j

$12$

seattle $0\mathrm{.}80\mathrm{.}5$

san$-$diego $0\mathrm{.}50\mathrm{.}8$ ;

Table d$2($r$,$j$)$ distance btw i and j

new$-$york chicago topeka

$12\mathrm{.}11\mathrm{.}41\mathrm{.}3$

$21\mathrm{.}91\mathrm{.}21\mathrm{.}4$ ;

Scalar f 'freight in dollars per case per thousand miles' $/90/$;

parameter

c$($i$,$r$,$j$)$ unit cost of transportation from i to j;

c$($i$,$r$,$j$)=$ f$*$d$1($i$,$r$)/1000+$f$*$d$2($r$,$j$)/1000$;

display c;

variable

z objective value $($total cost of transportation$)$

positive variable

x$($i$,$r$,$j$)$ amount transported from i to j

binary variable

w$($r$)1$ if DC is opened and $0$ otherwise

Equation

objective$\_$func this is ojective function

supply$1$ do not exceed capacity of plant

supply$2$ do not exceed capacity of DC

demand satisfy demand

;

objective$\_$func $..$ z $=$E$=$ sum$(($r$),$ fixdc$($r$)*$w$($r$))+$ sum$(($i$,$j$,$r$),$ c$($i$,$r$,$j$)*$x$($i$,$r$,$j$))$;

supply$1($i$)..$ sum$(($j$,$r$),$ x$($i$,$r$,$j$))=$L$=$ a$($i$)$;

supply$2($r$)..$ sum$(($i$,$j$),$ x$($i$,$r$,$j$))=$L$=$ q$($r$)*$w$($r$)$;

demand $($j$)..$ sum$(($i$,$r$),$ x$($i$,$r$,$j$))=$E$=$ b$($j$)$;

model tesc $/$all$/$;

$*$option optcr $=0$;

solve tesc using MIP minimizing z;

display x$.$L$,$ w$.$L$,$ z$.$L;