Index Sets:

S

Index set of candidate distribution facility locations

Parameters:

m

Number of selected distribution facilities

${\widehat{d}}_{js}$

Distance between warehouse location j and distribution facility s (in miles)

${\tilde{d}}_{sk}$

Distance between distribution facility s and demand locations k (in miles)

${\widehat{c}}_{js}$

FTL cost per truck from warehouse j to distribution facility s (in $/mile)

${\tilde{c}}_{sk}^1$

FTL cost per truck from distribution facility s to demand location k (in $/mile)

${\tilde{c}}_{sk}^2$

LTL cost per pound from distribution facility s to demand location k (in $/lbs.)

${\tilde{c}}_{sk}^3$

Cost of courier shipment from distribution facility s to demand location k (in $)

Decision Variables:

${\widehat{f}}_{jsl}$

Quantity of product l from warehouse j to distribution facility s (in lbs.)

${\tilde{f}}_{skl}$

Quantity of product l from distribution facility s to demand location k (in lbs.)

${\widehat{t}}_{js}$

Number of FTL trucks from warehouse location j to distribution facility s (in trucks)

${\tilde{t}}_{sk}^1$

Number of FTL trucks from distribution facility s to demand location k (in trucks)

${\tilde{t}}_{sk}^2$

Weight of LTL from distribution facility s to demand location k (in lbs.)

${\tilde{x}}_s$

$=\{\begin{array}{l}1\text{ifthereisanoperatingdistributionfacilityat}s\\ 0\text{otherwise}\end{array}$

${\widehat{z}}_{js}$

$=\{\begin{array}{l}1\text{ifanoperatingwarehouseat}j\text{servesanoperatingdistributionfacilityat}s\\ 0\text{otherwise}\end{array}$

${\tilde{y}}_{sk}$

$=\{\begin{array}{l}1\text{iftheoperatingdistributionfacilityat}s\text{servesdemandlocation}k\\ 0\text{otherwise}\end{array}$