Index Sets:

S

Index set of candidate distribution facility locations

Parameters:

m

Number of selected distribution facilities

d ^ j s

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

d ˜ s k

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

c ^ j s

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

c ˜ s k 1

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

c ˜ s k 2

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

c ˜ s k 3

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

Decision Variables:

f ^ j s l

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

f ˜ s k l

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

t ^ j s

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

t ˜ s k 1

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

t ˜ s k 2

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

x ˜ s

= { 1 ifthereisanoperatingdistributionfacilityat s 0 otherwise

z ^ j s

= { 1 ifanoperatingwarehouseat j servesanoperatingdistributionfacilityat s 0 otherwise

y ˜ s k

= { 1 iftheoperatingdistributionfacilityat s servesdemandlocation k 0 otherwise