Index Sets:

I

Index set of manufacturers

J

Index set of candidate warehouse locations

K

Index set of home customer demand locations

L

Index set of products

Parameters:

n

Number of selected warehouses

$r_{kl}$

Required quantity at demand location k for product l (in lbs.)

${\overline{d}}_{ij}$

Distance between manufacturer location i and warehouse location j (in miles)

$d_{jk}$

Distance between warehouse location j and demand location k (in miles)

${\overline{c}}_{ij}$

FTL cost per truck from manufacturer i to warehouse j (in $/mile)

$c_{jk}^1$

FTL cost per truck from warehouse location j to demand location k (in $/mile)

$c_{jk}^2$

LTL cost per pound from warehouse location j to demand location k (in $/lbs.)

$c_{jk}^3$

Cost of courier shipment from warehouse location j to demand location k (in $/shipment)

$a_{il}$

$=\{\begin{array}{l}\text{1}\text{if}\text{manufacturer}i\text{produces}\text{product}l\\ 0\text{otherwise}\end{array}$

Decision Variables:

${\overline{f}}_{ijl}$

Quantity of product l shipped from manufacturer i to warehouse j (in lbs.)

$f_{jkl}$

Quantity of product l shipped from warehouse j to demand location k (in lbs.)

${\overline{t}}_{ij}$

Number of FTL trucks from manufacturer i to warehouse location j

$t_{jk}^1$

Number of FTL trucks from warehouse location j to demand location k

$t_{jk}^2$

Weight of LTL shipment from warehouse location j to demand location k (in lbs.)

$x_j$

$=\{\begin{array}{l}1\text{ifthereisanoperatingwarehouseatlocation}j\\ 0\text{otherwise}\end{array}$

$y_{jk}$

$=\{\begin{array}{l}1\text{iftheoperatingwarehouseatlocation}j\text{servesdemandlocation}k\\ \text{0}\text{otherwise}\end{array}$