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.) |

${\tilde{x}}_{s}$ | $=\{\begin{array}{l}1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ifthereisanoperatingdistributionfacilityat}s\\ 0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{otherwise}\end{array}$ |

${\widehat{z}}_{js}$ | $=\{\begin{array}{l}1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ifanoperatingwarehouseat}\text{\hspace{0.17em}}j\text{\hspace{0.17em}}\text{servesanoperatingdistributionfacilityat}\text{\hspace{0.17em}}s\\ 0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{otherwise}\end{array}$ |

${\tilde{y}}_{sk}$ | $=\{\begin{array}{l}1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{iftheoperatingdistributionfacilityat}s\text{servesdemandlocation}\text{\hspace{0.17em}}k\\ 0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{otherwise}\end{array}$ |