Quantitative Methods Stateline

Polychem wants Stateline to pick up and transport waste products from its six plants to three waste disposal sites.  The chemical wastes that will be hauled can be hazardous to humans and the environment if they leak.  A number of towns and communities in the region where the plants are located prohibit hazardous materials from being shipped through their municipal limits.  Shipments must be handled carefully and transported at reduced speeds and traverse circuitous routes.  Calculations for cost of shipping a barrel from each of the six plants to each of the three disposal sites is:

                                                                        WASTE DISPOSAL SITE

                           Plant                   Whitewater                              Los Canos                      Duras

                           Kingsport             $12                                         $15                                 $17

                          Danville                  14                                            9                                    10

                           Macon                   13                                           20                                    11

                          Selma                    17                                           16                                    19

                          Columbus                7                                           14                                    12

                          Allentown               22                                          16                                     18

The plants generate the following amounts of waste products each week:

PLANT                               WASTE PER WEEK (bbl)

Kingsport                               35

Danville                                 26

Macon                                   42

Selma                                   53

Columbus                             29

Allentown                              38

The three waste sites of Whitewater, Los Canos and Duras can accommodate a maximum of 65, 80, and 105 barrels per week respectively.

The manager is considering using each of the plants and waste disposal site as intermediate shipping points.  Trucks would be able to drop a load at a plant or disposal site to be picked up and carried to the final destination by another truck and vice versa.  Stateline would not incur any handling costs because Polychem has agreed to take care of all local handling of the waste materials at the plants and the waste disposal sites.  The only cost Stateline incurs is the actual transportation cost.  The manager wants to consider the possibility that it may be cheaper to drop and pick up loads at intermediate points rather than ship them directly.  The estimated shipping costs per barrel between each of the six plants is:

PLANT                        Kingsport               Danville          Macon             Selma       Columbus         Allentown

Kingsport                      $____                   $6                   $4                    $9              $7                      $8

Danville                        $6                         _____              11                    10              12                       7

Macon                          $5                          11                  _____                3                7                       15

Selma                           $9                          10                   3                      ____          3                        16

Columbus                     $7                         12                    7                      3               ____                   14

Allentown                     $8                           7                    15                    16               14                      ____

the estimated shipping cost per barrel between each of the three waste disposal sites is:

WASTE DISPOSAL SITE                       WHITEWATER            LOS CANOS            DURAS

Whitewater                                              $______                        $12                          $10

Los Canos                                               $12                                $___                        $15

Duras                                                      $10                                $15                           $___

The manager wants to determine the shipping routes that will minimize Stateline's total cost in order to develop a contract proposal to submit to Polychem for waste disposal.  She wants to know if it would be cheaper to ship directly from the plants to the waste site or if she should drop and pick up some loads at the various plants and waste sites.  Develop a model to assist the manager and solve the model to determine the optimal routes.

SHOW THE WORK!