MS $3053-$ Case Report #$1$

Unless other arrangements are made and approved by the instructor, your submission for this case report is due, without exception, by $5$:$00$ p$.$m$.$ CDT on November $13,2024.$

Nortex Chemicals, Inc. is involved in the fossil fuel reclamation industry in the Texas Panhandle. One of its primary operations involves purchasing large tanks, each roughly the size of a rail car, of particular byproducts from natural gas processing. It purifies these byproducts into a usable form and then resells the tanks to industrial customers. Presently, the company is in possession of $18$ tanks in Canadian, $16$ tanks in Spearman, and $12$ tanks in Adrian. Each tank must be shipped by truck to one of its processing centers, which are located in Dalhart, Pampa, and Tulia, for further refinement. The cost of shipment depends roughly on distance, but also takes into account the driver's salary $($which is higher for routes that are difficult to navigate in a truck$),$ the cost of fuel, and hazardous materials permit fees. The following table provides the per$-$tank costs $($in dollars$)$ of shipping from the suppliers to the processing centers.

$\backslash$table$[[,$Dalhart,Pampa,Tulia$],[$Canadian$,581,249,588],[$Spearman$,487,531,665],[$Adrian$,425,423,372]]$

While the three processing centers are capable of processing any number of tanks, the number transported to Pampa must equal the number transported to Tulia, due to an existing greement between Nortex and its transportation provider.

After processing, the tanks will be shipped to customers in Stratford, Borger, Perryton, Clarendon, Friona, and Hartley. The cost of shipment depends on metrics similar to those mentioned above. The following table provides the total costs $($in dollars$)$ of shipping one tank from the processing centers to the customers. Note that certain combinations of processing facilities and customers are not possible due to factors such as regional non$-$compete clauses; these are indicated by dashes.

$\backslash$table$[[,$Stratford,Borger,Perryton,Clarendon,Friona,Hartley$],[$Dalhart$,127,155,227,-,228,-],[$Pampa$,532,-,353,309,-,484],[$Tulia$,-,300,-,208,131,256]]$

The current customer demands are: Stratford, $9$ tanks; Borger, $10$; Perryton, $8$; Clarendon, $7$; Friona, $11$; and Hartley, $8.$

Due to a competitor's bankruptcy, Nortex has also acquired $10$ tanks of processed byproducts that are currently located at a yard in Clayton, New Mexico. Because these tanks are already processed, a third$-$party company can ship these tanks directly to customers in Stratford $($at a cost of $$677$ per tank$),$ Borger $($at a cost of $$763$ per tank$),$ and Hartley $($at a cost of $$639$ per tank$)$ without needing to go through one of the processing centers.

Nortex has partnered with you to conduct an analysis and to make a recommendation that will help it to reduce costs by optimizing the performance of its natural gas byproducts distribution network.

MS $3053($Panda$)-$ Case Report #$1($Fall $2024)$

In summary, you must develop a linear programming model for this optimization problem, perform an appropriate analysis using Excel, recommend the number of tanks Nortex should transport along each possible route, and present a formal business report discussing your findings and conclusions.

To receive full credit for this case report, your submission must contain the following items. You may deviate from the given order if you desire; however, it is your responsibility to ensure that all required items are included in your submission and that the order is logical$.$ All items must be typed unless otherwise specified. As your submission will presumably contain multiple files $($e$.$g$.,$ a document containing your write$-$up and an Excel file containing the supporting Solver output$),$ please do not compress or archive the files into a format such as $.$zip. Cloud$-$based files will not be scored, as these cannot be annotated. Submissions or parts of submissions that are not viewable, are in a file format that cannot be opened, are not in the English language, or are otherwise incomprehensible will not be scored.

A cover page with the names and UTSA IDs $($abc$123)$ of all group members. You may work individually or in a group consisting of a maximum of six students. No names may be added to this cover page after submission, and individuals whose names have been handwritten will not be considered part of the group.

An executive summary of no more than one page summarizing the problem, the process used to solve the problem, and the major findings and recommendations based on your analysis.

A network diagram that illustrates the model for this scenario. This includes all origins and their capacities, all transshipment nodes, all destinations and their demands, the possible connections with associated decision variables, and their respective costs. The diagram must be fully labeled. The diagram may be hand$-$drawn, as long as it is legible.

A linear programming model used to