You work as an operations consultant for a textile company. Your client has a well-established distribution system in the US. The company has hundreds of stores and several distribution centers. You will work with your client to determine the best way to distribute goods from distribution centers to retail stores.

The following information will guide you in analyzing the facility location decisions.

• The company has 328 stores in 14 different states. See the locations in the Excel file.

• The company has 3 distribution centers: Salisbury NC, Ft. Worth TX and Salt Lake City UT.

• For each distribution center, information on

  • estimated monthly capacity (in terms of number of truckloads of goods that can be shipped), and

  • the distance between the distribution center locations and store locations

are provided in the Excel file.

• Your client tells you that the transportation cost will be $1.45 per mile per truckload.

• Following Zara’s strategy of “fast fashion” or fast-response supply chain, your client makes three deliveries to each store every week. Each delivery involves only one truckload. That is, a total of three truckloads of goods are shipped from the distribution centers to each retail store each week. In your analysis, assume that a month is only four weeks; this brings monthly store demand to 3×4=12 truckloads per month.

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You will analyze the information provided, build spreadsheet models, and use optimization to make a recommendation to your client on which distribution centers should supply which retail stores.

NOTE: SHOW ALL YOUR WORK.

You first analyze the cost of logistics network. For this problem, you will formulate a transportation problem and determine the monthly shipment plan that minimizes the total transportation costs. Your client is not familiar with optimization models. You must clearly explain your approach to computing the minimum transportation. To do so,

1. (3 points) Clearly define your decision variables in English. How many decision variables do you have?

NOTE: In your Solver model, the unit of shipment should be number of truckloads.

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1. (2 points) What is the objective function in this problem? Explain how you would compute the objective function (in English). The mathematical expression for the objective function is very long, so do NOT explicitly state the mathematical formula.

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1. (4 points) Clearly explain the constraints (in English). What type of constraints do you have? Do NOT provide the mathematical formula for the constraints.

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1. (2 point) What are the sign and type restrictions in optimization problems? Are there any sign or type restrictions in this problem? Clearly explain why or why not.

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1. Prepare a spreadsheet to determine the optimal production plan using Excel Solver.

1. (2 points) Provide a screenshot of your spreadsheet model. The screenshot should show all the cells involved in formulating the optimization problem. NOTE: Do not copy and paste your spreadsheet to your answer report as an Excel object. Instead, capture a screenshot in Excel and paste this as an image.

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1. (2 points) Provide a screenshot of your spreadsheet with the formula view. You can switch from normal view to formula view in Excel by clicking the CTRL and ~ keys on your keyboard simultaneously.

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1. (2 points) Prepare the Solver model by logging all the information to the Solver Parameters window in Excel. Provide a screenshot of the Solver Parameters window in Excel.

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NOTE: Ignore all type restrictions in this problem. Do not enforce your decision variables to be integer while using Excel Solver. If you formulate the problem correctly, the optimal solution provided by the Solver will be in whole numbers even without the type restrictions.

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1. (2 points) Finally, solve the optimization problem using the Simplex LP method in Excel Solver. What is the optimal solution, i.e. the optimal objective function value and the optimal values of decision variables?