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TCORP produces tomato sauce at three plants. This product can be shipped directly to the company's two customers or it can first be shipped to the company's two warehouses and then to the customers. The figure below is a network representation of TCORP's problem. Nodes 1, 2, and 3 represent the plants (these are the origins, denoted by S for supplier), nodes 4 and 5 represent the warehouses (these are the transshipment points, denoted by T), and nodes 6 and 7 represent the customers (these are the destinations, denoted by D). Note that some shipments are allowed among plants, among warehouses, and among customers. Also, some arcs have arrows on both ends. This means that flow is allowed in either direction. The cost of producing the product is the same at each plant, so TCORP is concerned with minimizing the total shipping cost incurred in meeting customer demands. The production capacity of each plant (in tons per year) and the demand of each customer are shown in the figure above. For example, plant 1 (node 1) has a capacity of 400, and customer 1 (node 6) has a demand of 800. In addition, the cost (in thousands of dollars) of shipping a ton of the sauce between each pair of locations is listed in the table below, where a blank indicates that TCORP cannot ship along that arc. We also assume that at most 400 tons of the product can be shipped along any arc. This is the common arc capacity. The goal of this report is to propose a shipping strategy for TCORP that minimizes transportation costs. According to the rubric below, the report should include 4 sections, see below for important information about what to include in each section: Introduction: Provide background and motivation about the problem you are analyzing. Why is it important for TCORP to minimize transportation costs? Model: Include the algebraic decision model, clearly identifying decision variables, objective function, and constraints. Explain each of the components. Optimal Solution: Present the shipping plan that you obtained by solving your algebraic model in Excel. Sensitivity Analysis: Present shadow prices and reduced costs, along with their ranges, where applicable. Discuss their implications for TCORP. What can TCORP change in terms of capacity or demand.

TCORP produces tomato sauce at three plants. This product can be shipped directly to the company's two customers or it can first be shipped to the company's two warehouses and then to the customers. The figure below is a network representation of TCORP's problem. Nodes 1, 2, and 3 represent the plants (these are the origins, denoted by S for supplier), nodes 4 and 5 represent the warehouses (these are the transshipment points, denoted by T), and nodes 6 and 7 represent the customers (these are the destinations, denoted by D). Note that some shipments are allowed among plants, among warehouses, and among customers. Also, some arcs have arrows on both ends. This means that flow is allowed in either direction.

The cost of producing the product is the same at each plant, so TCORP is concerned with minimizing the total shipping cost incurred in meeting customer demands. The production capacity of each plant (in tons per year) and the demand of each customer are shown in the figure above. For example, plant 1 (node 1) has a capacity of 400, and customer 1 (node 6) has a demand of 800. In addition, the cost (in thousands of dollars) of shipping a ton of the sauce between each pair of locations is listed in the table below, where a blank indicates that TCORP cannot ship along that arc. We also assume that at most 400 tons of the product can be shipped along any arc. This is the common arc capacity.

The goal of this report is to propose a shipping strategy for TCORP that minimizes transportation costs. According to the rubric below, the report should include 4 sections, see below for important information about what to include in each section:

Introduction: Provide background and motivation about the problem you are analyzing. Why is it important for TCORP to minimize transportation costs?

Model: Include the algebraic decision model, clearly identifying decision variables, objective function, and constraints. Explain each of the components.

Optimal Solution: Present the shipping plan that you obtained by solving your algebraic model in Excel.

Sensitivity Analysis: Present shadow prices and reduced costs, along with their ranges, where applicable. Discuss their implications for TCORP. What can TCORP change in terms of capacity or demand.

Added by Beatriz C.

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