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# Supply Chain Homework Problems

Problems 1 – 7 require use of an excel file called “FoodDesertData.xlsx”. The data provide the distance (in miles) between a set of Capital Region cities. For each city, the number of people, the number of children, and the number of seniors who have low access to a grocery store are given. This data was based on the 2010 data sources in the USDA's Food Environment Atlas https://www.ers.usda.gov/data‐ products/food‐environment‐atlas/ In addition, for each city, the costs to build a small corner grocery store (in millions of dollars) is given.

Problem 1.

Formulate an integer linear programming model to find the minimum facility costs of locating a small corner grocery store within a 15 mile distance of all people in the Capital Region who have low access to a grocery store. To receive full credit, be sure to define all notation, and classify all notation as sets, parameters, or decision variables. For each objective function and constraint, provide a brief description of its meaning in words. If you use set notation, also provide the specific values for the sets and parameters for this exercise (i.e., what is the specific collection of items in the set, what are the numeric values for all the parameters). (10 points)

Problem 2.

Solve your optimization model formulated in part 1. Report the number of small corner grocery stores built, their locations, and the total facility costs of your network design. (5 points)

Problem 3.

How does your model in Part 1, and your solution in Part 2, change if we focus on the Capital Region’s children with low access to a grocery store, rather than all people with low access to a grocery store? (4 points)

Problem 4.

Now suppose that the Capital Region has received a grant to reimburse residents’ transportation costs from their home to the corner shop and back to their home. Reimbursement is at the rate of \$0.50 per mile per person‐trip. In this scenario, the objective is to minimize the total cost of building small corner grocery store locations, plus the Annual transportation costs of all people in the Capital Region who have low access to a grocery store. Assume each person makes 12 grocery trips per year. Also, assume each small corner groceries stores, regardless of location, has a capacity of 800,000 person‐trips per year.

Formulate a mixed integer linear programming model to determine the most cost effective way to locate and allocate residents to small corner grocery stores. To receive full credit, be sure to define and classify all notation as sets, parameters, and decision variables. For each objective function and constraint, provide a brief description of its meaning in words. If you use set notation, also provide the specific values

for the sets and parameters for this exercise (i.e., what is the specific collection of items in the set, what are the numeric values for all the parameters). (12 points)

Problem 5.

Solve your optimization model formulated in part 4. Report the number of small grocery stores built, their locations, the allocation of each city’s grocery trips to store locations, and your total network design costs. Also, break down your network design costs into (a) total facility costs, and (b) total transportation costs. (5 points)

Problem 6

Compare your network design strategy in part 2 to your network design strategy in part 5. Comment on whether your facility location decisions (i.e., where you decide to locate a corner grocery store) are the same or different. Briefly explain why. (4 points)

Problem 7.

How does your model in Part 4, and your solution in Part 5, change if we focus on the Capital Region’s children rather than all people with low access? (4 points).

Problem 8: (10 points)

1. Explain in your own words the impact of variability on supply chains. (3 points)
2. Provide one specific current event example of the influence of variability in supply chain performance. To receive full credit, you should describe in your own words what the variability is and how it influenced supply chain decision making and performance. Provide the citation of the information source (e.g., website, journal article, newspaper article, and video). (4 points)
3. Identify one way to reduce the variability in the example you provided in part b. (3 points) Problem 9

In this class, we covered the following topics: Demand Forecasting, Aggregate Planning, Planning and Coordinating in a Supply Chain, Buffering against Variability, Inventory Management, Network Design, and Transportation Planning. Choose two of these topics and explain in your own words how the two concepts are related. Also, briefly describe the trade‐offs associated with decisions and/or objectives between your chosen two topics. (5 points)

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