Managerial Decision Analytics
Jaycee’s department store chain is planning to open a new store. It needs to decide how to allocate the 100,000 square feet of available floor space among seven departments. The accompanying data includes the expected performance of each department per month, in terms of square feet (sf). The company has gathered $20 million to invest in floor stock. The risk column is a measure of risk associated with investment in floor stock based on past data from other stores and accounts for outdated inventory, pilferage, breakage, and so on. For instance, electronics loses 24% of its total investment, furniture loses 12% of its total investment, and so on. The amount of risk should be no more than 10% of the total investment. Assume that it is not required that the entire available floor space be used. Answer parts a and b below.
a. Develop a linear optimization model to maximize profit.
Define variable names to use for the square feet for each department. For the purposes of this solution process, use E for square feet of Electronics, F for square feet of Furniture, M for square feet of Men’s clothing, C for square feet of Clothing, J for square feet of Jewelry, B for square feet of Books, and A for square feet of Appliances.
Next, identify the objective function. In this case, the objective function is the sum of the square feet of each department times their respective expected profits. Write the objective function.
maximum profit.
Next, write each constraint as a mathematical equation or inequality. In this case, the constraints are the amount of available floor space, investment capital, the maximum risk, and the minimum and maximum floor space for each department.
Write the constraint for the amount of floor space that can be used.
Write the constraint for the amount of investment capital that can be used.
Calculate the risk per square foot of floor space used by multiplying the risk as a percentage of money invested by the investment per square foot.
