Due to Increased Sales, a Company Is Considering Building Three

question 68

Essay

Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision.

The table below shows the cost ($ per item) for shipping from each DC to each region.
Region
$$\begin{array} { | c | c | c | c | c | } \hline \mathrm { DC } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } \\\hline 1 & 1 & 3 & 3 & 2 \\\hline 2 & 2 & 4 & 1 & 3 \\\hline 3 & 3 & 2 & 2 & 3 \\\hline\end{array}$$ The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units.
-Write the objective function for this problem.

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Definitions:

Correlation Matrix

A table showing correlation coefficients between variables, indicating the strength and direction of relationships.

Durbin-Watson Test

A statistical test used to detect the presence of autocorrelation at lag 1 in the residuals from a regression analysis.

First-Order Autocorrelation

The correlation between values in a series and their immediate predecessors, often used to detect patterns or trends in time series data.

Durbin-Watson Statistic

Utilized to check for the presence and intensity of autocorrelation between residuals in linear regression models.