Pickson Luthiers Corporation Is Studying Where to Locate a Phone

Essay

Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}\hline \begin{array}{l}\text { Pickson Luthiers } \\\text { Corporation }\end{array} & \text { Phone Recharging Points } & & \\\hline & & & \\\hline \text { Data } & & & \\\hline \\\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \\\hline \text { Measurements } & 2 & 5 & 27 \\ \hline \text { Paint } & 1 & 3 & 12 \\\hline \text { Electricals } & 4 & 2 & 25 \\\hline \text { Testing } & 3.5 & 5 & 5 \\\hline \text { Packaging } & 3 & 3 & 7 \\\hline & & & \\\hline \text { Maximum } & 4 & 5 &\\\hline\end{array}$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
From the above table, provide the objective function for the best location of the charging point. What kind of solution technique from Solver can be used to make the optimization model based on the data?