Let us consider the case of LaRosa Machine Shop (LMS). LMS is studying where to locate its tool bin facility on the shop floor. The locations of the five production stations appear in the figure below. Y 0 Subassembly 2 5 Tabrication Assembly 4 Paint Subassembly 1 X 3 4 5 Station v Demand Fabrication 1 4 11 23 Paint 2 Subassembly 1 2.5 2 Subassembly 2 3 5 6 Assembly 1 4. 16 In an attempt to be fair to the workers in each of the production stations, management has decided to try to find the position of the tool bin that would minime the sum of the distances from the tool binto the five production stations. We define the following decision variables Xhorizontal location of the tool in Yvertical location of the tool bin We may measure the straight ine distance from a station to the tool bin tocated at (x) by using Euclidean (straight-line) distance. For example, the distance from fabrication located at the coordinates (14) to the tool din located at the coordinates (x, y) is given by VOX -1) + (-4) (0) Suppose we know the average number of daily trips made to the tool bin from each production station. The average number of trips per day ace j1 for fabrication, 23 for Paint. 14 for Subassembly 1.6 for Subassembly, and 16 for Assembly, it seems as though we would want the tool bin closer to those stations with high average numbers of trips. Develop a new unconstrained model that minimizes the sum of the demand-weighted distance defined as the product of the demand measured in number of trips) and the distance to the station Mr (D) doive the model you developed in part() (Round your answers to three decimal places) exy Comment on the differences between the unweighted distance solution given of X = 2.230 and 3.349 and the demand-weighted solution The demand weighted solution shifts the optimal location towards the Sale sation Let us consider the case of LaRosa Machine Shop (LMS). LMS is studying where to locate its tool bin facility on the shop floor. The locations of the five production stations appear in the figure below. Y 0 Subassembly 2 5 Tabrication Assembly 4 Paint Subassembly 1 X 3 4 5 Station v Demand Fabrication 1 4 11 23 Paint 2 Subassembly 1 2.5 2 Subassembly 2 3 5 6 Assembly 1 4. 16 In an attempt to be fair to the workers in each of the production stations, management has decided to try to find the position of the tool bin that would minime the sum of the distances from the tool binto the five production stations. We define the following decision variables Xhorizontal location of the tool in Yvertical location of the tool bin We may measure the straight ine distance from a station to the tool bin tocated at (x) by using Euclidean (straight-line) distance. For example, the distance from fabrication located at the coordinates (14) to the tool din located at the coordinates (x, y) is given by VOX -1) + (-4) (0) Suppose we know the average number of daily trips made to the tool bin from each production station. The average number of trips per day ace j1 for fabrication, 23 for Paint. 14 for Subassembly 1.6 for Subassembly, and 16 for Assembly, it seems as though we would want the tool bin closer to those stations with high average numbers of trips. Develop a new unconstrained model that minimizes the sum of the demand-weighted distance defined as the product of the demand measured in number of trips) and the distance to the station Mr (D) doive the model you developed in part() (Round your answers to three decimal places) exy Comment on the differences between the unweighted distance solution given of X = 2.230 and 3.349 and the demand-weighted solution The demand weighted solution shifts the optimal location towards the Sale sation
