© Anita Lee-Post Facility Location Part 2 by Anita Lee-Post

© Anita Lee-Post Center-of-gravity method 1.Establish relative distances between existing facilities by placing them on a coordinate grid system; 2.Use the following formulas to find the X and Y coordinates for the location of the new facility: 1.Establish relative distances between existing facilities by placing them on a coordinate grid system; 2.Use the following formulas to find the X and Y coordinates for the location of the new facility:

© Anita Lee-Post Center-of-gravity method formulas C x = X coordinate of center of gravity C y = X coordinate of center of gravity d ix = X coordinate of the ith location d iy = Y coordinate of the ith location V i = volume of goods moved to or from ith location

© Anita Lee-Post Center of gravity method example Three automobile showrooms (Bowling Green, Elizabethtown, and Morehead) are located according to the following grid which represents coordinate locations for each showroom in Kentucky. Monthly demand of Z- Mobiles at each showroom is also given below. Three automobile showrooms (Bowling Green, Elizabethtown, and Morehead) are located according to the following grid which represents coordinate locations for each showroom in Kentucky. Monthly demand of Z- Mobiles at each showroom is also given below. Question: What is the best location for a new Z-Mobile warehouse/temporary storage facility considering only distances and quantities sold per month? XY Bowling Green (100,200) Elizabethtown (250,580) Morehead (790,900) (0,0) ShowroomNo. of Z-Mobiles sold per month Bowling Green Elizabethtown Morehead

© Anita Lee-Post Center-of-gravity example continued XY Bowling Green (100,200) Elizabethtown (250,580) Morehead (790,900) (0,0) To begin, you must identify the existing facilities on a two-dimensional plane or grid and determine their coordinates. You must also have the volume information on the business activity at the existing facilities. ShowroomNo. of Z-Mobiles sold per month Bowling Green Elizabethtown Morehead

© Anita Lee-Post Center-of-gravity example continued XY Bowling Green (100,200) Elizabethtown (250,580) Morehead (790,900) (0,0) You then compute the new coordinates using the formulas: New location Lexington

© Anita Lee-Post Transportation method using Excel Solver 1.Set up the transportation table with n rows (factories) and m columns (warehouse) showing: Demand requirements of each warehouse or destination; Demand requirements of each warehouse or destination; Supply availability at each factory or source; Supply availability at each factory or source; Shipping costs per unit of goods from each source to each destination. Shipping costs per unit of goods from each source to each destination. 1.Set up the transportation table with n rows (factories) and m columns (warehouse) showing: Demand requirements of each warehouse or destination; Demand requirements of each warehouse or destination; Supply availability at each factory or source; Supply availability at each factory or source; Shipping costs per unit of goods from each source to each destination. Shipping costs per unit of goods from each source to each destination.

© Anita Lee-Post Transportation method using Excel Solver 2.Set up a candidate solution table with n rows and m columns showing: Total units supplied from each source; Total units supplied from each source; Total units shipped to each destination; Total units shipped to each destination; The volume of goods to be shipped from each source to each destination (i.e., the shipping schedule/configuration). The volume of goods to be shipped from each source to each destination (i.e., the shipping schedule/configuration). 2.Set up a candidate solution table with n rows and m columns showing: Total units supplied from each source; Total units supplied from each source; Total units shipped to each destination; Total units shipped to each destination; The volume of goods to be shipped from each source to each destination (i.e., the shipping schedule/configuration). The volume of goods to be shipped from each source to each destination (i.e., the shipping schedule/configuration).

© Anita Lee-Post Transportation method using Excel Solver 3.Set up a cost calculation table Detailed shipping costs from each source to each destination; Detailed shipping costs from each source to each destination; Total cost of the shipping schedule. Total cost of the shipping schedule. 3.Set up a cost calculation table Detailed shipping costs from each source to each destination; Detailed shipping costs from each source to each destination; Total cost of the shipping schedule. Total cost of the shipping schedule.

© Anita Lee-Post Transportation method example Modified Center-of-Gravity example Monthly demand of Z-Mobiles at three existing automobile showrooms (Bowling Green, Elizabethtown, and Morehead) is: Monthly demand of Z-Mobiles at three existing automobile showrooms (Bowling Green, Elizabethtown, and Morehead) is: Monthly supply of Z-Mobiles at two new factories to be considered (Lexington, and Louisville) is: Monthly supply of Z-Mobiles at two new factories to be considered (Lexington, and Louisville) is: Modified Center-of-Gravity example Monthly demand of Z-Mobiles at three existing automobile showrooms (Bowling Green, Elizabethtown, and Morehead) is: Monthly demand of Z-Mobiles at three existing automobile showrooms (Bowling Green, Elizabethtown, and Morehead) is: Monthly supply of Z-Mobiles at two new factories to be considered (Lexington, and Louisville) is: Monthly supply of Z-Mobiles at two new factories to be considered (Lexington, and Louisville) is: ShowroomNo. of Z-Mobiles sold per month Bowling Green Elizabethtown Morehead FactoryNo. of Z-Mobiles supplied per month Lexington Louisville

© Anita Lee-Post Transportation method example continued Monthly supply of Z-Mobiles at two existing factories (Denver, and Detroit) is: Monthly supply of Z-Mobiles at two existing factories (Denver, and Detroit) is: Cost to transport an Z-mobile from each factory to each showroom is: Cost to transport an Z-mobile from each factory to each showroom is: Monthly supply of Z-Mobiles at two existing factories (Denver, and Detroit) is: Monthly supply of Z-Mobiles at two existing factories (Denver, and Detroit) is: Cost to transport an Z-mobile from each factory to each showroom is: Cost to transport an Z-mobile from each factory to each showroom is: FactoryNo. of Z-Mobiles supplied per month Denver Detroit From/To Bowling GreenElizabethtown Morehead Denver Detroit5025 Lexington Louisville Question: Which is a better location for a new Z-Mobile factory: Lexington or Louisville?

© Anita Lee-Post Transportation method using Excel Solver 1.Set up the transportation table for Lexington ABCDE 1From/ToBowling GreenElizabethtownMoreheadSupply 2Denver Detroit Lexington Requirements What is the total transportation cost if the new factory is located in Lexington?

© Anita Lee-Post Transportation method using Excel Solver 2.Set up a candidate solution table with formulae to compute the total units of Z- mobile shipped to each showroom and the total units of Z-mobile supplied from each factory: ABCDE 7 Candidate SolutionTotal Shipped 8Denver=SUM(B8:D8) 9Detroit=SUM(B9:D9) 10Lexington=SUM(B10:D10) 11 Total Supplied=SUM(B8:B10)=SUM(C8:C10)=SUM(D8:D10)

© Anita Lee-Post Transportation method using Excel Solver 3.Set up a cost calculation table with formulae to compute the detailed shipping costs from each factory to each showroom and the total shipping costs of the entire shipping schedule: ABCDE 13 Cost Calculations 14Denver=B8*B2=C8*C2=D8*D2 15Detroit=B9*B3=C9*C3=D9*D3 16Lexington=B10*B4=C10*C4=D10*D4 17Total cost=SUM(B14:B16)

© Anita Lee-Post Transportation method using Excel Solver Access Excel Solver Select Tools and then Solver from the Excel menu Select Tools and then Solver from the Excel menu Access Excel Solver Select Tools and then Solver from the Excel menu Select Tools and then Solver from the Excel menu

© Anita Lee-Post Transportation method using Excel Solver If Solver is not found at that location, then:If Solver is not found at that location, then: Select Tools and then Add-In from the Excel menu Select Tools and then Add-In from the Excel menu Select Solver Add- in from the Add- Ins Window Select Solver Add- in from the Add- Ins Window If Solver is not found at that location, then:If Solver is not found at that location, then: Select Tools and then Add-In from the Excel menu Select Tools and then Add-In from the Excel menu Select Solver Add- in from the Add- Ins Window Select Solver Add- in from the Add- Ins Window

© Anita Lee-Post Transportation method using Excel Solver Set parameters in the Solver Parameters windowSet parameters in the Solver Parameters window Target cell Target cell Minimization problem Minimization problem Changing cells Changing cells Constraints Constraints Click on the “Options” button to set solver optionsClick on the “Options” button to set solver options Set parameters in the Solver Parameters windowSet parameters in the Solver Parameters window Target cell Target cell Minimization problem Minimization problem Changing cells Changing cells Constraints Constraints Click on the “Options” button to set solver optionsClick on the “Options” button to set solver options

© Anita Lee-Post Transportation method using Excel Solver Set options in the Solver Options windowSet options in the Solver Options window Assume Linear Model Assume Linear Model Assume Non- Negative Assume Non- Negative Click “OK” to return to the Solver Parameter windowClick “OK” to return to the Solver Parameter window Set options in the Solver Options windowSet options in the Solver Options window Assume Linear Model Assume Linear Model Assume Non- Negative Assume Non- Negative Click “OK” to return to the Solver Parameter windowClick “OK” to return to the Solver Parameter window

© Anita Lee-Post Transportation method using Excel Solver Click “Solve” in the Solver Parameters window for solver resultsClick “Solve” in the Solver Parameters window for solver results Select “Keep Solver Solution” in the Solver Results windowSelect “Keep Solver Solution” in the Solver Results window Click “OK” to return to the spreadsheetClick “OK” to return to the spreadsheet Click “Solve” in the Solver Parameters window for solver resultsClick “Solve” in the Solver Parameters window for solver results Select “Keep Solver Solution” in the Solver Results windowSelect “Keep Solver Solution” in the Solver Results window Click “OK” to return to the spreadsheetClick “OK” to return to the spreadsheet

© Anita Lee-Post Transportation method using Excel Solver Shipping schedule Lexington cost

© Anita Lee-Post Transportation method using Excel Solver 1.Make a copy of the Lexington worksheet by selecting Edit and then Move or Copy sheet from the Excel menu 2.Make sure the “Create a copy” option is checked in the Move or Copy window 3.Click “OK” 1.Make a copy of the Lexington worksheet by selecting Edit and then Move or Copy sheet from the Excel menu 2.Make sure the “Create a copy” option is checked in the Move or Copy window 3.Click “OK” What is the total transportation cost if the new factory is located in Louisville?

© Anita Lee-Post Transportation method using Excel Solver 1.Set up the transportation table for Louisville 2.Access Excel Solver as before to solve the above transportation problem 1.Set up the transportation table for Louisville 2.Access Excel Solver as before to solve the above transportation problem ABCDE 1From/ToBowling GreenElizabethtownMoreheadSupply 2Denver Detroit Louisville Requirements

© Anita Lee-Post Transportation method using Excel Solver Shipping schedule Louisville cost Conclusion: It is cheaper to locate in Lexington (a saving of $ = $16000).