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bpman18

Course: INDE 6370, Fall 2008
School: U. Houston
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for BLOCPLAN Windows Introduction BLOCPLAN is a facility layout system that has been developed at the Industrial Engineering Department of the University of Houston for PC personal computer systems. Figure 1. Credits Screen for BLOCPLAN for Windows The program generates and evaluates block type layouts in response to user supplied data. It can be used for single story layouts, or multi-story, multi-site...

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for BLOCPLAN Windows Introduction BLOCPLAN is a facility layout system that has been developed at the Industrial Engineering Department of the University of Houston for PC personal computer systems. Figure 1. Credits Screen for BLOCPLAN for Windows The program generates and evaluates block type layouts in response to user supplied data. It can be used for single story layouts, or multi-story, multi-site problems. BLOCPLAN uses a "banding" procedure to develop layouts. This permits a large range of possible layouts for a problem. For a nine department problem, the number of possible layouts is close to 20 million, and for a 15 department layout there are more than 2.6 X 1013 possibilities. Each department will also be rectangular in shape. The structure that holds the departments will also be rectangular in shape, and the user may select the length/width ratio of the structure. There are several scoring procedures that may be used to evaluate a layout. The manual explains how the current version is used. BLOCPLAN-WIN is the name of the current version of BLOCPLAN. 1 Figure 2. Introduction Screen Data Input The system will first ask if a new problem is to be entered or if an existing problem is to be entered. 2 Figure 3. - Problem Source Screen The user will click on his/her choice. If an existing problem choice is made, a list of the saved problems will be shown, and the user will click on the problem name, and the data concerning the saved problem will then be entered. For a new problem, the screen shown in Figure 4 will be displayed. The user would then type in the name of each department (8 characters maximum) in the layout, and the area of each of them. BLOCPLAN can handle a maximum of 18 departments. When all departments and their areas have been entered, the user would click on the OK button. Figure 4. Department and Area Information Screen Figure 5 shows this display for an example problem. The total area for all the departments, the average department area, and the standard deviation of the department areas are calculated by the system and displayed The data in Figure 5 was taken from "Facilities Planning" by Tompkins and White, 1984. The user may change any data in the list of departments by simply changing the data on the screen. the cursor is placed on the screen in the proper position and the data entered. 3 Figure 5. Example Problem Data Relationship Data BLOCPLAN uses the relationship codes described by Muther in "Systematic Layout Planning", (Muther 1973, CBI Publishing, Boston, Mass). Figure 6 shows the screen display after the user has furnished the codes for each of the departmental relationships. This chart is called a Relationship Chart. The bottom of the screen gives a legend of acceptable codes and their definitions. An "A" indicates that it is absolutely essential that the two departments having this code be adjacent. An "E" indicates that it is essential etc. The "X" code indicates that it is undesirable. BLOCPLAN uses adjacencies for one type of layout analysis. Figure 7 gives the numeric worth of each of these codes. The user can change any of these values 4 Figure 6. - Relationship Chart Figure 7. Numeric Values For Relationship Codes 5 The numeric worth of each department is found by summing all of the numeric codes associated with the department. For example, from Figure 6, the PRESS department has two "O"s, and four "U"s associated it. The BLOCPAN numeric worth of these associations would be 2. (2 X 1) + (4 X 0). These scores for all departments in the example are shown in Figure 8. Figure 8. - Numeric worth of each department Length/Width Ratio The ratio of the length to the width of the facility that will contain the departments can be selected by the user. Figure 9 shows the display that is presented that permits this selection. There are five "selections" that are given. Selections 1,2,3, and 4 are standard L/W ratios. Selection 1 is 1.35/1, selection 2 is 2/1, selection 3 is 1/1, and selection 4 is 1/2. The user can choose any of these by clicking on the desired selection. If the user chooses selection 5, he/she will be asked for the desired L/W ratio. The user inputs the desired values of the L/W ratio of the facility that will contain the departments. Once the desired ratio has been selected, BLOCPLAN will calculate the length and the width of the facility outline so that it will have the required area to contain the departments. 6 contain the departments in the problem. Figure 9. - Screen presented during selection of Length/Width Ratio for layout. Material Handling Information BLOCPLAN allows the inclusion of Material Handling information in the layout analysis. This information is furnished by listing moves per time period between departments into a From/To Matrix. Figure 10 shows the format for giving material handling information. 7 Figure 10. - Screen Display for Entering Material Handling Information The user can change or enter new values into the matrix when it is on the screen BLOCPLAN Main Menu The menu of choices in the Main Menu is shown in Figure 11. There are six menu options available to the user. The user clicks on the selection choice to cause execution of the proper option. The user may return to this Main Menu a number of times when working on a layout. It allows him/her to introduce a new problem, to modify data on the current problem, to examine single story layouts, to examine multi-story layouts, to save the data on the current problem, or to exit from BLOCPLAN. After a selection is made from the Main Menu, the user will be presented with new menus and information that pertain to the selection that has been made. Figure 11. - BLOCPLAN Main Menu selections. 8 New Problem (Main Menu Selection #1) If the user wants to introduce a new problem to BLOCPLAN he/she uses Main Menu selection 1. The BLOCPLAN system will respond with the message given in Figure 3. If the user indicates the problem is one that has been stored on the disk, he/she is given a list of the previously stored problems and the user makes the choice of the problem to be entered. The system is asking how the new problem is to be entered. The user makes the appropriate response and the problem data is entered. The steps in data entry are the same as previously discussed beginning on page 1. If the new problem is from disk, the problem data is entered and displayed before the Main Menu is again shown. Edit/Adjust Data Menu (Main Menu Selection #2) When the user selects Main Menu Option 2, it indicates that he/she wishes to change the data that pertains to the current problem. An Edit/Adjust Data Menu will then be presented that contains the options that are available. Figure 12 shows this menu. A user may examine and/or change the department areas, the relationship information, the length to width ratio of the layout area, and the material handling information. He/she can also ask for a relationship chart that is based solely on material handling information, and he/she can restore the original relationship chart when needed. The current L/W ratio and the dimensions of the layout outline are shown in the lower right hand corner of the menu. The number of previously saved layouts is also shown for the problem. If the problem has been loaded from disk, the assigned name of the problem is also shown 9 Figure 12. - Edit /Adjust Data Menu Adjust Area/Relationship Data (Edit/Adjust Data Menu Selection #1) Selection 1 from the Edit/Adjust Data Menu allows the user to change the area and/or the relationship information currently in effect. After this option is selected, the display of Figure 1 appears, and the user is allowed to change any of the department areas. This is followed by the screen displays allowing for changes in the relationship data and the score vectors. When all the required changes are made the display shown in Figure 5 will be given. When the user depresses the enter key, the Edit/Adjust Data Menu is returned to the screen. It should be noted that all layouts that have been previously saved may now be reviewed under this new set of area and/or relationship parameters. Adjust Length/Width Ratio (Edit/Adjust Data Menu Selection #2) A new L/W ratio may be established by selecting menu selection 2 from the Edit/Adjust Data Menu. When this choice is made, the display of Figure 6 is brought to the screen, and the user selects the desired L/W ratio. All layouts currently saved can then be reviewed with the new ratio. After the new ratio is selected the system will return to the Edit/Adjust Data Menu. Review Material Handling Information (Edit/Adjust Data Menu Selection #3) The material handling information can be reviewed and changed, if desired, by using selection 3 from the Edit/Adjust Data Menu. After the selection is entered, the screen display of Figure 9 appears, and the user can inspect and/or modify any of the data. If there is currently no material handling information in the problem, it can be added with this selection. In this case, the screen display would have material handling data, and the user would use the "C" option to indicate a change is required. Use Material Handling Relationship Chart (Edit/Adjust Data Menu Selection #4) This selection will cause BLOCPLAN to develop an alternate REL chart that is based entirely on material handling. The example problem had material handling information that is summarized in Figures 9 and 10. Figure 10 shows the greatest amount of product flow is between departments 2 and 4 (400 unit loads). BLOCPLAN will divide this maximum flow figure by 5.0 to develop product flow values for REL codes A through U. 400/5 = 80. Thus, any product flow between 321 and 400 will be assigned an "A" code. A product flow from 241 to 320 will be assigned an "E", from 161 to 240 an "I", 81 to 160 an "O", and zero to 80 a "U" code. When Edit/Adjust Menu selection 4 is made, BLOCPLAN will make these calculations and assignments depending upon the current material handling information. It will then display the resulting REL chart. Figure 14 shows the REL chart that resulted for the example problem with the material handling information that is summarized in Figures 9 and 10. This REL chart is now the one that BLOCPLAN will use for its scoring calculations. Any layout scores or tables that are developed will use this REL chart. The user may alter any of the REL codes that 10 are in effect by using menu selection 1 in the Edit/Adjust Data Menu. (Adjust REL Info). If the material handling information is changed by using selection 4 in the Edit/Adjust Data Menu , the user will have to then call on this selection again (selection 4) to cause the REL chart to reflect these changes. A message on the screen will indicate if the material handling information is used to develop layouts. Restore Relationship Chart (Edit/Adjust Data Menu Selection #5) The REL chart that the user entered when creating the problem, along with any modifications that have been made to it, may be recalled from memory to replace a MaterialHandling REL chart, by using this menu selection. The chart is recalled from disk and displayed on the screen. It will then be the chart that is used for scoring any layouts. The Relationship Chart that was used will be displayed for any tables or layouts created. Figure 13. - REL chart resulting from menu selection 4 from the Edit/Adjust Data Menu. This REL chart is based entirely on the material handling information that is summarized in Figures 9 and 10. The user may make any changes desired. Return to Main Menu (Edit/Adjust Data Menu Selection #6) When this selection is made, the user transfers from the Edit/Adjust Data Menu and the Menu shown in Figure 11 is placed on the screen. 11 Single Story Layout Menu (Main Menu Selection #3) When the user decides that the layout is to be developed with all departments on the same level he/she uses selection #3 from the Main Menu. After this selection is made the Single Story Layout Menu will be displayed. This menu is shown in Figure 15. Manually Insert Departments (Single Story Menu Selection #1) The user can manually position departments in the layout by using this option. When it is evoked the screen display of Figure 14 appears. Figure 14. - Single Story Layout Menu. 12 Figure 15. - Screen display for manually locating departments. There are nine zones, and each zone may be divided into its left and right side. Department legend is on bottom of screen. BLOCPLAN provides nine zones for locating departments. These zones are designated A through I, and they are arranged in three tiers of three zones each, as can be seen in Figure 15. Each zone can be further divided into its left side or its right side. The layout outline for manual insertion is drawn according to the current L/W ratio. The display in Figure 15 is for a L/W ratio of 1/1. Suppose the user wants to place Dept.1 (RECVING) in the upper left hand side of the layout, and Dept 7 (SHIPPING) next to it on the right. He/she would click on the RECVING choice in the Department scroll at the bottom of the screen, Zone A for the zone choice, and specify that it is to be on the left side of the zone.. He would then click on the "Manually Locate Specified Department" option. He/she would do the same thing for RECVING, placing it in Zone A on the right side. After placing these two departments he would use the "Return" option. These two departments would be placed in those two locations for the rest of the analysis. 13 Figure 16 shows an example layout with these two departments placed in their specified locations. The L/W ratio for this layout was set at 1/1. Figure 16. - Screen display after departments 1 and 7 have been manually located. Adjacency Scoring The layout display shown in Figure 16 is the format that BLOCPLAN uses to display a single story layout that it has created. It has a layout score of .44 assigned to it. BLOCPLAN uses an adjacency criterion to develop this score. The departments that share a boundary in the layout are examined and the numeric value of each of their relationship codes are summed. The total value of all the normalized adjacency score for the layout of Figure 16 is 19/43 = .44 (rounded to two places). A 1.0 would be the highest possible adjacency score. Saving Layouts Figure 16 shows the options that are available to a user when a layout is created. These options are: "Save" to Save a layout, "Analysis" to have a layout Analysis performed, "Exchange" to Exchange departments in the layout, the "Print" option to get a hard copy of the layout being displayed.. BLOCPLAN is capable of saving 20 layouts in the Saved Layout area in memory. When the user uses the Save option, the layout currently on the screen will be stored. If there are currently 20 layouts stored when this option is used, the 20'th layout in memory will be replaced with the one currently on the screen. 14 Layout Analysis A layout analysis for the layout currently on the screen will be performed when the Analysis button is pressed. There are several screen displays of information that will be displayed when this option is used. Figure 17 shows the first display in this sequence. The centroid of each department, along with the department's length, width, and its Length/Width ratio in the current layout is given in the display. Figure 17. - Department Information for Layout in Figure 16 The next display given in the layout analysis shows the adjacencies that have been satisfied for the layout under consideration. The adjacencies that have been satisfied are displayed in upper case. The adjacencies that have not been satisfied are displayed in lower case. The next screen display of information resulting from the layout analysis is shown in Figure 19. This screen displays the results of using another criterion to evaluate a layout. The adjacency criterion that was discussed previously only involved departments that shared boundaries. The criterion that will now be used sums the products of the distance between each pair of departments and their corresponding relationship score. For example, from Figure 17 it can be seen that the centroid of department 1 is (41.78, 192.76). The centroid for department 4 is (185.20, 83.15.). Therefore, the distance between these departments, assuming rectilinear travel, is |41.78 185.20 | + |192.76 83.15 | = 253.03 feet. The relationship matrix (Figure 3) shows that departments 1 and 4 have an "I" relationship code, which has been assigned an equivalent score of 2. Therefore, the product of the distance and the relationship score for these 15 two departments is 253.03 X 2 = 506.06. These values are calculated and summed for each pair of departments in the layout. This sum is shown in Figure 19 at the bottom of the screen, and is 7984.00. The better layouts should have a lower Rel-Dist score. BLOCPLAN normalizes this score. Figure 18. - Adjacencies that have been Satisfied for Layout of Figure 16. 16 Figure 19. - Screen display giving Distance Between Departments for Current Layout BLOCPLAN will create a vector of these 21 distance values from the lowest to the highest. This vector D would be: D = d1 ,d2......, d21 A vector of the 21 values numeric values of the relationship chart for the problem is also developed. This vector S would also go from the lowest to the highest. S = s1, s2, ......., s21 A lower bound for the Rel-Dist score for the layout would be: Lower Bound = d21s1 + d20s2 + .... + d1s21 The highest value in the D vector is multiplied by the lowest value in the S vector, the next highest D value by the next lowest S value, etc.. An upper bound for Rel-Dist score can be found by: Upper Bound = d1s1 + d2s2 +... + d21s21 17 It should be noted that these bounds may not be obtainable for a given layout, and they will vary for each layout for a given set of departments. The lower and upper bounds for the Rel-Dist score for the layout is shown on the right side of the display in Figure 19. The actual distances are used in the D vector instead of the entries in the distance matrix. The entries in the distance matrix have been divided by 10 and integerized to control the size of the matrix for the display. The normalized score for this criterion is also shown on the right side of Figure 19. It is labeled R-SCORE. It is calculated by: R-Score = 1 - (Rel-Dist Score - Lower Bound)/(Upper Bound - Lower Bound) For the example, the value is 1-(7984.00 3802.92)/(10773.38 -3802.92) or 0.40. An RSCORE of 1.0 would be a perfect layout, and a value of zero would be the worst possible. The last display that results from the Analysis option is shown in Figure 20. This is the product flow screen. If there has been no product information given for a problem, this display will not be generated, and the layout display of Figure 16 will be returned to the screen. 18 Figure 20. - Screen display giving product flow information. This is still another display that results from a layout analysis. It is suppressed if no product data has been supplied. The matrix in Figure 20 shows the product of the unit loads and the distance between them for each pair of departments. The value has been divided by 1000 and rounded to the closest integer to control the size of the matrix. The divisor in this normalization is problem dependent. At the bottom of the screen the total unit load-distance value for the problem is shown. In this example the value is 264853.63 unit load feet. The two departments having the greatest contribution to this total are departments 2 and 4, which have approximately 53,000 unit load feet of product flow between them. This display will stay on the screen until the user depresses the continue button. The layout that has just been analyzed with a Layout Analysis will then be returned to the screen, with the display of Figure 16. 19 Exchanging Departments When a layout is displayed the user the exchange button appears at the of bottom the screen. This allows the user to switch the locations of any two departments in the layout. When the exchanged button is pressed, the screen in figure 21 appears. In figure 21, the departments 7 and 1 have been entered for exchange. The exchange is executed by pressing the Make Change button. The layout is then updated with the change. This process is repeated for each set of departments to be exchanged. The total number of changes is the combinations of departments taken two at a time. For example for seven departments the formula for the combinations is: = 7! / (5! 2!) =21 combinations Figure 21. Exchanging Departments The system will make the necessary adjustments in the positioning of the other departments so that the exchange can take place. The layout will be scored and the user has the same options available that were given with a new layout. Improvement Algorithm (Single Story Menu Selection 3) The improvement algorithm operates on a layout that has been previously saved. It then successively interchanges each pair of departments in that layout, and scores each resulting layout. If it has a score that is the best up to that point the layout is temporarily saved. The Improvement Algorithm will then operate on this newly saved layout in order to get a better 20 score. This process will continue until it cannot get a layout with a better score, and this layout will be presented. For example, if the user could insert the number 1 to indicate that saved layout #1 is the one to be used as the base layout for the algorithm. If the response would be a number greater than the number of layouts currently saved, the system would respond with an error message and return the Improvement Algorithm screen. TABLE 2 Number of Iterations for Exchange/Improvement Algorithm Departments 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Iterations 1 3 6 10 15 21 28 36 45 55 66 78 84 105 120 136 153 Each iteration would give a different layout with the location of two departments switched. The layout presented in each iteration can be saved and examined. The options available to the user as each iteration is displayed can be seen on the left side of Figure 25. Depressing the return key will clear the screen and cause the next iteration to be displayed. If the last iteration is on the screen when this option is used, the Single Story Menu will appear. A layout analysis of the current layout can be obtained by using the Analysis option. The current iteration will be returned to the screen after the analysis is completed. If the user uses the "Terminate" option, the sequence of iterations will be terminated, and the Single Story Menu will be returned to the screen. An iteration layout can be saved by using the "Save" option. 21 Automatic Search (Single Story Menu Selection #4) The Automatic Search option that is available in BLOCPLAN-WIN (Single Story Menu Selection 4) greatly simplifies this task. The procedures that an experienced BLOCPLAN user used in obtaining a "good" layout were studied and these procedures have been incorporated into BLOCPLAN-WIN. When this option is selected, the first prompt that the system will give asks for the number of layouts desired. The user responds with a number between 1 and 20. The layouts that result from the automatic search procedure will be stored in memory in the common Saved Layout Area. The next screen display will afford the user with the opportunity to manually locate some departments before the automatic search begins. The display will be the same as in Figure 15, and the user either manually locates some department(s), or indicates that no departments are to be fixed. Thee system starts with an initial random "seed" layout, and operates on this layout until it is not able to improve it. This final layout is saved. Another seed layout is created and the process is continued until the number of desired layouts have been created. A table showing the information on the saved layouts is then displayed. The display of Figure 22 shows this table for the example problem Figure 22. - Resulting table of layouts after the Automatic Search Procedure was used. Five layouts were requested. 22 The table of Figure 22 is essentially the same as any table of saved layouts produced by BLOCPLAN. It gives the Adjacency Scores, The REL-Dist Scores (normalized and unnormalized), and the product movement for the five layouts that were requested by the automatic Review Saved Layouts (Single Story Menu Selection #5) Layouts that have previously been saved can be reviewed by using menu selection 5. When this selection is made the screen will be cleared and the message: STARTING POINT FOR REVIEW ? Figure 27. - Screen display during review of saved layouts. Saved Layout 1 is currently shown. The user has the "A", "T", and the "E" options available. Using the return key will bring Saved Layout 2 to the screen. The user can have a layout analysis performed (option "A"), he/she can terminate the review of the remainder of the saved layouts (option "T"), or look at a layout with two of the departments exchanged (option "E"). At this point the save option ("S") is not given, since the layout has already been saved. If departments are exchanged however, the "S" option is given for the resulting layout when it is displayed. If the review saved layout option is asked for when there are no layouts currently saved, the message: NO LAYOUTS SAVED will appear on the screen for an instant and the Single Story Layout Menu will be returned. Table of Saved Layouts (Single Story Menu Selection #6) This option will create a table of scores for all layouts that are currently saved. Figure 26 shows this table for the example problem after five layouts have been saved. The table shows the scores and rankings of the five layouts.The score of each layout using the adjacency Figure 28. Table displayed for review of saved layouts (Single Story Menu Selection 6). Five layouts have been saved and each of their scores are shown with three scoring criteria. Rankings are also displayed. criterion, the REL-Dist criterion, and the total product movement is given. For the REL-Dist criterion, the normalized and un-normalized scores are both shown. If no product information If no product flow has been given for a problem, the product movement column will contain all zeroes. Once the table has been displayed the user is given an opportunity to delete a layout from 23 LAYOUT NUMBER FOR DELETION ? to be displayed. The user types in the layout number to be deleted, and the table is again displayed with that layout removed. If the user indicates that no layout is to be deleted (an "N" response), the Single Story Layout Menu is returned. 24 Multistory Layout Menu (Main Menu Selection #4) If the user wants to investigate the multistory mode (Ref 2,4), for the solution to a problem, he/she should respond with this selection to the Main Menu. The display that will then be given is shown in Figure 29. Figure 29. - Multistory Layout Menu (Main Menu Selection #4) Manual Partition (Multistory Menu Selection #1) When a user places BLOCPLAN in multistory mode he/she is examining layouts where all of the departments are not required to be on the same level. When the Manual Partition selection is made the first prompt will be: NUMBER OF STORIES (2-6) ? The user is being asked to indicate the number of levels (stories) that he/she wants to use in the problem. There is a maximum of six stories that can be used. Using the example problem, if it is assumed that the number of stories has been given as 2, the screen display of Figure 30 would then appear.Suppose the user would like to have RECVING(Dept 1), SHIPPING (Dept 7), and ASSEMBLY (Dept 5), on one floor and the remaining four departments on another. He/she would respond with the department numbers (1,7,5) to the prompt in Figure 30, to indicate those departments are to be on one level. The legend of the departments is at the bottom of the screen. The department number is entered and then the return key. A zero and return is entered after the 25 desired departments for the story have been entered. Figure 31 shows the screen display when the suggested assignments for the two stories have been entered. Figure 30. - Screen display for example problem. The system is asking for the first partition of departments. Figure 31. - Screen display showing the assignments for the two stories. 26 27 As soon as the enter key after the zero for the second story has been made, the screen will be cleared, and the display of Figure 32 will be shown. The display of Figure 32 shows the areas of each of the two stories to be 32,000 sq. ft. for story #1, and 38000 sq. ft. for story #2. BLOCPLAN calculates an Actual Area Difference Factor (ADF) for the layout. The total required area for all the departments in the example is 70,000 sq. ft.. For a two story problem the best possible arrangement of departments would have the area of each story the same. This would be accomplished with each story having an area equal to 70,000/2 or 35,000 sq. ft.. The ADF score that is calculated for a multi-story layout by BLOCPLAN is: ADF = Max [SMax-SMean)/ SMean ; (SMean-SMin)/SMean] where: SMean = Optimum mean area for each story. SMax = Maximum story area for layout. SMin = Minimum story area for layout. For the example of Figure 32, the value of SMax is 38,000, SMin is 32,000, and SMean is 35,000. Therefore, ADF = Max [ (38,000-35,000)/35,000 ; (35,000-32,000)/35,000 ] ADF = Max [ .09, .09 ] = .09 The ADF score is a measure of the maximum deviation from the optimal story size. DEPTS ON STORY # 1 1 7 5 DEPTS ON STORY # 2 2 3 4 6 STORY AREAS 32000 38000 ACTUAL AREA DIFFERENCE FACTOR 0.09 PARTITION SCORE 0.29 (11/38) 1 RECVING 2 MILLING 3 PRESS 28 S-TO SAVE ? RET FOR MENU E-EXCHANGE 4 SCR. MCH 5 ASSEMBLY 6 PLATING 7 SHIPPING Figure 32. Screen display showing the results of the manual partition of departments 1,7, and 5 into one story and departments 2,3,4,and 6 into the other. Another measure of the effectiveness of a multistory layout is given in Figure 32 and is called the Partition Score. The Partition Score uses the current Relationship Chart and is a measure of how well the story assignments satisfy the relationships. It assumes that departments on different stories will not be adjacent, and also assumes that all departments on a story will be adjacent to each other. In the example the Partition Score is .29. The adjacencies on Story #1 are (1,7), (1,5), and (5,7). From Figure 3, these three adjacencies are U, O, and I. The equivalent score values for these three codes are 0, 1, and 2. The sum of the adjacencies for Story #1 is 3.0. For Story #2 the adjacencies are (2,3), (2,4), (2,6), (3,4), (3,6), and (4,6). The sum of these adjacency scores for Story #2 is 8.0, and the total sum for the two stories is 11.0. The Partition Score is this total sum divided by the total of all positive relationships in the REL chart 11.0/38.0 or .29. The lower right hand portion of Figure 32, shows the options available to a user when a multistory layout has been developed. The options are "S" for Save, "E" for Exchange, and the return key to get back to the Multistory Menu. If the user enters "S", the partition of departments currently on screen will be saved, and the Multistory menu will again appear on the screen. If the response is "E", the system will ask for the two departments that are to be exchanged. The user supplies the index numbers of a pair of departments to be interchanged and BLOCPLAN will give the same display as shown in Figure 32, only now the places of the two requested departments will switched. All of the scoring will now reflect the effect of the switch. If the user uses the return key, the Multistory Menu will be returned. Automatic Partition (Multistory Menu Selection #2) If the user wants BLOCPLAN to decide on the partitions of departme...

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U. Houston - INDE - 6370
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INDE 6370 Homework #5 Due 6 MAR 08 The objective of this assignment is to further develop your model building skills with ARENA. All work is to be completed individually. Modify the previous assignment to include: 1. A new interarrival rate of expo(2
U. Houston - INDE - 6370
INDE 6370 Homework #4 Due 28 FEB 08 The objective of this assignment is to introduce you to model building with ARENA. All work is to be completed individually. Model and animate a simple one queue one server system which represents a customer servic
U. Houston - INDE - 6370
INDE 6370 Homework #6 Due 13 MAR 08 The objective of this assignment is to further develop your model building skills with ARENA. All work is to be completed individually. Modify the previous assignment to include: 1. The presence of customers prior
U. Houston - INDE - 6370
INDE 6370 HOMEWORK Due 21 FEB 06 Objective. The objective of this homework is to familiarize you with data collection and analysis of input data. 1. Data Collection From the video viewed in class, create an Excel spreadsheet to determine the average
U. Houston - INDE - 6370
AGENDANon-terminating AnalysisContinuous and combined event modelingTYPES OF NON-TERMINATINGSYSTEMSMost manufacturing systemsService systems that do not closeService systems where the customer leaves something to be picked up at another time
U. Houston - INDE - 6370
11.1010.9610.3211.8410.3710.5510.1311.1210.5810.319.3311.0710.068.979.0111.679.569.1611.049.858.588.8611.1610.028.2310.989.738.5810.609.9911.0711.519.6910.7210.8710.5810.0710.2710.2510.388.568.6610.239.128.
U. Houston - INDE - 6370
AGENDATerminating systemsThree or more model comparisonsTHREE OR MORE ALTERNATIVE COMPARISONSANOVAONE WAYANALYSIS OF VARIANCEDetermines if one or more alternatives is different than the othersBased on a ratio of the variance between and with
U. Houston - INDE - 6370
AGENDAAnalyzing Input DataData collection exerciseHomework assignmentTHE USE OF INPUT DATA IN SIMULATIONObserve input dataFit to theoretical distributionGenerate data from theoretical distributionANALYZING INPUT DATADetermining underlying t
U. Houston - INDE - 6370
AGENDABalkingRenegingJockeyingBALKINGQueue is too full when entity arrivesEntity does not enter the queueEntity goes elsewhereModeled within QUEUE blockCapacity - deterministic or probabilisticBalk label RENEGINGEntities enters a queue
U. Houston - INDE - 6370
AGENDAContinuous and combined event modelingEnd term reviewCONTINUOUS AND COMBINED MODELINGWhat is continuous event modelingContinuous event related blocksContinuous event related elementsAnimating continuous event modelsWHAT IS CONTINUOUS
U. Houston - INDE - 6370
AGENDAData collection updateReviewDATA COLLECTION UPDATECollectionAnalysisREVIEWBasic simulation issuesInput data analysisRandom number generationModelingBASIC ISSUES.Simulation processManual event listPerformance measures BASIC SIM
U. Houston - INDE - 6370
AGENDAProject progress reportsArrivals elementResource related elementsSystem statusARRIVALS ELEMENTForce entities to appearModeling customers waiting before opening timeMake entities appear for demonstration purposes.ARRIVALS ELEMENTGen
U. Houston - INDE - 6370
AGENDAEnd term review for exam on 17 APR 08REVIEWValidationReplication analysisExperimental DesignOutput analysis of two systemsOutput analysis of more than two systemsNon-terminating system analysisVALIDATIONFaceStatisticalData collec
U. Houston - INDE - 6370
AGENDAConveyorsAdditional Modeling StructuresTYPES OF CONVEYORSNon-AccumulatingAccumulating CONVEYOR RELATEDSTRUCTURESBlocksAccessConveyExitElementsConveyorsSegmentsAnimationACCESS BLOCKHolds the entity in a queue until sufficient
U. Houston - INDE - 6370
AGENDAIntroduction to ARENABasic model blocksBasic experiment elements INTRODUCTION TO ARENAGraphically oriented simulation packageToolbarsProject barModel WindowFlow chart viewSpreadsheet viewMODULESBuilding blocks for modelsFlowchart
U. Houston - INDE - 6370
AGENDAEntity related Resource and queue relatedStatistics relatedHomeworkReviewBRANCH BLOCKUsed to control flow of entities through the modelPrimary entitySecondary entities may be clonedMore than one branch may be takenTypesProbabilisti
U. Houston - INDE - 6370
AGENDABasic Simulation Study ProcessCourse ProjectsAn example projectBASIC SIMULATION PROCESSProblem DefinitionProject PlanningSystem Definition / Model FormulationInput Data Collection and AnalysisModel TranslationVerificationValidation
U. Houston - INDE - 6370
AGENDAQueues relatedResource relatedSystem statusQUEUE RELATEDDuplicateMatchArrivals elementDUPLICATEUsed to generate additional entities from original entitiesAll duplicates inherit attribute valuesIf to be later rejoined, must have ide
U. Houston - INDE - 6370
AGENDATransportersReviewTRANSPORTER USESMaterial handling equipmentForkliftsDollysWorkers that process orders for later pickupValetStarbucks coffee makerSonic fast food carhopTYPES OF TRANSPORTERSFree pathFork liftCan go between any a
Penn State - EARTH - 530
Online Discussion Rubric1 Promptness and Initiative Does not respond to most postings; rarely participates freely 2 Responds to most postings several days after initial discussion; limited initiative Errors in spelling and grammar evidenced in sever
Penn State - DJO - 5000
DANIEL J. OTTO 456 East Beaver Ave. apartment 602 State College, PA 16801 484-433-5533 Djo5000@psu.edu EDUCATION: The Pennsylvania State University Division of Undergraduate Studies Anticipated graduation 2008 The Tatnall School, June 2004 EXPERIENCE
Penn State - AJT - 5037
John Lennon started this journey in 1957 with his band the Quarrymen. Through this group he would meet Paul McCartney, George Harrison and in a couple of years, Ringo Starr. However, before Ringo Starr came into the group the bands permanent drumme
U. Houston - M - 1310
Definition and Example 1Monday, March 03, 2008 1:13 PMMethods for combining functions: 1. Sum 2.(f + g )(x ) = f ( x ) + g( x ) Difference (f - g )(x ) = f ( x ) - g( x )(fg )(x) = f ( x)g( x) 4. Quotient f ( x ) = f ( x ) g( x ) provided
U. Houston - M - 1312
M 13125.41Theorem 5.4.1: The altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other and to the original right triangle.CADBTheorem 5.4.2: The length of
U. Houston - MATH - 4377
U. Houston - MATH - 6397
Stochastic Processes - Spring 2008Practice Problems for Final ExamBernhard Bodmann, PGH 636 Duration: 150 minutes First Name: Last Name:Show all work. No points will be given for numerical answers without working being shown.(1) Consider the (c
U. Houston - MATH - 6397
Stochastic Processes - Spring 2008Bernhard Bodmann, PGH 636 Exercise Sheet 2, with Solutions Do all Exercises individually. (1) Let X1 , X2 , . . . , Xn , . . . be i.i.d. with P(Xi = 1) = p and P(Xi = 1) = 1 p = q. Let a, b N. Dene Sn = X1 + . . .
U. Houston - MATH - 4377
Exam 2 Math 4377 November 20, Fall 2008Show all the work for full credit. In this exam no calculators are allowed. Answer all of the following questions. The maximum score is 150. 1. (15 Points) Let V = R2 and W be the vector space of all real 22 m
U. Houston - MATH - 6397
Stochastic Processes - Spring 2008Practice Problems for Final ExamBernhard Bodmann, PGH 636 Duration: 150 minutes First Name: Last Name:Show all work. No points will be given for numerical answers without working being shown.(1) Consider the (c
U. Houston - MATH - 4377
Department of MathematicsUniversity of HoustonMath 4377 Advanced Linear AlgebraFall 2008Homework Set 9, due Tuesday, Nov 4, 1pmSection 3.51 In R3 , let 1 = (1, 0, 1), 2 = (0, 1, -2) and 3 = (-1, -1, 0). (a) If f is a linear functional on R3
U. Houston - MATH - 4377
Department of MathematicsUniversity of HoustonMath 4377 Advanced Linear AlgebraFall 2008Homework Set 8, due Tuesday, Oct 28, 1pmSection 3.32 Let V be a vector space over the eld of complex numbers and suppose T is an isomorphism of V onto C3
U. Houston - MATH - 4377
Department of MathematicsUniversity of HoustonMath 4377 Advanced Linear AlgebraFall 2008Homework Set 10, due Tuesday, Nov 11, 1pmSection 3.61 Let n be a positive integer and F be a field. Let W be the subspace of all vectors (x1 , x2 , . . .
U. Houston - MATH - 4355
10 f f1 f2 f386420!2 !4!3!2!10123440 f f1 f2 f33020100!10!20!30!40 !4!3!2!1012341.75 1.7 1.65 1.6 1.55 1.5 1.45 1.4 1.35 1.3 0.2 a=0.3134 b=1.29490.30.40.50.60.70.80.91
U. Houston - MATH - 4377
U. Houston - MATH - 6397
U. Houston - MATH - 4377
U. Houston - MATH - 1432
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U. Houston - V - 001
HOUSTON JOURNAL OF MATHEMATICS, Volume 1, No. 1, 1975.THE HOPF EXTENSIONTHEOREMFOR TOPOLOGICALSPACESKiiti MoritaIn celebration of the start of Houston Journal of Mathematics1. Introduction. Let X be a topological space. Then by the cover
U. Houston - MATH - 3334
Math 3334 Fall 2008 Professor William OttExamination 3Problem 1. Compute the integral2 0 4 2yex dx dy. Hint: Use the Fubini theorem. Problem 2. Prove that 4e5[1,3][2,4]2ex2+y 2dA4e25 .Hint: You do not need to evaluate the integral