bpman03
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bpman03

Course Number: INDE 6370, Fall 2008

College/University: U. Houston

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BLOCPLAN for 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 entered or if an existing problem is to be entered. Figure 3 shows these choices. 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. 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 the type in the name of each department 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. 2 Figure 4 Department and Area Information Screen and the user types the required area for the first department. This series of prompts is given for each of the departments to be included in the layout. When all department names and areas have been entered, a display of the data is given. 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 4 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 for its area. The area is entered and the display in Figure 4 is repeated with this new information included. Relationship Data 3 BLOCPLAN uses the relationship codes described by Muther in "Systematic Layout Planning", (Muther 1973, CBI Publishing, Boston, Mass.)). Figure 5 shows the initial screen display that prompts the user to furnish the codes for each of the departmental relationships. The bottom of the screen gives a legend of the acceptable codes. In Figure 5 the system is prompting for the relationship code between departments 1 and 2 (RECVING-MILLING). The cursor is located at row 1 and column 2 of the matrix, and when the user keys in the code, it will be placed in the matrix, and the cursor moved to the next position. After the relationship matrix has been entered, the user is given an opportunity to change any of the entries. Figure 3 shows the screen display with the completed matrix and the change prompt on the bottom of the screen. If the response is "Y", the system will prompt: COORDINATES OF CHANGED CODE __ The user will give the row and column in the matrix for the element to be changed. The row and column values are separated with a comma. The cursor will appear at that location in the RELATIONSHIP CHART 2 3 4 5 6 1 RECVING . . . [] . . . . . 2 MILLING . . . . . . . . . 3 PRESS . . . . . . . . . 4 SCR. MCH. . . . . . . . . 5 ASSEMBLY . . . . . . . . 6 PLATING. . . . . . . . . 7. SHIPPING . . . . . . . . 7 FOR DEPARTMENTS RECVING - MILLING A - ABSOLUTELY ESSENTIAL E - ESSENTIAL IIMPORTANT O - ORDINARY CLOSENESS U - UNIMPORTANT X UNDESIRABLE Figure 2. Screen display before initial entry of relationship data. Legend of acceptable relationship codes is given on bottom of screen. Cursor is positioned in matrix for code for departments 1 and 2. 4 RELATIONSHIP CHART 2 3 4 5 6 1 RECVING . E O I O U 2 MILLING . . U E I I 3 PRESS . . . U U O 4 SCR. MCH . . . IU U 5 ASSEMBLY . . . . A 6 PLATING . . . . . E 7. SHIPPING . . . . . N) __ 7 U U U I . WANT TO CHANGE RELATIONSHIP CHART (Y/ Figure 3. Screen display after all relationship data has been entered. matrix, and the new code is entered by the user. The revised matrix and the prompt of Figure 3 will then appear to allow for further changes. When the user indicates there are no more changes to be made in the relationship matrix, the system will establish the worth of the relationship codes. Values of Relationship Codes BLOCPLAN needs to know the worth of each of the six possible relationship codes. For example, in one application the user may feel that an "A" code is three times as important as an "E" code, and in another problem only 1.5 times as important. Figure 4 shows the screen display that is given when the system is prompting for this information. CODE SCORES A 10 E 5 I 2 0 1 U 0 X -10 WANT TO CHANGE VECTOR (Y/N) __ 5 Figure 4. Default vector of code equivalent values. The system has a default vector of code equivalent values that is shown to the user to see if it is acceptable. From Figure 4 it can be seen that an "A" is worth 10 points, an "E" is worth 5 points, an "I" 2 points, an "O" 1 point, a "U" zero points, and an "X" -10 points. Therefore an "A" is twice as important as an "E", five times as important as an "I", etc.. If the user wants to change these scores the response is "Y". If no changes are to be made, the response is "N", or a single depression of the enter key. When the user indicates that changes are to be made, the cursor is placed over each of the scores in sequence, and the user types in the new values. When a score vector is accepted, BLOCPLAN will begin to make some preliminary computations. The screen will be cleared and the message: COMPUTING... will appear on the screen. This usually will last a second or two. Departmental Scores Using the relationship matrix and the vector of code equivalents, BLOCPLAN develops and displays a score for each department in the problem. Figure 5 shows this display for the example problem. A departmental score is the sum of all the relationship code equivalents for the department. For example, from Figure 3, the PRESS department in the sample problem has four "U" codes and two "O" codes associated with it. A "U" is worth zero points and an "O" is worth one point. Therefore, the departmental score for the PRESS department is (4 X 0) + (2 X 1) = 2 points. The display in Figure 5 shows these scores for all the departments. The scores are only presented to the user as information. They will stay on the screen until the user depresses the enter key. If the user wants a hard copy of any of the screen displays to be produced on the printer he/she should use the print screen key. DEPARTMENT 1 2 3 4 5 6 7 RECEIVING MILLING PRESS SCR. MCH ASSEMBLY PLATING SHIPPING 6 9 14 2 9 17 18 7 SCORE HIT RETURN KEY TO CONTINUE ANALYSIS Figure 5. Display of departmental scores for example problem. Length/Width Ratio The ratio of the length to the width of the layout outline that will contain the departments can be selected by the user. Figure 6 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 entering the desired selection number. If the user chooses selection 5, he/she will be asked for the ratio. When selection 5 is made, the screen will be cleared and BLOCPLAN will prompt: LENGTH __ The user inputs the desired numerator for the L/W ratio, and the system will then prompt: WIDTH __ and the user responds with the denominator in the desired L/W ratio. Once this desired ratio has been selected, BLOCPLAN will calculate the length and the width of the outline so that it will have the required area to contain the departments in the problem. Product Flow Information BLOCPLAN allows the inclusion of product information in the layout analysis. This information may be furnished by listing products and the departments that they must traverse, and/or by furnishing elements of a FROM/TO matrix directly. The prompt that asks the user if this information is to be included is: DO YOU WANT TO SUPPLY PRODUCT INFORMATION (Y OR N) __ Figure 6. Display screen presented during selection of Length/Width Ratio for layout outline. 7 f the user responds "N" the layout analysis is continued without any data on products or product flow. If the response is "Y" the prompt will be: NUMBER OF PRODUCTS (MAX 13) __ The user responds with the number of products to be included in the analysis. BLOCPLAN allows a maximum of 13 different products. It should be noted that the user has the option of specifying zero products in response to this prompt. This would indicate that the flow information will come from direct entries into a FROM/TO matrix. For the initial example, it will be assumed that the user indicates that three products are to be included in the analysis. The system will then ask: GIVE 3 CHARACTER IDENTIFIER FOR PRODUCT 1 ___ The user gives any arbitrary three character identifier for the first product that is to be included in the analysis. Assume the user responds "AAA". BLOCPLAN will then prompt: UNIT LOADS FOR AAA___ The response will be the unit loads of product "AAA" that are required to be moved for some implied time period. The dimensions of the unit loads, and the length of the time period are not specified, but it is assumed that the user is consistent with all products. These two prompts are given for all the products. After all the products have been identified and their unit loads specified, BLOCPLAN will then ask for the sequence of departments that each product must move through for its processing. For the example problem, assume that three products have been given; AAA with 150 unit loads, BBB with 75 unit loads, and CCC with 200 unit loads. The screen display shown in Figure 7 will be given. DEPARTMENT SEQUENCE FOR PRODUCT AAA DEPARTMENT INDEX-RETURN, O TO TERMINATE -- 1 RECVING ASSEMBLY 6 PLATING 2 MILLING 7 SHIPPING 3 PRESS 4 SCR. MCH 5 8 Figure 7. Screen display prompting for department sequence for processing "AAA". Legend of departments given on bottom of screen. Assume that the sequence of departments for product "AAA" is Receiving, Milling, Plating, and Shipping. The user would type the sequence 1,2,6, and 7 to furnish this information. The numbers used in the sequence match the department numbers in the legend given on the bottom of the screen in the display. The enter key is used after each number is typed. The sequence is terminated when the user types a zero. Figure 8 shows the screen as the sequence for "AAA" is terminated. The department sequences for products "BBB" and "CCC" would be requested and entered in the same manner. A maximum of 13 departments are allowed in a product sequence. DEPARTMENT SEQUENCE FOR PRODUCT AAA DEPARTMENT INDEX-RETURN,0 TO TERMINATE 1 2 6 7 0 1 RECVING ASSEMBLY 6 PLATING 2 MILLING 7 SHIPPING 3 PRESS 4 SCR. MCH 5 Figure 8. Screen display when department sequence for product "AAA" has been entered. Product moves from Receiving, to Milling, to Plating, and finally to Shipping. When all the product information for all products has been entered, the system will display a summary of the data for inspection. Figure 9 shows this display for some assumed data for the example problem. PRODUCT SUMMARY PROD # 1 2 3 NAME AAA BBB CCC UN. LDS 150 75 200 1 2 6 7 1 3 4 6 1 4 2 4 9 7 5 7 C-CHANGE PRODUCT INFO M-MATRIX ENTER KEY FOR RETURN TO MENU 1 RECVING 2 MILLING 3 PRESS 4 SCR. MCH 5 ASSEMBLY 6 PLATING 7 SHIPPING Figure 9. Summary of product information. User is given an opportunity to modify the data if desired. Figure 9 presents the user with three choices. He/she may respond to the prompt with a "C" for Change product information, an "M" for a Matrix of product flow, or the enter key to bring the BLOCPLAN Main Menu on the screen. If the user responds "C", the system will ask at the bottom of the screen: PRODUCT NUMBER FOR CHANGE __ The product number is specified by the user. From Figure 9 it can be seen that "AAA" is product 1, "BBB" is product 2, and "CCC" is product 3. If the user wants to add a new product the response would be "4". If there are no products currently in the problem, the product display of Figure 9 would have no product data, and the user would respond with "1" to enter a product. In the example, assume the user wants to change the information on product "BBB". The response will be "2" to the prompt. The system will then say: DO YOU WANT TO ELIMINATE PRODUCT BBB __ (Y/N) __ If product "BBB" is to be completely removed from the problem the response will be "Y", and the display of Figure 9 will be shown with Product "BBB" eliminated. Product "CCC" would now be the second product in the display. If the user responds "N" to the prompt, BLOCPLAN will ask: CHANGE UNIT LOADS (U) OR SEQUENCE (S) __ The system is asking if only the unit loads for the product are to be changed, or if the sequence of departments through which the product flows is to be changed. If the user response is "U" the prompt will be: 10 NEW UNIT LOADS FOR PRODUCT BBB __ The new unit load value for the product is entered, and the display of Figure 9 is then shown incorporating this new value. If the response is "S" to the "U" or "S" prompt, indicating that a change in the sequence of departments is required, BLOCPLAN will place on the screen a display similar to Figure 7, asking for a new sequence for "BBB". The user will enter a new sequence of departments for product "BBB", terminating with a zero. The screen will be cleared and a new summary display similar to Figure 9 will be given. This display will contain the new department sequence for "BBB". It should be noted that the product index numbers may change in the summary display as alterations are made. The user responds with an "M" to the prompt of Figure 9, to request a matrix of product movement. This matrix will show the total product movement, in unit loads, between each pair of departments in the problem. Figure 10 shows this matrix for the example problem, assuming the product information of Figure 9. Figure 10. Total product flow matrix for example problem. Each element is the total unit loads between departments i and j divided by 10. This matrix shows, for example, that the total flow between departments 6 and 7 is 23. This results from a flow of 150 unit loads of "AAA" between the two departments, plus a flow of 75 unit loads of "BBB". The total of 225 unit loads is divided by 10 and rounded to give the matrix entry of 23. The coefficient of variation (CV) of the flow is also shown on the screen. Vollmann and Buffa discuss how this can be used as a measure of "flow dominance" (Vollmann and Buffa, 1965). The prompt that is given on the bottom of the screen when the Total Flow Matrix is displayed asks: DISPLAY ADDITIONS MATRIX (Y/N) __ If the user responds "Y", a matrix showing additions (if any) that are in the Total Flow Matrix. This Additions Matrix shows any FROM/TO data that has been entered that is independent from product data already entered. Figure 11 shows the Additions Matrix for the example problem. It is empty, which indicates that all flow in the Total Product Flow Matrix came from the product information. The prompt given with the Additions Matrix (Fig. 11) asks: CHANGE ADDITIONS MATRIX (Y/N) __ If the user wants to add additional flow information, the response is "Y", and the next prompt will be: GIVE DEPT NUMB'S (I,J) I < J OF FLOW ELEMENT __ 11 The user gives the numbers of the departments involved. The i'th department number must be less than the j'th department number. The next prompt will then ask for the value of the flow element for the two departments. For example, suppose the user wants to increase the flow from Milling (Dept 2) to Assembly (Dept 5) by 200 unit loads. The prompt and responses to accomplish this would be: GIVE DEPT NUMB'S (I,J) I < J OF FLOW ELEMENT 2,5 VALUE 200 1 RECVING 2 MILLING 3 PRESS ASSEMBLY 6 PLATING 7 SHIPPING ADD-FLOW/10 4 SCR. MCH 5 CHANGE ADDITIONS MATRIX (Y/N)___ Figure 11. Additions Matrix for example problem. It is empty which indicates all the flow between departments in the Total Flow Matrix came from product data. The user entries are underlined. When the entry is made, the Total Flow Matrix (Figure 10) is shown again, only now the additional flow information would be included. If the user now asked for the Additions Matrix to be displayed, it would show the single additions element of 200 at the 2,5 element in the matrix. More additions entries could then be made. Each time an entry is made in the Additions Matrix, the system will display the Total Matrix with the new entry included. Any time the Additions Matrix is not asked for, the BLOCPLAN Main Menu will be displayed. BLOCPLAN Main Menu The menu of choices in the Main Menu is shown in Figure 12. There are six menu options available to the user. The user enters a menu selection number 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. 12 MAIN MENU --------1. NEW PROBLEM 2. EDIT/ADJUST DATA MENU 3. SINGLE-STORY LAYOUT MENU 4. MULTI-STORY/SITE LAYOUT MENU 5. SAVE PROBLEM DATA 6. STOP Make Selection__ Figure 12. BLOCPLAN Main Menu selections. 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: YOU MAY WANT TO SAVE THE PROBLEM DATA BEFORE WORKING ON A NEW PROBLEM. M-BACK TO MAIN MENU RETURN FOR NEW PROBLEM __ The message is intended to remind the user that the current problem data will be lost if a new problem is introduced at that point. If the user responds with an "M", a return to the Main Menu is made and the user is given a chance to save the current problem. If the user depresses the return key the message will be: 13 DATA FROM DISK (D) OR KEYBOARD (K) __ 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 13 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 product information. He/she can also ask for a relationship chart that is based solely on product 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 name of the problem is shown in the upper right hand corner. MANEX EDIT/ADJUST DATA MENU 1. ADJUST AREA/REL INFO 2. ADJUST L/W RATIO 3. REVIEW PRODUCT INFO 14 4. USE PROD-FLOW REL CHART 5. RESTORE REL CHART 6. MAIN MENU NUMBER LAYOUTS SAVED 9 Make selection __ CURRENT L/W RATIO 1 LENGTH 264.6 WIDTH 264.6 Figure 13. 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 Product Information (Edit/Adjust Data Menu Selection #3) The product 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 product information in the problem, it can be added with this selection. In this case, the screen display would have no product data, and the user would use the "C" option to indicate a change is required, and the product number he/she would specify would be "1". 15 Use Product Flow Relationship Chart (Edit/Adjust Data Menu Selection #4) This selection will cause BLOCPLAN to develop an alternate REL chart that is based entirely on product flow. The example problem had product 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 product information. It will then display the resulting REL chart. Figure 14 shows the REL chart that resulted for the example problem with the product 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 are in effect by using menu selection 1 in the Ed/Adj Data Menu. (Adjust REL Info). If the product information is changed by using selection 4 in the Ed/Adj Data Menu , the user will have to then call on this selection again (selection 4) to cause the REL chart to reflect these changes. In the upper right hand corner of displays an asterisk will be shown whenever the product-flow REL chart is in use. 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 ProductFlow 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. There will be no asterisk in the upper right hand corner of display screens to indicate that the original REL chart is in effect. RELATIONSHIP CHART 2 3 4 5 6 7 RECVING . . . . . . O U I U U U MILLING . . . . . . . U A U O U PRESS . . . . . . . . . U U U U SCR. MCH . . . . . . . . . . I U U ASSEMBLY . . . . . . . . . . . U I PLATING . . . . . . . . . . . . I 1 2 3 4 5 6 WANT TO CHANGE RELATIONSHIP CHART (Y,N) ___ 16 Figure 14. REL chart resulting from menu selection 4 from the Edit/Adjust Data Menu. This REL chart is based entirely on the product information that is summarized in Figures 9 and 10. The user may make any manual 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 Main Menu shown in Figure 12 is placed on the screen. 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 16 appears. MANEX SINGLE-STORY LAYOUT MENU -----------------1. MANUALLY INSERT DEPARTMENTS 2. RANDOM LAYOUT 3. IMPROVEMENT ALGORITHM 4. AUTOMATIC SEARCH 5. REVIEW SAVED LAYOUTS 6. TABLE OF SAVED LAYOUTS 7. MAIN MENU 17 NUMBER LAYOUTS SAVED 9 Make selection __ CURRENT L/W RATIO 1 LENGTH 264.6 WIDTH 264.6 Figure 15. Single Story Layout Menu. FIXED DEPTS 1 RECVING 2 MILLING 3 PRESS 6 PLATING 7 SHIPPING 4 SCR.MCH 5 ASSEMBLY WANT TO MANUALLY LOCATE DEPARTMENT(Y/N) ___ Figure 16. 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 16. 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 16 is for a L/W ratio of 1/1. The prompt at the bottom of the screen asks: WANT TO MANUALLY LOCATE DEPARTMENT (Y/N) __ The user responds "Y" and the new prompt message on the bottom of the screen will be: 18 DEPARTMENT NUMBER FOR MANUAL LOCATION __ Assume the user wants to fix the Receiving department (Dept. 1)in the upper right hand corner of the layout outline, and the Shipping department (Dept. 7) in the lower left hand corner of the outline. First the Receiving department will be fixed, so the response will be "1". BLOCPLAN will then ask for the zone where it is to be placed with the prompt: ZONE FOR INSERTION __ Since Department 1 is to be in the upper right hand corner, the response will be "C". The system will then ask: IN ZONE C 1-LEFT SIDE 2-RIGHT SIDE SELECTION __ Since the department is to be located at the extreme upper right hand corner, the response will be "2" for the right side of zone C. An entry: 1-C-R will be placed under the "FIXED DEPTS" heading of Figure 16 to show that Department 1 has been fixed in the right side of zone C, and the prompt: WANT TO MANUALLY LOCATE DEPARTMENT (Y/N) __ will again appear on the bottom of the screen. The Shipping department (Dept.7) is to be also fixed in the lower left hand corner, so the response would be "Y", and the system will ask for the desired zone (zone G) and the left or right side of the zone (left side). Once these entries have been made the display of Figure 17 would appear. Since the two departments that were to be manually fixed have been placed, the user would now respond "N" to the prompt of Figure 17, and the Single Story Menu would again be placed on the screen. From this point on, any layouts that are created by the random layout algorithm (Single Story Menu selection 2), will have departments 1 and 7 in their fixed positions. In order to "unfix" departments, the user should call for the Manual Insert selection again, and respond "N" to the first prompt, when asked if departments are to be fixed. 19 Figure 17. Screen display after departments 1 and 7 have been manually located. System is asking if more departments are to be fixed. Random Layout (Single Story Menu Selection #2) When a random layout is requested, BLOCPLAN will create a layout without regard to any of the relationship or product information. The departments will be placed in the prescribed layout area in a random manner. Each department will be drawn to scale, and the resulting layout will be scored and displayed. The time to create a layout is dependent upon the number of departments it contains, but even with the maximum number of departments (18), a random layout is created, drawn, and scored in less than two seconds. Figure 18 shows a random layout for the example problem. Figure 18. Random layout created for example problem. Adjacency Scoring The layout display shown in Figure 18 is the format that BLOCPLAN uses to display a single story layout that it has created. It has a layout score of .55 assigned to it. BLOCPLAN uses an adjacency criterion to develop this score. Figure 19 shows the relationship matrix of Figure 3 with the relationship codes replaced by their code equivalent values of Figure 4. 20 1. 2. 3. 4. 5. 6. 7. 2 RECVING 5 MILLING PRESS SCR. MCH ASSEMBLY PLATING SHIPPING 3 1 0 4 2 5 0 5 1 2 0 2 6 0 2 1 0 10 7 SUM 0 9 0 9 0 1 0 2 2 12 5 5 TOTAL = 38 Figure 19. Relationship matrix for example problem with relationship codes replaced by equivalent scores. The sum of positive scores for the matrix is 38. Table 1 shows the adjacency relationships of the layout in Figure 18, and the value of each of them. An adjacency relationship between departments exists when the departments share a boundary. Table 1 Adjacency Relationships and Scores of Figure 18 Layout 1-4 (2) 1-5 (1) 1-7 (0) 1-6 (0) 2-7 (0) 2-3 (0) 2-6 (2) 3-6 (1) 4-7 (0) 5-6 (10) 6-7 (5) The total value of all the existing adjacency relations in Table 1 is 21. This sum is normalized by dividing it by the sum of all the positive relationships in the relationship matrix. This value is 38, (see Figure 19). Therefore, the normalized adjacency score for the layout of Figure 18 is 21/38 = .55. A 1.0 would be the highest possible score. Saving adjacency Layouts 21 Figure 18 shows the options that are available to a user when a layout is created. These options are: "S" to Save a layout, "A" to have a layout Analysis performed, "E" to Exchange departments in the layout, and the Return or enter key to get back to the Single Story Layout Menu. BLOCPLAN is capable of saving 20 layouts in the Saved Layout area in memory. When the user uses the "S" option, the layout currently on the screen will be stored in memory. 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. The message: MAXIMUM ALREADY SAVED will flash on the screen for an instant before the replacement is made. After a layout has been saved, the Single Story Layout Menu will appear on the screen. Layout Analysis A layout analysis for the layout currently on the screen will be performed when the "A" option (Figure 18) is used. There are several screen displays of information that will be displayed when this option is used. Figure 20 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. The lower left hand corner of the layout outline is the (0,0) origin. This display will remain on the screen until the user hits the enter key. 22 Figure 20. Display of department information for current layout. This is the first display given when the Analysis option is executed. The lower left hand corner of the layout is the (0,0) point. The next display given in the layout analysis shows the adjacencies that have been satisfied for the layout under consideration. It shows the original relationship chart with the relationship codes shown in upper case for the departments in the layout that have a common boundary, and lower case for departments that do not have a common boundary. If a color monitor is being utilized, the codes for departments without the common boundary will be in red. Figure 21 shows the screen display for the layout of Figure 18. It shows, for example, that RECEIVING and MILLING (depts 1,2) have an "E" relationship that is not satisfied. Another "E" relationship between departments 2 and 4 has also not been satisfied. Figure 21. Adjacencies that have been satisfied for layout of Figure 18. The next screen display of information resulting from the layout analysis is shown in Figure 22. 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 20 it can be seen that the centroid of department 1 is 148.8, 204.1. The centroid for department 4 is 49.6, 204.1. Therefore, the distance between these departments, assuming rectilinear travel, is | 148.8 - 49.6 | + |204.1 - 204.1 | = 99.2 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 two departments is 99.2 X 2 = 198.4. These values are calculated and summed for each pair of departments in the 23 layout. This sum is shown in Figure 22 at the bottom of the screen, and is 6884.624. The better layouts should have a lower Rel-Dist score. BLOCPLAN normalizes this score. Figure 22. Screen display giving results of Relationship-Distance analysis of current layout. This is another display that results from a layout analysis. The matrix in the upper left hand side of Figure 22 shows the distance between each pair of departments. The matrix entries have been divided by 10 and integerized, thus the entry for departments 1 and 4 is Integer(99.2/10) = 10. A vector D, of all these 21 distances in the matrix in ascending order would be: D = 8, 8, 8, 10, 12, 13, 13, 14, 16, 18, 19, 19, 20, 20, 21, 24, 25, 25, 27, 33, 34 24 The matrix in Figure 19 shows the relationship matrix with all the relationship codes replaced by their equivalent scores. A vector S, of all these 21 values in ascending order would be: S = 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 5, 5, 5, 10 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 the score can be found by: Upper Bound = D1S1 + D2S2 +... + D21S21 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 22. 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 22. 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-(6884.624 - 4056.031)/(10433.24 -4056.031) or 0.56. An RSCORE of 1.0 would be a perfect layout, and a value of zero would be the worst possible. The display of Figure 22 will remain on the screen until the user depresses the enter key. The last display that results from the Analysis option is shown in Figure 23. If there has been no product information given for a problem, this display will not be generated, and the layout display of Figure 18 will be returned to the screen. 25 Figure 23. 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 23 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 350,550.3 unit load feet. The two departments having the greatest contribution to this total are departments 2 and 4, which have approximately 81,000 unit load feet of product flow between them. This display will stay on the screen until the user depresses the enter key. The layout that has just been analyzed with a Layout Analysis will then be returned to the screen, with the display of Figure 18. Exchanging Departments The layout display of Figure 18 shows that the user may use an "E" entry which will permit two departments to exchange their positions in the layout. When this option is entered, a prompt on the bottom of the screen will ask: GIVE DEPT. NUMBERS FOR EXCHANGE, SEPARATED BY COMMA ? Suppose the user wanted to exchange departments 1 and 2. The reply to the prompt would be: 1,2 The system will then clear the screen and construct a layout with departments 1 and 2 exchanging relative positions in the layout. 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, scores each resulting layout, and displays it. Assume that the layout in Figure 18 has been saved, and it is the first one saved. The first prompt after the user has asked for Single Story Menu selection 3 is: 26 LAYOUT NUMBER FOR BASIS __ The user would respond with "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 the message: LAYOUT NUMBER OUT OF RANGE and return the Single Story Menu to the screen. If the layout number selected is within range the prompt will be: DO YOU WANT SOME DEPARTMENTS FIXED __ The system is asking if the user wants some departments in the base layout to stay in their same relative position, and not be included in the department switching that the algorithm will perform. If the response is "N", all departments will be included in the switching, and the algorithm will begin. If the response is "Y", the screen will be cleared and the display of Figure 24 will appear. Figure 24. Screen display for fixing some departments before improvement algorithm is started. The user will enter the department numbers that are not to be included in the algorithm. One department number per line is entered, and the sequence is terminated by entering a zero. When this sequence has been entered, the screen will be cleared, and the layout with the first interchange will be shown on the screen. Figure 25 shows the first display that would result. In this example no departments have been fixed, so the first layout has interchanged departments 1 and 2, in the base layout of Figure 18. At the top of the screen the iteration count is shown as "ITERATION 1". Each iteration that the algorithm performs will be counted. Table 2 shows the number of iterations that will be performed by the algorithm for various problem sizes. The number of departments in the table are the number of departments that have not been fixed in place before the algorithm is executed. It can be seen in Figure 25 that the score for the 27 Figure 25. Screen display for first iteration of improvement algorithm. Departments 1 and 2 have exchanged positions from the base layout shown in Figure 18. layout after departments 1 and 2 have been switched is .68. The score for the base layout (.55) is also shown in the display. TABLE 2 Number of Iterations for Improvement Algorithm Departments 2 28 Iterations 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 3 6 10 15 21 28 36 45 55 66 78 84 105 120 136 153 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 "A" option. The current iteration will be returned to the screen after the analysis is completed. If the user uses the "T" 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 "S" option. Automatic Search (Single Story Menu Selection #4) The usual procedure that a user used in previous versions of BLOCPLAN to obtain a satisfactory layout was to generate a layout, using the random layout or the the layout algorithm, and then use the improvement algorithm in order to improve it. If there were a small number of departments it usually did not take very long before a "good" layout was obtained. However if there were more than seven or eight departments this could be frustrating and time consuming. The Automatic Search option that is available in BLOCPLAN-90 (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-90. When this option is selected, the first prompt that the system will give is: DESIRED NUMBER OF LAYOUTS (MAX 20) ? 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. Any saved layouts that have been previously stored in the area will be lost when this procedure begins. If the user wants to preserve these layouts, he/she should save the problem data before the automatic search procedure is called. The next screen display will afford the user with the 29 opportunity to manually locate some departments before the automatic search begins. The display will be the same as in Figure 16, and the user either manually locates some department(s), or indicates that no departments are to be fixed. The automatic search procedure then begins. The screen will give the message: COMPUTING LAYOUT #1........... The string of periods after #1 in the message will increase and decrease in length as the computations proceed. Every time the string terminates and begins again it indicates that a layout improvement has been made. The system starts with an initial random "seed" layout, and operates on this layout until it is not able to improve it. This improved layout then becomes the "seed" and improvements on it are attempted by pairwise interchange of departments. This continues until no further improvements can be made, and the final resulting layout is saved. If more than one layout has been requested, the procedure begins again with a new seed. The display of Figure 26 is given when the procedure is completed. Figure 26. Resulting table of layouts after the Automatic Search Procedure was used. Five layouts were requested. The table of Figure 26 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 search request. It also shows the rankings of the layouts with each criteria. However, in the lower right hand corner of the display it gives the average time for each of the layouts that were generated. In this example the time was 15.19 seconds. If the user were to request 20 layouts from the automatic search procedure the total time that would be required would be approximately 20 X 15.19, or 303.8 seconds. There is no intervention required by the user once the automatic search procedure starts. However, for problems with large numbers of departments there may be a significant amount of time required for the search algorithm to 30 produce good layouts. This time is very dependent on the speed of the computer that is being utilized. A user may want to ask for a single layout from the automatic search procedure to get an idea of the average time to create a number of them. On some machines the average time may be several minutes per layout for 18 department problems, so the total time required to generate 20 layouts can be considerable. The automatic search procedures have been documented and tested (Pire, 1989) and consistently produces a variety of much better layouts than an experienced BLOCPLAN user could produce with earlier versions of BLOCPLAN during the same time. 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 ? The user responds with the layout number for the beginning point of the review. For example, if there are currently 15 layouts that are stored, and the user only wants to look at the last three, the response would be "13", and layout 13 would appear on the screen. Figure 27 shows the screen display when saved layout 1 from the table of Figure 26 is shown. 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. 31 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 the collection of those that have been saved. A response of "Y" to the prompt shown at the bottom of Figure 26 will cause the question: 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. 32 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. 33 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 (...

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U. Houston - INDE - 6370
C.E. DONAGHEY I.E. Dept. Univ. of Houston Houston, TX 77204Dr. William C. Moor I.E. Dept. Arizona State University Tempe, AZ 85287-5906
U. Houston - INDE - 6370
MULTISTORY-BLOCPLAN for 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. The existing version called BLOCPLAN-WIN
U. Houston - INDE - 6370
BLOCPLAN for 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
U. Houston - INDE - 6370
TYPE Y (ENTER) IF PROBLEM DATA IS TO BE STOREDThe program is asking if the user would like to save the data in memory. If the response is Y followed by the enter key, the next prompt would be:PROBLEM NAME_The user would assign a name to the pro
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WINFLOC VERSION 1.0 11/21/05 WINFLOC VERSION 1.0 11/21/05 WINFLOC VERSION 1.0 11/21/05 WINFLOC VERSION 1.0 11/21/05
U. Houston - INDE - 6370
BLOCPLAN (Single Story) for 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 BLOCP
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WINFLOC USER'S MANUAL WinFLOC is a collection of Material Handling and Facility Location models that can be run on PC's in a Windows environment. The models were developed in the Industrial Engineering Department at the University of Houston (1,2,3).
U. Houston - INDE - 6370
INDE 6370 Individual Lab Assignment #2 Due 30 MAR 06 The objective of this assignment is to further develop your model building skills with ARENA. All work is to be completed individually. Model and animate a customer service center which has a total
U. Houston - INDE - 6370
INDE 6370 - Digital Simulation General: This course covers the quantitative modeling of manufacturing, service, and engineering systems; analysis of input distributions; verification and validation; statistical comparison of alternatives; and animati
U. Houston - INDE - 6370
INDE 6370 Individual Lab Assignment #1 Due 2 MAR 06 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
U. Houston - INDE - 6370
INDE 6370 HW9 Due Thursday 17 April 2008 For this homework assignment you will reuse the model from HW8. This model contains 5 identical resources. Modify the file as necessary to also experiment with alternatives with 4 and 6 resources. For each of
U. Houston - INDE - 6370
INDE 6370 Individual Homework #1 Due 29 January 2008 The objective of this assignment is to introduce you to the concept of a simulation event list. 1. Develop an event list for the following interarrival and service time delays for a one queue, one
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INDE 6370 Lab 4 Due Tuesday 18 April 2006 Download the file lab4.zip from the website. It contains lab4.doe. You are interested in determining the effects of three different operating policies with respect to the order processing clerk (clerk02). The
U. Houston - INDE - 6370
INDE 6370 Lab 3 Due Tuesday 11 April 2006 Download the file lab3.zip from the website. It contains lab3.doe and lab3.txt. The file lab3.txt contains actual observation validation ASCII data. 1. Modify the model as necessary to obtain individual syste
U. Houston - INDE - 6370
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
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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
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AGENDAData collection updateReviewDATA COLLECTION UPDATECollectionAnalysisREVIEWBasic simulation issuesInput data analysisRandom number generationModelingBASIC ISSUES.Simulation processManual event listPerformance measures BASIC SIM
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AGENDAProject progress reportsArrivals elementResource related elementsSystem statusARRIVALS ELEMENTForce entities to appearModeling customers waiting before opening timeMake entities appear for demonstration purposes.ARRIVALS ELEMENTGen
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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
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AGENDABasic Simulation Study ProcessCourse ProjectsAn example projectBASIC SIMULATION PROCESSProblem DefinitionProject PlanningSystem Definition / Model FormulationInput Data Collection and AnalysisModel TranslationVerificationValidation
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AGENDAQueues relatedResource relatedSystem statusQUEUE RELATEDDuplicateMatchArrivals elementDUPLICATEUsed to generate additional entities from original entitiesAll duplicates inherit attribute valuesIf to be later rejoined, must have ide
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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
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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
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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
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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
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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
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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
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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
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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
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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
Penn State - ZUX - 103
An Improved Approach to Passive Testing of FSM-based SystemsHasan Ural, Zhi Xu and Fan Zhang SITE, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada {ural, zxu061, fzhang}@site.uottawa.ca AbstractFault detection is a fundamental part of passiv
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IE 327 Introduction to Work DesignDr. Andris Freivalds Class #24IE 327 1Ch. 17 Wage Incentives Can workers be motivated? Blue-collar: White-collar: Direct financial plans = pay proportional to output Indirect plans: Fringe benefits Vacat
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Geoscience 001 Spring 2006 Field Trip Lab The Bellefonte Formation and Nealmont Formations Materials: Students: hand lens, field notebooks Site: Hwy 322 By-Pass, 2 locations, along the east side of the road. This is a busy road, so stay well off the
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ANSWERS TO END-OF-CHAPTER 6 QUESTIONS6-1a. The probability distribution for complete certainty is a vertical line. b. The probability distribution for total uncertainty is the X-axis from - to +.6-2Security A is less risky if held in a divers
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Computer Science 6365February 7 and 12, 2008Lecture #8 and 9: Interconnection NetworksProfessor: S. Lennart Johnsson TA:Wei Ding1NetworksA bus based parallel architectures is practical only for a small number of processors. For several tho
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Pipelined Merging of Two sorted list in a constant time (Coles Algorithm) Leaves contain the value Internal nodes merge at each time by updating the values Lv: the sequence of values of descendants of v Qv(j): At time j, a sorted sequence v has.
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CHAPTER 2THE ORGANIZATIONAL BUYING PROCESSImportant Topics of the Chapter Changing Role of Business Buyer. The Business Buying Process. Business Buying and Buying Center. Environmental Forces and Buying Decision.Objectives of Business Buyers
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Compound interest. If one invests P dollars at an annual interest rate of i percent then the return S1 at the end of the rst year will be S1 = P + rP or S1 = P (1 + r) where r = .01i. The return S2 at the end of the second year can be viewed as inve
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Erich Schaefer 9/19/06 MIS 204 There are many advantages to using a computer in todays world. First and foremost would be the speed at which information can be conveyed. The list of things that a computer can process is virtually never ending. From m