ProfitPress Mega CDROM2 Shareware Freeware (MSDOS)(1992)(Eng)

home *** CD-ROM | disk | FTP | other *** search

/ ProfitPress Mega CDROM2 …eeware (MSDOS)(1992)(Eng) / ProfitPress-MegaCDROM2.B6I / APPS / BUSINESS / LP10026.ZIP / LP100.MAN < prev next >

Wrap

Text File | 1990-07-11 | 63.2 KB | 2,179 lines

ScanSoft(tm) LP100 Linear Programming Optimizer Version 2.60 (C)1988-1990 Cornel Huth LP100 OPERATIONS MANUAL -------------------------------------- [OVERVIEW] LP100 is a linear programming optimizer developed for either maximizing or minimizing small to medium sized mathematical programming problems in which all the relationships between variables are linear. It finds a BEST feasible solution to any continuous, integer, or mixed-integer optimization problem of this type and reports on the activities and levels required to maximize profit or minimize cost. LP100 also reports on alternate optima, shadow prices, ranges over which the shadow prices are valid and ranges over which profit/cost inputs and right-hand-side (RHS) values can vary without altering the solution. LP100 can use either LOTUS 1-2-3/Symphony spreadsheet files or ASCII files for data input. Output may be sent to most printers, any ASCII disk file, or directly to a LOTUS 1-2-3 spreadsheet file. Output may consist of useful model debugging information such as objective function and constraint listings, a condensed matrix map, and the full tableaux. LP100 handles problems with thousands of variables and thousands of con- straints. [INPUT FILE] LP100 reads a user created file for data input. Any text editor or word processor that can output unformatted ASCII text may be used. LOTUS 1-2-3 or Symphony (or any 1-2-3 compatible spreadsheet such as VP-Planner or Excel) can be used for creating the data file, as well. A batch facility is available in LP100. This allows LP100 to solve up to six LP problems per run without the need of using DOS's COMMAND batch facility. Such a file is to include only the LP filenames followed by any command line options and should contain no blank lines. To specify a batch file to LP100, precede the filename with an @ on the command line. E.g., if the batch file is named BATCHRUN.BLP, use C>LP100 @BATCHRUN.BLP. NOTE: The length of any one line should not exceed 2300 characters. 2 LP100 OPERATIONS MANUAL -------------------------------------- - EXAMPLE TITLE: An example of an LP100 data file. OUTPUT: EXAMPLE.OUT LISTING: YES MAP: YES TABLEAU: YES ANALYSIS: YES * anything after a '*' on a line is a comment VAR: 3 LTE: 2 GTE: 0 EQU: 1 FUNCTION: MAX: .185 stock + .090 bond -.150 loan MxLoan loan <= 5000 * no coefficient implies 1.00 MxStk stock <= 4000 MxCash stock + bond - loan = 10000 END: NOTE: It is not neccesary to use + operators between variables, e.g., ...MAX: .185 stock .090 bond -.150 loan is acceptable, as is ...MAX: +.185 stock +.090 bond + -.150 loan. 3 LP100 OPERATIONS MANUAL -------------------------------------- [STARTING LP100] To give LP100 a go, have LP100.EXE in your PATH and EXAMPLE.LP in the current directory, then type: C>LP100 EXAMPLE.LP In just a few seconds it's finished. Now do (printer on?): C>COPY EXAMPLE.LP PRN ... then do (you may want to advance the printer to the top-of-page): C>COPY EXAMPLE.OUT PRN The file EXAMPLE.LP is the data file that LP100 used and EXAMPLE.OUT is the file that LP100 created for the output. If you do not have a printer, have LPEDIT.COM in your PATH and EXAMPLE.OUT in the current directory, then type: C>LPEDIT EXAMPLE.OUT 4 LP100 OPERATIONS MANUAL -------------------------------------- [LINE OPTIONS] /B use with non-color composite displays connected to color card /C:nnn specify the attribute for color screens (fg+(bg*16)) <=255 - the above switches have no effect within LP100 batch files /O:filename specify the output destination (can include drive/path) /I:nn specify all-integer solution max of nn cutplanes (nn=0-99) /M:nn specify mixed-integer solution max of nn cutplane (nn=0-99) /Z:nn specify tolerance of zero (nn=.000000000001-.9) /PL:OFF suppress printer page length codes (page length from 88 to 66) /PW:OFF suppress printer page width code (for 15" printers) /FF:OFF suppress all form feeds except at end of report /L or /NL turn listing on or off (/Nx turns switch off) /MA or /NM turn map on or off /T or /NT turn tableaux on (first and last only) or off /A or /NA turn analysis on or off /VM use with problems too large for DOS memory C>LP100 EXAMPLE.LP /O:PRN /NL /NM /NT /NA /C:31 5 LP100 OPERATIONS MANUAL -------------------------------------- [COMMENTS] COMMENTS can be used in an LP100 data file. They may appear anywhere except on the TITLE: line. To include comments in the input file, begin the comment with an asterisk. All characters following the * to the end of that line are skipped. E.g., * LP data file for BUDGETING 1990 MODEL A1B. VAR: 233 * the constraints & variables were developed LTE: 35 * jointly by the OR & MIS departments GTE: 55 * EQU: 22 [KEYWORDS] Keywords are used to declare the problem to LP100. All keywords in LP100 end with a colon. TITLE: Trial MX01 * this is optional VAR: 52 LTE: 22 GTE: 44 EQU: 0 * these are required FUNCTION: MAX: 59.03 var1 + 35.57 var2 * these are required Keywords may be either upper or lower case. - TITLE: TITLE: is an optional keyword. Its purpose is to allow the user to specify the title used for each page heading. The keyword NAME: may be used interchangably with TITLE:, e.g., TITLE: Operations Research Planning Model 20A or, NAME: Operations Research Planning Model 20A If TITLE: or NAME: is not used, the input filename is used by default. NOTE: Only the first 48 characters following TITLE: will be used. Comments should not appear on the comment line. 6 LP100 OPERATIONS MANUAL -------------------------------------- - OUTPUT: OUTPUT: is an optional keyword. Its purpose is to allow the user to specify which device the output is to be sent. To send the output directly to the printer, use PRN after OUTPUT:, e.g., OUTPUT: PRN * or any valid DOS device name (\DEV\devicename) To send the output to disk, indicate the pathname after OUTPUT:, e.g., OUTPUT: C:\OR\B90\MODEL20A.OUT To send output in LOTUS 1-2-3 WKS format, specify a filename extension of WKS, e.g., OUTPUT: C:\123\MODEL20A.WKS NOTE: Only the analysis and solution sections are in 1-2-3 format; the listings, map, and tableaux are in ASCII format and will be overwritten if there are no errors in the data file. If OUTPUT: is not used, the input filename.OUT is used by default. - LISTING: LISTING: is an optional keyword. Its purpose is to allow the user to specify if listings of the objective function and constraints are to be output. The listing numbers each objective function variable, showing its name and coefficient and whether the objective is to maximize or minimize the function. For each constraint, its name, matrix row position, and the coefficient and name of the non-zero variables and the value of the RHS is given. The LTE's fill from row 1 down, GTE's fill from the last GTE up, EQU's fill from the last GTE+1 down in the matrix (to handle negative RHS's). If the RHS of a constraint is negative, an N precedes its name. It will have been multiplied through by -1 and the type changed if an inequality. To activate the listing, use YES. For no listing use NO. E.g., LISTING: YES * If LISTING: is not used, NO is used by default. 7 LP100 OPERATIONS MANUAL -------------------------------------- - MAP: MAP: is an optional keyword. Its purpose is to allow the user to specify if a mapping of the initial matrix is to be output. The map is shown in condensed form with variable names output vertically and the constraint names along the left. For each matrix position a symbol is used to indicate in which range that value is. For instance, all zero elements show as blanks, all one elements as 1, greater than 1 but less than 10 as W, and so on. To activate the mapping, use YES. E.g., MAP: YES * If MAP: is not used, NO is used by default. NOTE: The matrix fills from the top down for LTE's and from the bottom (actually right before the first EQU) up for GTE's. - TABLEAU: TABLEAU: is an optional keyword. Its purpose is to allow the user to specify if tableaux are to be output. The tableau that is output is of the last iteration completed. The objective function variables and values are listed. The variables in the current basis along with their row elements and RHS's follow. A Z follows the objective function evalua- tion and an R follows each of the RHS values. To activate tableau output of the initial and last tableaux only, use YES, or I&L. To output all tableaux, use ALL. E.g., TABLEAU: YES * or TABLEAU: I&L * or, for all, TABLEAU: ALL * If TABLEAU: is not used, NO is used by default. - ANALYSIS: ANALYSIS: is an optional keyword. Its purpose is to allow the user to specify if an analysis of the solution is to be output. The analysis is divided into two summaries. In the variable summary, each variable name, alternate optima check, activity level, shadow price, input coefficient, and range over which the input coefficient may vary without 8 LP100 OPERATIONS MANUAL -------------------------------------- altering the solution set is given. Also shown is the variable ENTERING the basis when this range is exceeded. In the constraint summary, each name, type, unused capacity/- excess demand, shadow price, input RHS, and range over which the RHS may vary without altering the solution set is given. Also shown is the variable EXITING the basis when this range is exceeded. To activate analysis output, use YES. E.g., ANALYSIS: YES *If ANALYSIS: is not used, YES is the default. - BIG-M: BIG-M: is an optional keyword. Its purpose is to allow the user to specify the objective function coefficient given to artificial variables. LP100 uses the BIG-M improved SIMPLEX algorithm. Starting the SIMPLEX algorithm requires an artificial variable for the GTE: with the largest RHS and one for each EQU: constraint. To ensure that the algorithm removes these as quickly as possible from the basis, a very large value is given it. BIG-M: allows the user to specify this value. NOTE: In minimization problems, values in the objective function are interpreted as contributions to cost. Thus, absolute values should be used, i.e., 37.6667 MAT123 for the contribution to cost of MAT123. To specify BIG-M: use the absolute value after the keyword. E.g., BIG-M: 1000000 * If BIG-M: is not used, 1,000,000 is default. * 1D+006 may be used instead of 1000000. - TZERO: TZERO: is an optional keyword. Its purpose is to allow the user to specify a tolerance value for zero. LP100, like most computer software, deals with numbers in a finite precision. In repeated manipulations of numbers that have been truncated to a specific precision, round-off errors may occur. TZERO: allows for this somewhat in critical areas 9 LP100 OPERATIONS MANUAL -------------------------------------- by forcing the algorithms and output routines to interpret very small values near 0.00 as 0.00. LP100 uses IEEE double-precision floating-point numbers. With an 80x87 math coprocessor, very fast and precise computations are made. If an 80x87 is not installed, software emulation is used. To specify TZERO: use the absolute value after the keyword. E.g., TZERO: 1D-012 * If TZERO: is not used, 1D-012 is default. * .000000000001 may be used instead of 1D-012. * If INTEGER:/MIXED:, .00001 is used unless /Z: is used. - INTEGER: INTEGER: is an optional keyword. Its purpose is to allow the user to specify that an all-integer solution is to be sought. LP100 uses a cutplane algorithm to solve an all-integer problem. All constraint coefficients/RHS should be integer. The maximum number of cutplanes that will be used to find a solution is to follow the keyword INTEGER:. The range is from 0 to 99. If the maximum number of cutplanes is reached, LP100 exits and uses the current solution. NOTE: If the cutplane technique is going to find a solution, it generally does so quickly. The range analysis will not be valid since it is calculated for continuous ranges. EQU constraints cannot be analyzed. The memory requirement increases by one constraint and variable for each cutplane requested. Because rounding errors are more pronounced, TZERO: is set to .00001. This can be changed only with /Z:. Solu- tions cannot be guaranteed. This feature should be used only for small problems. - MIXED: MIXED: is an optional keyword. Its purpose is to allow the user to specify that a mixed-integer solution is to be sought. LP100 uses a cutplane algorithm to solve a mixed-integer problem. Any integer constraint should have integer coeffi- cients and RHS. The maximum number of cutplanes that will be 10 LP100 OPERATIONS MANUAL -------------------------------------- used to find a solution is to follow the keyword MIXED:. The range is from 0 to 99. If the maximum number of cutplanes is reached, LP100 exits and uses the current solution. To specify a decision variable or slack (or surplus) variable to have an integer value in the solution, begin the decision variable or constraint name with a CAPITAL letter between I and N (I,J,K,L,M,N). The notes for INTEGER: apply to MIXED:. - VAR: LTE: GTE: EQU: VAR:, LTE:, GTE:, EQU: are all required keywords. VAR: declares the number of decision variables in the model. LTE:, GTE:, and EQU: declare the number of less-than-equal-to, greater-than-equal-to, and equal-to constraints, respectively. E.g., VAR: 22 LTE: 5 * 3 of these LTE: constraints have negative RHS's GTE: 3 EQU: 2 NOTE: If the RHS of an LTE: or GTE: is negative, the LTE: or GTE: number will be adjusted by LP100, e.g., there are 5 LTE:'s and 3 GTE:'s, yet 3 LTE:'s have negative RHS's. LP100 will transform those 3 LTE:'s to GTE:'s and adjust the LTE: number to 2 and GTE: to 6. - FUNCTION: FUNCTION: is a required keyword. FUNCTION: is to mark the start of the problem definition portion of the model. - MIN: MAX: MIN: and MAX: are required keywords, though only one may be specified. MIN: indicates to LP100 that the objective function following is a cost function that is to be minimized; MAX: indicates that the function is a profit function that is to be maximized. 11 LP100 OPERATIONS MANUAL -------------------------------------- - END: END: is an optional keyword. Its purpose is to indicate the end of the problem definition portion of the model. Any data following END: is not used. This keyword is useful if the model is to be extensively documented. All comments that appear before END: will slow the parsing process. Therefore, extensive comments should appear after the END: keyword. NOTE: END: must have nothing else on its line. [OBJECTIVE FUNCTION] The objective function contains variables and coefficients to those variables representing the variable's profit or cost. The coefficients used normally should be positive for both profit and cost problems; the values are interpreted accordingly by specifing MIN: or MAX:. If, however, in a profit function a cost is associated with a variable, then that variable's coefficient should be negative. Likewise in a cost function, if a profit is associated with a variable, its coefficient should be negative. All decision variables (number following VAR:) in the problem must be in the objective function, including those with coefficients equal to zero (so that LP100 can later recognize them). E.g., FUNCTION: MAX: 10 VAR01 + 15.59 VAR02 + 0 VAR03 - VAR04+... [VARIABLES] Variables are used in linear programming problems to represent an activity of an operation. Only decision variables (number following VAR:) are to be input to LP100. Slack, surplus, and artificial variables of the constraints are created by LP100, as needed. These variables take the name of their constraint and are preceded by a - for slack, + for surplus, and ! for artificial variables. Each variable may be up to six characters (the first being a letter) and must be unique, as must variables within con- straints, i.e., don't have two identical variable names in the same constraint. LP100 has error detection and reporting schemes to indicate these type errors. 12 LP100 OPERATIONS MANUAL -------------------------------------- Any variable not preceded by a coefficient is given a value of 1.00. NOTE: Do not use + or - in a variable name nor use E or D alone as a variable name (it would then be interpreted as a number). [CONSTRAINTS] Constraints are used in linear programming problems to repre- sent limitations to the objective function. For each less-- than-equal-to (LTE) constraint, LP100 adds to the objective function a slack variable that is named as the constraint, preceded by a -, and has a coefficient of 0. For each GTE constraint, a surplus variable is added, preceded by a +, with a coefficient of 0. In addition, one artificial variable is added for the GTE with the largest RHS, preceded by a ! and a coefficient of BIG-M. For each EQU an artificial variable, preceded by a ! and a coefficient of BIG-M, is added. The number of each type of constraint is indicated in the declaration portion (LTE:, GTE:, EQU:). Constraints may be entered in any order, but LTE, GTE, EQU is recommended. Each constraint is to be named (as the variables are), should include only the non-zero variables, and end with the RHS value preceded by the corresponding relational operator (<=, >=, =). E.g., CON001 5X11 -X22 <= 5000. - SLACK For each LTE constraint in the linear programming problem, LP100 adds a slack variable. This slack variable is to represent the amount of unused capacity. If, for instance, the total number of hours available for use of a machine is 280 per month, then if in the optimal solution the total hours for that machine is 260, then 20 hours is unused, or slack. This slack capacity has an associated shadow price which indicates the rate of change of the value of the objective function when the available resource (capacity) varies. (If there is unused capacity then the value of additional capacity is 0.00, of course.) This shadow price is valid only over 13 LP100 OPERATIONS MANUAL -------------------------------------- the range of optimality for that variable. If one unit more were available, profit would increase (cost would decrease) by the shadow price; if one less unit were available, then profit would decrease (cost increase). A shadow price of zero is given to a slack variable in the final solution and also to any alternate optima. A slack variable is named for its constraint, is preceded by a -, and has an objective function coefficient of 0. - SURPLUS For each GTE constraint in the linear programming problem, LP100 adds a surplus variable. This surplus variable is to represent the amount in excess of demand. If, for instance, the total number of desks needed by contract is 100 per month, then if in the optimal solution, the total desks to be produced that month is 105, an excess, or surplus, or 5 desks exists, relative to the contract constraint. This surplus demand has an associated shadow price which indicates the rate of change of the value of the objective function when the requirement (demand) varies. This shadow price is valid only over the range of optimality for that variable. If one unit more were required, profit would increase (cost would decrease) by the shadow price; if one less unit were required, then profit would decrease (cost increase). A shadow price of zero is given to a surplus variable in the final solution and also to any alternate optima. A surplus variable is named for its constraint, is preceded by a +, and has an objective function coefficient of 0. - ARTIFICIAL For each EQU constraint in the linear programming problem, LP100 adds an artificial variable. For the GTE constraint with the largest RHS, LP100 adds an artificial variable. The other GTE constraints are temporarily transformed into LTE con- straints by multipling through by -1. This is a requirement for starting the SIMPLEX algorithm. If there are no GTE constraints, a dummy artificial variable is added, nonetheless. 14 LP100 OPERATIONS MANUAL -------------------------------------- An artificial variable is named for its constraint, is preceded by a !, has an objective function coefficient of BIG-M and, if in the final solution, must have an activity level of zero. NOTE: If an artificial variable of a redundant equality constraint occurs in the solution with an activity level of zero, the sensitivity analysis and shadow prices may have been grossly misstated. Therefore, it is suggested that those equality constraints with artificial variables in the final solution (indicated by a !) be removed from the model or changed to a GTE and the model run again. [DISPLAY SCREEN] Date, time, coprocessor status(87 or EmuLATION)/speed index- (PC=1.0), virtual memory status, and available memory remaining are shown on top line. The FILES In/Out display the rightmost 20 characters of the filenames. OPTIONS displays the status of the output switches. If degeneracy is detected, DEGENERATE is displayed below PROFIT EVALUATION. INTEGER, MIXED, BIG-M, and TZERO are displayed. Constraint and variable counts are displayed. The SIMPLEX STATUS indicates the time the SIMPLEX algorithm was entered and its estimated finish. Iterations equals SIMPLEX pivots. Elapsed time is actual time spent in SIMPLEX (which excludes tableau output and cutplane formulation). PROFIT EVALUATION is the function value at the current iteration. FILE DISPOSITION lists files in queue. The status of the current file is continually displayed. [OUTPUT] The output may be sent either to a disk file or directly to a printer. Output may include the problem definition listings, 15 LP100 OPERATIONS MANUAL -------------------------------------- a condensed matrix map, tableaux, and solution analysis in addition to the final solution. ASCII output is formatted to 132 columns and a page break is generated for each page with appropriate section headings. Beginning each output are the necessary printer control codes for the 132 column output and 88 lines/page. Ending each output are the codes to restore the printer to normal. These codes are EPSON compatible printer codes and work with the most dot-matrix printers. Disk output may be edited by any ASCII text editor, imported to wordprocessor programs, or sent directly to a WKS spreadsheet file. NOTE: Make sure that sufficient disk space is available if output is directed to disk - especially a 360KB floppy. - LISTING SECTION The listing section is the LP100 interpretation of the data file. The data in this section is the actual data used by the program. If LISTING: has been requested then the objective type (maximization or minimization), the number of variables, and the variables and coefficients are displayed, 4 per line. The constraints follow. For each of the constraints, the name, row position in the initial tableau, coefficient and name for non-zero variables is output followed by the operator (<=, >=, =) and RHS. If the RHS was negative, an N precedes this. If LP100 detects an error, such as a duplicate variable name, and listing has been requested, then the error message is output at the point of the error. If no listing has been requested, the error message alone is output. - MAP SECTION The map section contains a condensed listing of the initial matrix including the decision variables and constraints. Atop each map section page a legend of the symbols used is shown. The map heading showing the variable names follows. The objective function and variable symbols are next, and for each constraint, its type, name, initial variable coefficients, plus RHS value, are shown. 16 LP100 OPERATIONS MANUAL -------------------------------------- The map is useful for debugging. It can show most wildly-off data entries, as well as positional type errors. NOTE: If output to a printer, the map should extend no more than the columns available with the printer. Printers with 132 columns can print up to 60 variables/line before the following data wraps to the next line. Many text editors allow column widths of 512 characters or more. With such an editor, the map can be displayed without the confusing wrap-around. - TABLEAU SECTION The tableau section contains the objective function, its evaluation, the basic variables, matrix coefficients, and RHS's at that particular tableau. Either the initial and last tableaux or all tableaux may be output, depending on TABLEAU:. The tableaux can be used for debugging. It is a detailed version of the matrix map, and is available at every iteration, whereas the map is available for the initial tableau only. It also can display all the variables without wrap-around problems since it formats the output for 8 variables per line, using as many lines as are necessary. For ease of spotting, a Z follows the objective function evaluation, and an R follows every RHS. The SIMPLEX algorithm as implemented in LP100 always solves the problem as a maximization type. Minimization problems have the original objective function multiplied through by -1. This will in no way affect the outcome. It is mentioned here since the label MAXIMIZE is at the beginning of each tableau. - ANALYSIS SECTION The analysis section contains a wealth of information that the user will find extremely useful. This section is divided into two sections, the variable summary, and the constraint summary. Within the variable summary (for each variable) an indication is given if that variable is an alternate optima, the activity level of that variable (blank if not in the solution), its shadow price, and a sensitivity analysis (or range of optimal- ity) of the input coefficient. This ranging indicates the lower and upper values that the input coefficient may take, everything else remaining the same, and not alter the solution set (activities and levels of the solution). Where a range is 17 LP100 OPERATIONS MANUAL -------------------------------------- exceeded, the name of the variable ENTERING the basis is given (though not necessarily the final solution). In the constraint summary for each constraint, its type, amount of slack/surplus, shadow price, and range of optimality for the RHS value is given. Where a range is exceeded, the name of the variable EXITING the basis is given. - SOLUTION SECTION The solution section is the bottom line of the linear program- ming problem. It indicates a set of variables and activity levels that optimizes the objective function given the con- straints. The objective function evaluation is the first entry in this section and equals the optimal profit or cost. Each of the solution variables, its associated activity level, input coefficient, and extended amount (of profit or cost) follow. NOTE: The FUNCTION activity level represents the optimal value of the profit function (maximize) or cost function (minimize). It will normally have a positive value - a cost function should be interpreted as having this much cost. Each of the extended amounts are likewise representing profit or cost. NOTE: There should be no artificial variables (!) in the solution set unless the activity level of that variable is zero. If positive, the problem is considered infeasible. [ALTERNATE OPTIMA] ALTERNATE OPTIMA, or ALT OPT, indicates that a variable not in the solution set was qualified to be so. Its shadow price will necessarily be zero. To force this variable into the solution set, scan over to the range analysis for that variable. Altering that variable's input to exceed that range by a small amount will cause the alternate variable to most likely enter the solution (solve the problem again). Additionally, re- arranging variable or constraint order may cause the alternate to enter the solution. Best, though, is to use a GTE inequal- ity at the level required for that variable. If the LP problem is found to be unbounded, the variable that is responsible is indicated by UNB in the ALT OPT column. 18 LP100 OPERATIONS MANUAL -------------------------------------- NOTE: If after the first run, you wish to FORCE an alternate optimum into the solution, DO NOT use an equality constraint. Instead, use a >= inequality. E.g., X22 is ALT OPT - use CONADD X22 >= 50 as a new constraint, not CONADD X22 = 50. [ACTIVITY LEVEL] Activity level is the value that a variable is to take in order to achieve the optimal profit (or cost). Blank activity levels should be interpreted as being zero. The activity level of FUNCTION in the solution section should be interpreted as the optimal profit or cost evaluation of the objective function. It is normally positive. [SHADOW PRICE] Shadow prices fall into two categories. One category indicates the rate of change in the objective function evaluation if an activity that is not in the solution set is introduced in the solution anyway. This marginal cost represents the amount by which that activity, or variable, is 'too expensive' to be included in the solution set. This category is attributable to the decision variables in the VARIABLE SUMMARY. The other category indicates the rate of change in the objec- tive function evaluation when the RHS value of a constraint changes. This marginal cost represents the amount by which the objective function value will vary with changes in the RHS. This category is attributable to the constraints (and the slack and surplus variables in the VARIABLE SUMMARY) in the CON- STRAINT SUMMARY. Shadow prices are valid only over that variable/constraint's range of optimality. [UNUSED CAPACITY] The unused capacity in the constraint summary of the analysis section represents the amount of left-over resource for that LTE constraint. It is included in the solution set as a slack variable. 19 LP100 OPERATIONS MANUAL -------------------------------------- [EXCESS DEMAND] The excess demand in the constraint summary of the analysis section represents the amount of over-produced requirement for that GTE constraint. It is included in the solution set as a surplus variable. [RANGE ANALYSIS] Range analysis, also called sensitivity analysis, gives the user useful information on the sensitivity of the data used in the problem. Since accurate data may be expensive to obtain, a model using the best available data can be used initially. The analysis section can then be used to determine which data are the most sensitive. These can then be further researched. Range analysis is performed on each of the variables and constraints. For each variable, its input coefficient is analyzed to see over which range of values it may take while not altering the solution set, everything else remaining the same. Likewise for each constraint, except its RHS value is analyzed. Additionally, the variable ENTERING (variable EXITING for constraints) the basis (solution set) when a range is exceeded is shown. This variable may or may not be part of the final solution set, since additional iterations of the simplex algorithm may be needed. [DEGENERATE] If there are redundant constraints in a problem, it is possible that a degenerate solution may develop (if so, DEGENERATE will be displayed on the screen). Degeneracy in itself does not pose any problems, usually. It may, however, lead to a problem known as cycling. Cycling, once developed, causes the computer code to endlessly cycle with no improvement in the objective function. Fortunately, this seldom occurs with real-world problems. Altering the order of constraints or variables usually corrects this problem, should it ever occur. Another problem associated with degeneracy is when an ALT OPT variable is forced into a succesive LP100 solution set by using an equality (=) constraint. This constraint will 20 LP100 OPERATIONS MANUAL -------------------------------------- necessarily be redundant. Use an inequality (>=), instead. Otherwise, the sensitivity analysis and shadow prices may be grossly misstated. This problem is easily identified by: one, an artificial(!) variable(s) will be in the solution set (at zero) and two, a shadow price(s) will be grossly misstated (by BIG-M). At this point, the equality constraint(s) with its artificial (!) in the solution should be removed or changed to an inequality (>=), and rerun. Degeneracy may occur even if there are no redundant constraints. [ABORTING] Pressing Esc will have the following effect on LP100. If LP100 is: PARSING DECLARATIONS, or PARSING OBJECTIVE FUNCTION, or PARSING CONSTRAINTS, or OUTPUTTING SOLUTION pressing Esc will end the current problem, or if: OUTPUTTING MAP, or OUTPUTTING TABLEAU, or OUTPUTTING ANALYSIS pressing Esc will skip that particular section, or if: FINDING FEASIBLE SOLUTION, or ADDING CUTPLANE, or OPTIMIZING pressing Esc will cause LP100 to complete the current simplex iteration as if it had found an optimal solution. Also available is an immediate abort key: <Ctrl><F1>. Upon pressing this key combination, the entire LP100 session is immediately aborted to DOS. [SPREADSHEET] LP100 allows the user to use LOTUS 1-2-3 or Symphony as a tool to create LP100 data files. 1-2-3 versions through 2.01 and Symphony through 1.1 can be directly read by LP100. Future versions of these spreadsheets may or may not produce compat- ible file ID bytes. If a version later than those above is used and LP100 reports an unknown LOTUS file format (unlikely), save the 1-2-3 data in WKS, WK1, WRK, WR1 format. These formats are known to be compatible with LP100. If the OUTPUT: specifies that output should be sent to a file with an extension of WKS, then LP100 will format the analysis and solution sections in LOTUS 1-2-3 version 1A format. This 21 LP100 OPERATIONS MANUAL -------------------------------------- file can be read by many spreadsheet programs, not just those of LOTUS. The listings, matrix map, and tableaux will also be output, but in ASCII format. If there are no errors, this ASCII output will be overwritten by the analysis and solution sections in WKS format. [LPEDIT.COM] To put a linear program in LP100 readable form requires an ASCII text editor (or Lotus, et. al). Many word processors also allow their output to be in ASCII and even some spread- sheets programs can 'print' to an ASCII file. Included with the LP100 package is a full-screen text editor that allows basic text editing. To edit a new file, include the new filename on the command line after LPEDIT, or, use an existing one to edit an old file. E.g., C>LPEDIT EXAMPLE.LP Commands are issued via the F keys and are displayed on the last line. The maximum file size is 64KB. Maximum editing width of a line is 248 columns. The keypad keys are used to position the cursor and <Ctrl> left/right-arrow is used to pan left and right. A minimum of 68K of free RAM is needed by the editor. If 132K is available, print/mark/cut/paste are functional. NOTE: The F3-PRINT key is used to print marked text only. [VIRTUAL MEMORY] For problems too large for available RAM, use the /VM command line switch. This will write the matrix to disk and call it in as needed. The speed penalty will be very dependent on the speed of your virtual storage device. If you have a RAM disk in extended or expanded RAM, expect the problem to take 3 times longer than if you had that RAM available to DOS. Not bad when you consider the problem could not be solved at all without this feature. If you use this mode, INTEGER, and MIXED will be turned off. Tableaux can only be printed by using LPDUMP.EXE, and only if TABLEAU was YES. LP100 will use the DOS variable TMP to locate LP100V23.VMM, 22 LP100 OPERATIONS MANUAL -------------------------------------- and, if TABLEAU is YES, LP100V23.DIC. If TMP is not defined, the current directory is used. [LPDUMP.EXE] This program will dump the final tableau of problems solved with the /VM switch to a WKS file. TABLEAU must have been YES. LPDUMP will use the LP100V26.VMM & LP100V26.DIC files to create a Lotus 1-2-3 1A WKS spreadsheet, readable by most spreadsheet programs. The number of columns that your spreadsheet can handle should be at least the value of RHS + 1 (RHS can be found in the LP100V26.DIC file). LPDUMP.EXE uses the TMP DOS variable to locate the VMM, DIC, & WKS files or will use the current directory if TMP is not defined. E.g., C>LPDUMP will use LP100V26.VMM, LP100V26.DIC, LP100V26.WKS or, C>LPDUMP filename will use filename.VMM, filename.DIC, filename.WKS. You are given the chance to alter any of the pathnames in LPDUMP. 23 LP100 OPERATIONS MANUAL -------------------------------------- - LP100V26.VMM LP100V26.VMM is the virtualized matrix. Its format is: x=don't care OFC=obj func coef m=RHS-1 x OFC1 OFC2 OFC3 ... OFCm Z Z=obj func value B1 MC11 MC12 MC13 ... MC1m RHS1 RHS=right-hand side B2 MC21 MC22 MC23 ... MC2m RHS2 MC=matrix coefficient B3 MC31 MC32 MC33 ... MC3m RHS3 B=basis Bn MCn1 MCn2 MCn3 ... MCnm RHSn n=# of constraints It's streamed without any delimiters. Each value is an IEEE 8-byte double-precision float. The matrix is in row-major order. To determine where each row begins use this formula: FirstByteOfRow(i) = (i-1)*((RHS + 1)*8) where i is 1-based. RHS can be found in LP100V26.DIC. - LP100V26.DIC LP100V26.DIC is only created if TABLEAU is YES. It is an ASCII text file describing the LP problem. CON is number of con- straints (rows) not including the objective function RHS is the right-hand side column of the matrix VAR is the number of decision variables LTE is the number of less-than-or-equal to constriants GTE is the number of greater-than-or-equal to constriants EQU is the number of equal to constriants. The names of the variables in the basis (Bn above) follow BASIS. The column names (OFCm above) follow COLUMN NAMES. [ERRORS] - FILE File errors occur when LP100 is unable to access either the input data file or create the output file. These type errors cause LP100 to abort to the next file in the queue. FILE NOT FOUND indicated file was not found CANNOT OPEN INPUT indicated file cannot be opened (bad name) CANNOT OPEN OUTPUT indicated file cannot be opened (bad name) 24 LP100 OPERATIONS MANUAL -------------------------------------- - DECLARATION Declaration errors occur when LP100 is unable to properly format the model as given. Since an output channel may not have been assigned, error reporting is done on the disposition line of the display screen. If a single error was detected, the error itself, followed by its code, is listed on this line. If, however, more than one error was detected, the error message *** MULTIPLE DECLARATION ERRORS is listed followed by a code indicating the errors. LP100 then aborts to the next file in the queue. The error codes are: 00000001 VAR: NOT FOUND In the case of multiple errors, 00000010 LTE: NOT FOUND combinations of these codes will 00000100 GTE: NOT FOUND be output, e.g., 00001001 means 00001000 EQU: NOT FOUND that VAR: and EQU: were not found 00010000 FUNCTION: NOT FOUND in the LP data file. 00100000 MAX: or MIN: NOT FOUND 01000000 UNKNOWN CHARACTER IN DECLARATION - OBJ FUNCTION Objective function errors occur when LP100 is unable to properly read and interpret the objective function. Since an output channel will have been made by this point, the error report is sent to the output. The display screen will show the error message *** OBJECTIVE FUNCTION ERROR and the error code and LP100 aborts to the next file in the queue. The error codes are: 00000001 FORMULATION BAD NEAR VARIABLE too many operators(+/-) 00000010 UNKNOWN VARIABLE # indicated variable not expected 00000100 DUPLICATE VARIABLE # indicated variable used > once Multiple errors are not detected. - CONSTRAINT Constraint errors occur when LP100 is unable to properly read and interpret a constraint. Since an output channel will have been made by this point, the error report is sent to the output. The display screen shows the error message *** CONSTRAINT ERROR and the error code and LP100 aborts to the next file in the queue. The error codes are: 25 LP100 OPERATIONS MANUAL -------------------------------------- 00000001 FORMULATION BAD too many operators (+/-) 00000010 UNKNOWN VARIABLE indicated variable not in FUNCTION: 00000100 DUPLICATE NAME indicated name used more than once 00001000 ILLEGAL CONSTRAINT NAME indicated name is illegal 00010000 LTE: count does not match declaration 00100000 GTE: count does not match declaration 01000000 EQU: count does not match declaration 10000000 MATRIX ALLOCATION OVERRUN LTE:+GTE: does not match - 123 READ When input is taken from a LOTUS file the following errors may occur. These cause LP100 to abort to the next file in the queue. FILE NOT FOUND indicated file was not found CANNOT OPEN INPUT indicated file cannot be opened (bad name) UNKNOWN OR CORRUPT LOTUS FILE format unknown - 123 WRITE When ouput is sent to a WKS file the following error may occur. This causes LP100 to abort to the next file in the queue. CANNOT OPEN OUTPUT indicated file cannot be opened (bad name) - INFEASIBLE MODEL An INFEASIBLE MODEL error occurs if, at the time SIMPLEX algorithm has found an optimal solution, an artificial variable remains in the basis (solution set) at a positive activity level. The next file is begun. - UNBOUNDED MODEL An UNBOUNDED MODEL error occurs if, at anytime in the SIMPLEX algorithm, a variable can be introduced without bound. The unbounded variable is identified by UNB in the ALT OPT column. The next file is begun. - ABORT An ABORT error occurs if the user presses <Esc> to abort the current problem that LP100 is solving or if the user presses 26 LP100 OPERATIONS MANUAL -------------------------------------- <Ctrl><F1> to immediately abort the LP100 session to the system. NOTE: If Esc is pressed in certain LP100 routines, that and only that routine is exited early. Output will indicate this if it occurs. - RUN-TIME A RUN-TIME error may occur under certain circumstances. These are rare and in such an event, the LP100 session is aborted to DOS. 6 NUMBER OVERFLOW 24 DEVICE TIMEOUT 7 OUT OF FAR MEMORY 25 DEVICE FAULT 11 DIVISION BY ZERO 27 OUT OF PAPER 14 OUT OF NEAR MEMORY 61 DISK FULL 71 DRIVE NOT READY BASIC error numbers 52 to 76 are mostly hardware/disk related. If a run-time error continues to occur see REPORT BUGS TO... In addition to the RUN-TIME error number, the MODULE and LEVEL at which the error occured are indicated on the disposition line. Run-time errors 7 and 14 are handled specially by LP100. The message OUT OF MEMORY will be displayed on the disposition line with no MODULE or LEVEL report available. This generally means that the problem you have specified is too large for the RAM available. [REPORT BUGS TO...] Though LP100 has been through significant testing, minor bugs may occur. If you experience any problems in using LP100 write a complete description of the problem using BUG REPORT FORM form as a guide. Also include a listing of the model, and if possible, include the model on a 5 1/4" floppy. Send this to: Cornel Huth ATTN: LP100 v2.60 REPORT 6402 Ingram Rd. San Antonio, TX 78238 If necessary, call (512)684-8065 (9am-9pm Central Time). Assistance can be given only in the use of LP100, not with the linear programs/models that need to be formulated. 27 LP100 OPERATIONS MANUAL -------------------------------------- - BUG REPORT FORM Program: LP100 v2.60 S/N: - Have you registered? ------- -- ---- Name: -------------------------------------------------------- Addr: -------------------------------------------------------- -------------------------------------------------------- -------------------------------------------------------- Phone: ( ) - ext. (only if collect) ------ --------- ------ Describe the problem, the circumstances of its happening, and any errors reported by LP100 or the system. Include a descrip- tion of the hardware and operating system and any other software loaded in memory. Any suggestions for improvement are welcome. 28 LP100 OPERATIONS MANUAL -------------------------------------- [SPECIFICATIONS] MINIMUM REQUIREMENTS: 256K IBM-PC or compatible DOS 2.1, one floppy drive 216,000 bytes free of system memory as reported by CHKDSK.EXE The maximum problem size depends on available memory. Use this formula to APPROXIMATE the number of K bytes needed by LP100 as displayed in the upper-right corner of the display screen at start-up (at 99%). {[(VAR:+LTE:+GTE:+EQU:+2)*(LTE:+GTE:+EQU:+1)*8]+32000}/1024 = K RAM needed This is about 100 constraints and 400 variables, not counting slacks. In /VM mode you will be able to solve much larger problems, typically 1000 variables and 1000 constraints on 640K machines (with adequate virtual storage and time). The 8087/80287 math coprocessor will be used if available. 29 LP100 OPERATIONS MANUAL -------------------------------------- [INCLUDED FILES LIST] README initial instructions & information LP100.EXE linear programming optimizer LPHELP.EXE help program LPDEMO.EXE demonstration program LPDUMP.EXE dumps /VM final tableau to WKS LPEDIT.COM full-screen ASCII text editor LP100.HLP data file used by the help program LP100.MAN LP100 Operations Manual EXAMPLE.LP ASCII LP data file (simple example) INTEGER.ILP ASCII LP data file (all-integer example) MIXED.MLP ASCII LP data file (mixed-integer example) EXAMPLE.WKS WKS LP data file (similar to EXAMPLE.LP) PROJECT.ILP ASCII LP data file (project assignment example) NRC85.WKS WKS LP data file (diet example) NOTE: Be sure to make a working copy of this disk. 30 LP100 OPERATIONS MANUAL -------------------------------------- [SHAREWARE] Shareware is a means that software authors have of releasing their product without the overhead costs of marketing and packaging. This gives users the option of obtaining a quality product at a truly reasonable price. It also may be the only means of obtaining software that is not available elsewhere, at any price. What this means is that users can use the product on a trial basis without any obligation to purchase the software. Generally, users may freely distribute the product to others provided that any licensing agreement or stipulations that the author has specified be followed. The shareware concept does not allow a user to continue using the product after the trial period unless the license agreement has been fulfilled or otherwise been given permission by the author. ************************* NOTICE ****************************** All LP100 *.EXE programs in the INCLUDED FILES LIST are the sole property of Cornel Huth and are Copyright 1988-1990 by Cornel Huth. - LICENSE AGREEMENT USAGE: LP100 may be used on a trial basis for 30 days. After this, the user promises to fulfill this license agreement or discontinue using LP100. By using LP100 you agree to abide by this LICENSE AGREEMENT. FULFILLMENT: A limited license for using LP100 on a single computer may be purchased for $50.00. Site licenses are available. After receiving payment, a current, registered version and receipt of payment is sent. DISTRIBUTION: LP100 may be distributed without the author's permission only if the following three stipulations are followed: 1. The LP100 package must be distributed complete, including ALL files listed in INCLUDED FILES LIST. 2. The LP100 package CANNOT be sold for profit. Recovery of costs associated with distribution is allowed (NO PROFIT). 3. ONLY the SHAREWARE version of the LP100 package may be distributed. 31 LP100 OPERATIONS MANUAL -------------------------------------- - REGISTRATION FORM Name of licensee: ----------------------------------------- Amount paid: $ ($50.00 ea. Site licenses available) --------- Comments: ----------------------------------------------------- ----------------------------------------------------- Contact: Phone:( ) - ---------------------- ---- ----------- Would you like to be added to our mailing list? -------------- Mail to: ----------------------------------------------------- ----------------------------------------------------- ----------------------------------------------------- ----------------------------------------------------- Send payment to: Cornel Huth ATTN: LP100 v2.60 REGISTRATION 6402 Ingram Rd. San Antonio, TX 78238 32 LP100 OPERATIONS MANUAL -------------------------------------- [TRADEMARKS] * Microsoft, QuickBASIC, and Excel are registered trademarks of Microsoft Corp. * Lotus, 1-2-3, Symphony are registered trademarks of Lotus Development Corp. * VP-PLANNER is a registered trademark of Paperback Software International * IBM is a registered trademark of International Business Machines Corp. * ScanSoft, LP100, LP OPTIMIZER are trademarks of ScanSoft, Inc. [DISCLAIMER] By using this software you, the user, agree that any and all problems or errors made by or caused by this software is the sole responsibilty of you, the user. 33