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Operations planning and scheduling problems in an FMS: An integrated approach
Computers ind. Engng Vol. 35, Nos 3-4, pp. 443-446, 1998 © 1998 Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain PII: S0360-8352(98)00129-6 0360-8352/98 $19.00 + 0.00
Pergamon
OPERATIONS PLANNING AND SCHEDULING PROBLEMS IN AN FMS: AN INTEGRATED APPROACH N. S. MOHAMEDI Associate Professor Design & production Engineering Department, Faculty of Engineering, Ain Shams University, Cairo, EGYPT
ABSTRACT Operations planning and scheduling (OPS) problems in advanced manufacturing systems, such as flexible manufacturing systems, are composed of a set of interrelated problems, such as part-type hatching, machine grouping, tool loading, routing, part input sequencing and on-line scheduling. In this paper, an integrate~l, simulation=based approach to the OPS problems is discussed. A detailed simulation model is develol~ using FORTRAN and SLAM I1 which integrates loading, part inpuuing, routeing and dispatching issues of the OPS. An experimental frame is developed which provides statistical analysis of the simulation output by developing an experimental design. Statistical analyses concerning a number of system parameters (e.g. loading strategies and scheduling rules) are performed on a set of performance measures. © 1998Published by Elsevier Science Ltd. All rights reserved. INTRODUCTION Generally, when an FMS is being planned, the objective is to design a system which will be most efficient in production of an entire range of parts. The effective installation requires solutions to design, production planning, scheduling and the actual control problems of an FMS. The operation planning and scheduling (OPS) problem of an I~MS consists of a set of problems dealing with part-type batching, machine groupin[g, tool loading, routing, part input sequencing and on line scheduling. The multi-criteria nature of the production planning and scheduling problems has been recognized by many researchers (for example see Ammons et al. 1985, Kumar et a/. I987a, b, Lee and Jtmg 1989, O'Grady and Menon 1985,1987, Ro and Kim 1990. A review of pertinent literature revealed that most researchers have concentrated their efforts in developing either optimization (single and multi-criteria) models and heuristic-based models to study the parts and tool loading problem or simulation models to investigate the performance of scheduling rules (Gupta et al. 1991). In this paper, an integrated simulation-based approach to the operation planning and scheduling problems of an FMS is discussed. More specifically, fh'st, a detailed simulation model is developed using FORTRAN and SLAM If. This simulation model integrates part inputting, loading, routing and dispatching issues and, thereby, serves as an integrated system to the OPS problems. Second, an output analysis model is developed which provides managers with a statistical analysis of the speeific scenario under consideration by developing an experimental design. Next, the usefulness of proposed integrated approach is demonstrated through a hypothetical FMS. Then, an experimental design is suggested which consists of three loading strategies, six scheduling rules, two levels of due date tightness factors and three levels of part inter-arrival times. Subsequently, extensive statistical analyses are performed on a set of performance measures, such as mean flowtime, mean tardiness, mean earliness and system utilization. INow on leave: Mechanical Engineering Department, American Universit2,.'in Cairo, E~'pt 443
Selectedpapersfrom the 22ndICC&IEConference
444
RESEARCH METHODOLOGY Simulation models are developed to integrate various loading strategies and scheduling rules, and conducted experiments to analyse the impact of different levels of independent variables on various performance measures. The Model In this research, a four-nughine-centre production system which processes eight different part types is modeled. Each part type requires up to three operations, while the machine centres are able to perform any of the operations if they are allocated appropriate tools. The data on the number of operations, the number of tool slots required, the route numbers, and the machine centre for each part type were determined randomly and remained fixed for each part number throughout the experiment. However the unit processing times were randomly generated from an exponential distribution. Experimental Criteria In this study, data was collected and analysed for a number of criteria (or dependent variables) which have been studied extensively in the literature: mean flowtime F , mean tardiness T, mean earliness E , mean waiting time W, and mean system utilization U. Loading strategies. There are three loading strategies used in this study: ,4 single criterion loading strategy (LSI). The objective of this strategy is to balance the workload among machines. In this algorithm, a subset of parts from a pool of available parts is selected for processing in the next shift such that the load on all the machines is bManced. The algorithm allocates part operations on the machines by taking into consideration the available processing times on machines and tool slots in tool magazines. Each part type has alternate routes for its operations. A bi-criterion loading strategy (LS2). The objective of this model is to balance the workload and minimize the job lateness. The pool of parts is subdivided into four categories (overdue parts, u~ent parts, very urgent parts, and normal parts). The steps of the/.~1 algorithm are applied to a subset of parts which are 'overdue'. All the part operations of the overdue category are allocated to the system first. If the system capacity is not fully allocated, i.e. machine times and tool slots, operations of the p a ~ in the second category (i.e. 'urgent parts') are then assigned to the system. The process continues until either all the part operations are allocated or all the system capacity is fully used. ,4 multi-criteria loading strategy (1,53). The three objectives considered in this strategy are: (a)to balance the workload; (b) to minimize the lateness; and (c) to minimize the number of pert movements. This algorithm is an extension of the algorithm mentioned for the second loading strategy. In this algorithm, while allocating the part operations to machines, the information on machine visitations is utilized to give a higher priority to a part that its consecutive operations can be allocated to a single machine.
Du¢ date assignment Policy. In this study, the batches of parts are formed subject to four due date categories: overdue, very urgent, urgent and normal. The due dates are determined using the TWK method which assigns the due date based on total work content. Part type arrivals. For the simulation model in this study, independent and identically distributed exponential inter-arrival times are assumed with the mean values of 18, 19 and 20time units. These values were selected after an extensive preliminary simulation analysis of the pilot run. The experimental design comprising of the above mentioned independent variables consist of 108 designs or alternatives Table 1, which are evaluated for a set of dependent variables.
445
Selected papers from the 22nd ICC&IE Conference
Table 1 Level of independent variables
A. I. ~ m g
indq,md m
strategies
2.
i. Singlecriterion (LSI) ii. Bi-criterion (LS2) iii. MuRi-criterion (LS3)
i. Shortestprocessingfime(Rl) iv. Modified operation due dme (R4) ii. FJ'liestdue date 0U) v. Minimum slack time (R5) iii. Modified due date ~3) vi. Critical ratio (R6)
S. I. Due date tishmess factor i. 5 (DI) ii. 15 (D2)
epend
nriab 2.
i. meanoflgmin. ii, meanofl9min.
inter-arrivaltimes (Xl) iii. mee~6f20min. (Z2)
Part
(L3)
Output Data Analysis The complete database consists of 324 (I08 designs x 3 replications)sets of statistics.Table 2 shows the overall statisticsfor the dependent variables.These statisticsare computed over a period of 100 shiftsfor three replications.On average, 27.15 parts are manufactured during a shiftof 480 minutes, and a part-type spends 222.95 minutes in the system with a standard deviation of 17.75 minutes. The minimum and maximum times spent in the system by any part are 184.81 and 269.19 minutes, respectively.The mean work-in-process is 12 parts with a standard deviation ofl.91 units with an overall system utilizationlevel of 71.6%. The mean tardiness is 279.50 minutes, whereas the mean earliness is 15.70 minutes. An evaluation of these statistics and the overview provided in the pilot run suggest that the simulated manufacturing system can be viewed as a prototype of a real-lifesystem. Table 2 Overall statistic for dependent variables Variable Mean flowtime Mean earliness Mean tardiness System utilization
(F) (E) (T) (U)
N 324 324 324 324
Mean 222.93 15.71 279.49 0.72
SD 17.74 7.49 80.90 0.06
Minimum 184.81 0.97 835.08 0.81
Maximum 269.19 25.98 447.27 0.77
EXPERIMENTAL RESULTS Extensive tests are performed to analyse the impact of various levels of independent variables. The results are summarized for each of dependent variables in Figures la to lc. As one would expect, the performance of a manufacturing system (measured on a selected set of dependent variables) is affected by an increment in the complexity of loading objectives (i.e. from single criterion to multi-criterion based loading), while the objective of balancing the workload is effectively met by implementing the /~1. The overall system utilization rate of 71% is achievedwith a standard deviation of 1% for LSI, whereas for /~2 and LS3 the overall system utilization rates of 72% with the standard deviations of 3%, and 4% respectively. This shows that the objective of balancing the workload is achieved more effectively by the LS1 and with an added complexity. As a result, the improvements in the performance of dependent variables (such as mean flowtime, mean tardiness and mean waiting time) for/.~1 are observed over LS2 and LS3. Note that for most of the dependent variables,/~1 outperforms the other loading strategies no matter which scheduling rule is used (see Figures la and lc). The LS2 loading strategy consists of two objectives: balancing the workload and minimizing the lateness. In this strategy, since the parts are selected (for loading purposes) based on a due date based classification one would expect some improvements in the lateness related performance measures such as minimizing earliness and tardiness. Figure Ib, shows that LS2 outperforms /,S! and ZS3 for dependent variables: mean earliness. These results are consistent with its objectives. The results for other dependent variables are also comparable with LSI.
446
Selected papers from the 22nd 1CC&IE Conference
The LS3 strategy adds one more objective in I,$2 (i.e. minimizing the part movement). In this strategy, an attempt is made to assign the simultaneous operations to the same machine (if possible). The analysis of the results (Figures la and It) suggests that although this strategy does not provide the best results for any of the dependent variables, for mean flowtime, mean tardiness and earliness, the results are compared with those for/,5'/ and /,$2, and LS3 performs better with the SPT scheduling rule for mean tardiness as the performance criterion. Figures la, lb, and lc show that the SPT rule gives comparatively better results for all three of the loading strategies for the dependent variables: mean flowtime, mean earliness, and mean tardiness. The EDD rule, on the other hand, performs better for the dependent variables: mean earliness for all of the three loading strategies.
181
I.R
1.)
).m
),Jr
~
(b)
lid
Lit
~
).B
(el
Fig. 1 Effect of loading strategies and scheduling rules on performance measures. CONCLUSION The overall system utilization was higher for the bi-criterion LS2 and the multi-criterion LS3 strategies. The objective of balancing the system was better achieved by the single-criterion loading strategy LSI as compared to the other two strategies. LS1 performed better than the LS2 and LS3 for the dependent variables: F , and T, whereas LS2 performed better for E. Since one of the objectives in LS2 included minimizing lateness, the results are intuitively correct. The results for LS3 were comparable with results of the other two strategies. It performed best for T. The SPT rule dominated the other rules for most of the dependent variables. It performed best with the single-criterion loading strategy for all the dependent variables (except for E, where the EDD rule performed better). Surprisingly, the local and simple rules (such as SPT and EDD) outperformed global rules (SLACK, MDD, MOD and CRATIO) which is counter to the generally held belief. REFERENCES Ammons, J.C., Lofgren, C.B. and McGinnis, L.F. (1985). A large scale machine Ioading problem in flexible assembly. Annals of Operation Research, 3, 319-332. Gupta, Y.P., Evans, G.W. and Gupta, M.C. (1991). Multi-criterion approaches to FMS scheduling problem. InternationalJournal of Production Economics, 22, 13-31. Kumar, P., Singh, N. and Tewari, N.K. (1987) a. Multicriterion analysis of the loading problem in flexible manufacturing systems using rain-max approach. The International Journal of Advanced Manufacturing Technology, 2, 13-20. Kumar, P., Singh, N. and Tewari, N.K. (1987) b. A nonlinear goal programming model for loading problem in a flexible manufacturing system. Engineering Optimization, 12, 315-323. Lee, S.M. and Jung, H, (1989). A multi-objective production planning model in a flexible manufacturing environment. International Journal of Production Research, 27, 1981-1982. O'Grady, P.J. and Menon, U. (1985). A multi criteria approach for production planning of automated manufacturing. Engineering Optimization, 8, 161-175. O'Grady, P.J. and Menon, U. (1987). Loading a flexible manufacturing system. InternationalJournal of Production Research, 25, 1053-1068. Ro, ln-kyo and Kim, Joong-In. (1990). Multi-criteria operation control rules in flexible manufacturing systems. InternationalJournal of Production Re:eareh, 28, 47-63.
Pergamon
OPERATIONS PLANNING AND SCHEDULING PROBLEMS IN AN FMS: AN INTEGRATED APPROACH N. S. MOHAMEDI Associate Professor Design & production Engineering Department, Faculty of Engineering, Ain Shams University, Cairo, EGYPT
ABSTRACT Operations planning and scheduling (OPS) problems in advanced manufacturing systems, such as flexible manufacturing systems, are composed of a set of interrelated problems, such as part-type hatching, machine grouping, tool loading, routing, part input sequencing and on-line scheduling. In this paper, an integrate~l, simulation=based approach to the OPS problems is discussed. A detailed simulation model is develol~ using FORTRAN and SLAM I1 which integrates loading, part inpuuing, routeing and dispatching issues of the OPS. An experimental frame is developed which provides statistical analysis of the simulation output by developing an experimental design. Statistical analyses concerning a number of system parameters (e.g. loading strategies and scheduling rules) are performed on a set of performance measures. © 1998Published by Elsevier Science Ltd. All rights reserved. INTRODUCTION Generally, when an FMS is being planned, the objective is to design a system which will be most efficient in production of an entire range of parts. The effective installation requires solutions to design, production planning, scheduling and the actual control problems of an FMS. The operation planning and scheduling (OPS) problem of an I~MS consists of a set of problems dealing with part-type batching, machine groupin[g, tool loading, routing, part input sequencing and on line scheduling. The multi-criteria nature of the production planning and scheduling problems has been recognized by many researchers (for example see Ammons et al. 1985, Kumar et a/. I987a, b, Lee and Jtmg 1989, O'Grady and Menon 1985,1987, Ro and Kim 1990. A review of pertinent literature revealed that most researchers have concentrated their efforts in developing either optimization (single and multi-criteria) models and heuristic-based models to study the parts and tool loading problem or simulation models to investigate the performance of scheduling rules (Gupta et al. 1991). In this paper, an integrated simulation-based approach to the operation planning and scheduling problems of an FMS is discussed. More specifically, fh'st, a detailed simulation model is developed using FORTRAN and SLAM If. This simulation model integrates part inputting, loading, routing and dispatching issues and, thereby, serves as an integrated system to the OPS problems. Second, an output analysis model is developed which provides managers with a statistical analysis of the speeific scenario under consideration by developing an experimental design. Next, the usefulness of proposed integrated approach is demonstrated through a hypothetical FMS. Then, an experimental design is suggested which consists of three loading strategies, six scheduling rules, two levels of due date tightness factors and three levels of part inter-arrival times. Subsequently, extensive statistical analyses are performed on a set of performance measures, such as mean flowtime, mean tardiness, mean earliness and system utilization. INow on leave: Mechanical Engineering Department, American Universit2,.'in Cairo, E~'pt 443
Selectedpapersfrom the 22ndICC&IEConference
444
RESEARCH METHODOLOGY Simulation models are developed to integrate various loading strategies and scheduling rules, and conducted experiments to analyse the impact of different levels of independent variables on various performance measures. The Model In this research, a four-nughine-centre production system which processes eight different part types is modeled. Each part type requires up to three operations, while the machine centres are able to perform any of the operations if they are allocated appropriate tools. The data on the number of operations, the number of tool slots required, the route numbers, and the machine centre for each part type were determined randomly and remained fixed for each part number throughout the experiment. However the unit processing times were randomly generated from an exponential distribution. Experimental Criteria In this study, data was collected and analysed for a number of criteria (or dependent variables) which have been studied extensively in the literature: mean flowtime F , mean tardiness T, mean earliness E , mean waiting time W, and mean system utilization U. Loading strategies. There are three loading strategies used in this study: ,4 single criterion loading strategy (LSI). The objective of this strategy is to balance the workload among machines. In this algorithm, a subset of parts from a pool of available parts is selected for processing in the next shift such that the load on all the machines is bManced. The algorithm allocates part operations on the machines by taking into consideration the available processing times on machines and tool slots in tool magazines. Each part type has alternate routes for its operations. A bi-criterion loading strategy (LS2). The objective of this model is to balance the workload and minimize the job lateness. The pool of parts is subdivided into four categories (overdue parts, u~ent parts, very urgent parts, and normal parts). The steps of the/.~1 algorithm are applied to a subset of parts which are 'overdue'. All the part operations of the overdue category are allocated to the system first. If the system capacity is not fully allocated, i.e. machine times and tool slots, operations of the p a ~ in the second category (i.e. 'urgent parts') are then assigned to the system. The process continues until either all the part operations are allocated or all the system capacity is fully used. ,4 multi-criteria loading strategy (1,53). The three objectives considered in this strategy are: (a)to balance the workload; (b) to minimize the lateness; and (c) to minimize the number of pert movements. This algorithm is an extension of the algorithm mentioned for the second loading strategy. In this algorithm, while allocating the part operations to machines, the information on machine visitations is utilized to give a higher priority to a part that its consecutive operations can be allocated to a single machine.
Du¢ date assignment Policy. In this study, the batches of parts are formed subject to four due date categories: overdue, very urgent, urgent and normal. The due dates are determined using the TWK method which assigns the due date based on total work content. Part type arrivals. For the simulation model in this study, independent and identically distributed exponential inter-arrival times are assumed with the mean values of 18, 19 and 20time units. These values were selected after an extensive preliminary simulation analysis of the pilot run. The experimental design comprising of the above mentioned independent variables consist of 108 designs or alternatives Table 1, which are evaluated for a set of dependent variables.
445
Selected papers from the 22nd ICC&IE Conference
Table 1 Level of independent variables
A. I. ~ m g
indq,md m
strategies
2.
i. Singlecriterion (LSI) ii. Bi-criterion (LS2) iii. MuRi-criterion (LS3)
i. Shortestprocessingfime(Rl) iv. Modified operation due dme (R4) ii. FJ'liestdue date 0U) v. Minimum slack time (R5) iii. Modified due date ~3) vi. Critical ratio (R6)
S. I. Due date tishmess factor i. 5 (DI) ii. 15 (D2)
epend
nriab 2.
i. meanoflgmin. ii, meanofl9min.
inter-arrivaltimes (Xl) iii. mee~6f20min. (Z2)
Part
(L3)
Output Data Analysis The complete database consists of 324 (I08 designs x 3 replications)sets of statistics.Table 2 shows the overall statisticsfor the dependent variables.These statisticsare computed over a period of 100 shiftsfor three replications.On average, 27.15 parts are manufactured during a shiftof 480 minutes, and a part-type spends 222.95 minutes in the system with a standard deviation of 17.75 minutes. The minimum and maximum times spent in the system by any part are 184.81 and 269.19 minutes, respectively.The mean work-in-process is 12 parts with a standard deviation ofl.91 units with an overall system utilizationlevel of 71.6%. The mean tardiness is 279.50 minutes, whereas the mean earliness is 15.70 minutes. An evaluation of these statistics and the overview provided in the pilot run suggest that the simulated manufacturing system can be viewed as a prototype of a real-lifesystem. Table 2 Overall statistic for dependent variables Variable Mean flowtime Mean earliness Mean tardiness System utilization
(F) (E) (T) (U)
N 324 324 324 324
Mean 222.93 15.71 279.49 0.72
SD 17.74 7.49 80.90 0.06
Minimum 184.81 0.97 835.08 0.81
Maximum 269.19 25.98 447.27 0.77
EXPERIMENTAL RESULTS Extensive tests are performed to analyse the impact of various levels of independent variables. The results are summarized for each of dependent variables in Figures la to lc. As one would expect, the performance of a manufacturing system (measured on a selected set of dependent variables) is affected by an increment in the complexity of loading objectives (i.e. from single criterion to multi-criterion based loading), while the objective of balancing the workload is effectively met by implementing the /~1. The overall system utilization rate of 71% is achievedwith a standard deviation of 1% for LSI, whereas for /~2 and LS3 the overall system utilization rates of 72% with the standard deviations of 3%, and 4% respectively. This shows that the objective of balancing the workload is achieved more effectively by the LS1 and with an added complexity. As a result, the improvements in the performance of dependent variables (such as mean flowtime, mean tardiness and mean waiting time) for/.~1 are observed over LS2 and LS3. Note that for most of the dependent variables,/~1 outperforms the other loading strategies no matter which scheduling rule is used (see Figures la and lc). The LS2 loading strategy consists of two objectives: balancing the workload and minimizing the lateness. In this strategy, since the parts are selected (for loading purposes) based on a due date based classification one would expect some improvements in the lateness related performance measures such as minimizing earliness and tardiness. Figure Ib, shows that LS2 outperforms /,S! and ZS3 for dependent variables: mean earliness. These results are consistent with its objectives. The results for other dependent variables are also comparable with LSI.
446
Selected papers from the 22nd 1CC&IE Conference
The LS3 strategy adds one more objective in I,$2 (i.e. minimizing the part movement). In this strategy, an attempt is made to assign the simultaneous operations to the same machine (if possible). The analysis of the results (Figures la and It) suggests that although this strategy does not provide the best results for any of the dependent variables, for mean flowtime, mean tardiness and earliness, the results are compared with those for/,5'/ and /,$2, and LS3 performs better with the SPT scheduling rule for mean tardiness as the performance criterion. Figures la, lb, and lc show that the SPT rule gives comparatively better results for all three of the loading strategies for the dependent variables: mean flowtime, mean earliness, and mean tardiness. The EDD rule, on the other hand, performs better for the dependent variables: mean earliness for all of the three loading strategies.
181
I.R
1.)
).m
),Jr
~
(b)
lid
Lit
~
).B
(el
Fig. 1 Effect of loading strategies and scheduling rules on performance measures. CONCLUSION The overall system utilization was higher for the bi-criterion LS2 and the multi-criterion LS3 strategies. The objective of balancing the system was better achieved by the single-criterion loading strategy LSI as compared to the other two strategies. LS1 performed better than the LS2 and LS3 for the dependent variables: F , and T, whereas LS2 performed better for E. Since one of the objectives in LS2 included minimizing lateness, the results are intuitively correct. The results for LS3 were comparable with results of the other two strategies. It performed best for T. The SPT rule dominated the other rules for most of the dependent variables. It performed best with the single-criterion loading strategy for all the dependent variables (except for E, where the EDD rule performed better). Surprisingly, the local and simple rules (such as SPT and EDD) outperformed global rules (SLACK, MDD, MOD and CRATIO) which is counter to the generally held belief. REFERENCES Ammons, J.C., Lofgren, C.B. and McGinnis, L.F. (1985). A large scale machine Ioading problem in flexible assembly. Annals of Operation Research, 3, 319-332. Gupta, Y.P., Evans, G.W. and Gupta, M.C. (1991). Multi-criterion approaches to FMS scheduling problem. InternationalJournal of Production Economics, 22, 13-31. Kumar, P., Singh, N. and Tewari, N.K. (1987) a. Multicriterion analysis of the loading problem in flexible manufacturing systems using rain-max approach. The International Journal of Advanced Manufacturing Technology, 2, 13-20. Kumar, P., Singh, N. and Tewari, N.K. (1987) b. A nonlinear goal programming model for loading problem in a flexible manufacturing system. Engineering Optimization, 12, 315-323. Lee, S.M. and Jung, H, (1989). A multi-objective production planning model in a flexible manufacturing environment. International Journal of Production Research, 27, 1981-1982. O'Grady, P.J. and Menon, U. (1985). A multi criteria approach for production planning of automated manufacturing. Engineering Optimization, 8, 161-175. O'Grady, P.J. and Menon, U. (1987). Loading a flexible manufacturing system. InternationalJournal of Production Research, 25, 1053-1068. Ro, ln-kyo and Kim, Joong-In. (1990). Multi-criteria operation control rules in flexible manufacturing systems. InternationalJournal of Production Re:eareh, 28, 47-63.