INTEGRATED PROCESS PLANNING AND SCHEDULING WITH SETUP TIME CONSIDERATION BY ANT COLONY OPTIMIZATION

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1 Proceedings of the 1st International Conference on Computers & Industrial Engineering INTEGRATED PROCESS PLANNING AND SCHEDULING WITH SETUP TIME CONSIDERATION BY ANT COLONY OPTIMIZATION S.Y. Wan, T.N. Wong, Sicheng Zhang, Luping Zhang Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong. Tel: Abstract: This paper presents an ant colony optimization (ACO) approach in solving integrated process planning and scheduling (IPPS) with the consideration of setup time. Lots of approaches are proposed to solve the IPPS problem. Most of these approaches ignored the consideration of setup time in order to simplify the problem. This practice may be justifiable for some situations. However, it is not practical for the job involving a lot of sequent-dependent setup time. This paper will also discuss the importance of the consideration of setup time in handling IPPS problem. Keywords: Integrated process planning and scheduling; Setup time; Ant Colony Optimization 1. Introduction In recent years, lots of research effort has been spent in solving the manufacturing process planning and job shop scheduling problems with the Integrated Process Planning and Scheduling (IPPS) approach. IPPS is the concept of conducting process planning and scheduling concurrently. Its objectives are to eliminate or reduce scheduling conflicts; to reduce flow time and work in process; to improve production resources unitization; and to enhance the flexibility to adapt to uncertainties such as irregular shop floor disturbance (Lee and Kim 1). Various IPPS models and solution approaches have been proposed. These approaches are able to illustrate the feasibility of IPPS implementation. However, the IPPS problem domain is usually simplified with the assumption that setup times are negligible or absorbed completely in the processing times. In this paper, we are going to illustrate the importance of considering setup time separately in the IPPS approach. In addition, we will propose an ant colony optimization approach to solve the IPPS problem with setup time consideration. A survey on scheduling research involving setup considerations was conducted by Allahverdi and Gupta (1999), it summarized the researches showing the importance of setup time in the manufacturing environment. It also reviewed that the separated consideration of setup time allows operations to be performed simultaneously and hence improves performance. Treating setup time separately in scheduling can cohere with other production management philosophies and technique such as Just-in-time, cellular manufacturing and time-based competition. Some survey papers such as (Cheng, Gupta et al. ), (Yang and Liao 1999), (Potts and Kovalyov ), (Allahverdi, Gupta et al. 1999), (Allahverdi, Ng et al. 8) have summarized the increasing amount of researches in this topic. Regarding IPPS, the incorporation of setup time has only been mentioned in a few researches. Lasserre (199) proposed an integrated model for job shop planning and scheduling, it decomposed planning alternatively for instances with setup time and without setup time in job-shop. Moon, Kim et al. () proposed an integrated process planning and scheduling model for multi-plant supply chain which considered alternatives machines and sequence, sequence-setup, and distinct due dates. Shang and Fan () proposed an integrated optimization model of production plan and scheduling with the purpose of minimizing diffident cost involved in production. Setup time is considered separately in the proposed model. Li and McMahon 7 (7) proposed a mathematical model with the strategy of achieving processing flexibility, operation sequencing flexibility and scheduling flexibility. In the model, setup and tool changing 998

2 Proceedings of the 1st International Conference on Computers & Industrial Engineering time are included in the consideration during the computation. In these previous researches, setup time was considered separately. However, they do not specify the impact and importance of including the consideration of setup time in the IPPS. Ant Colony Optimization was proposed by Marco Dorigo in 199, since then, ant colony optimization algorithms have been widely applied to complex combinational optimization problems such as travelling salesman problem, quadratic assessment problem and job shop scheduling problem. For instance, Leung et al. (1) have illustrated the success of implementing ant colony optimization in solving integrated process planning and scheduling problem Nevertheless, set-up time was not considered separately in the processing requirements. The objective of this current paper is to apply the ACO approach to solve IPPS problem with setup time consideration. The proposed approach is to use the effect of the heuristic desirability and pheromone quantities to include the consideration of setup time in the ACO algorithm.. Integrated Process Planning and Scheduling with separated setup time consideration For most of the IPPS approaches, setup time is assumed to be negligible or to be part of the process time. This assumption is justifiable for setting up requirement which depends only on the job to be processed (sequence-independent). In contrast, setting up which depends on both the job to be processed and the immediately preceding job is sequence-dependent. With sequence-dependent setup times, performance of the job shop cannot be effectively improved unless the process plans and jobshop schedules are selected such that the setup times can be reduced or neglected. In the case of machines or tools used in the previous operation are same as the current operation, the setup time cannot be reduced or neglected. The traditional IPPS approach cannot be applied in such case. To illustrate, a sample part from Li (Li, Ong et al. ; ) (Li and McMahon 7) is shown in Figure 1, with the AND/OR graph in Figure presenting the alternate process plans. Tables 1,, 3 list the relevant technical specification for these operations. The processing data has been modified to simplify the problem. Tool C1 is asumed to be pre-set on all the milling machines before any operation start. We use operations 1,, 18,,, 11 to demonstrate the effect of sequent-dependent setup time in scheduling. We assumed that Operation 1 works with machine M and tool C. Table shows the setup time involved when the operation and relative alternative machine and tool are chosen as the next operation. Fig. 3 shows the Gantt chart when operation is performed after operation 1 with the machine M and tool C.With a proper matching of the assignment of tool and machine, the setup time can be reduced or neglected. Thus, the makespan can be reduced. This is in contrast to the traditional approach whereby setup and tool changing times are not to be changed or neglected and hence the schedule does not reflect the actual manufacturing status. Fig.1 Illustration of Part 1 S1 O 1 O O 18 O O O 11 O 3 O 1 O 7 O 13 O 8 O O 17 O 1 O 9 O 1 O 19 O 1 O 1 O F1 Fig. Process Plan of Part 1 999

3 Proceedings of the 1st International Conference on Computers & Industrial Engineering Feature Operations Machine candidates (Tool needed) Machining time F1 Milling(Oper1) M(C),M3(C7),M(C8),,3 F Milling(Oper) M(C),M3(C7),M(C8),,3 F3 Milling(Oper3) M(C),M3(C),M(C),,1 F Drilling(Oper) M1(C),M(C7),M3(C),M(C7) 1,1,1,7 F Milling(Oper) M(C7),M3(C7),M(C8) 3,3, F Milling(Oper) M(C7),M3(C8),M(C8) 1,1,11 F7 Milling(Oper7) M(C),M3(C3),M(C) 3,3, F8 Drilling(Oper8) Reaming(Oper9) Boring (Oper1) M1(C9),M(C9),M3(C9),M(C9) M(C1),M3(C1),M(C1) M(C7),M3(C8),M(C7),M(C8) 1,8,8,13 1,1,7 1,1,7,1 F9 Milling(Oper11) M(C7),M3(C8),M(C7) 1,1,11 F1 Drilling(Oper1) Reaming(Oper13) Boring (Oper1) M1(C),M(C3),M3(C),M(C) M(C9),M3(C9),M(C9) M(C1),M3(C1),M(C1),M(C1) 8,,,3,,18,,18,3 F11 Drilling(Oper1) Tapping(Oper1) M1(C1),M(C1),M3(C1),M(C1) M(C),M3(C),M(C),,,1,,1 F1 Milling(Oper17) M(C7),M3(C8),M(C7) 1,1,1 F13 Milling(Oper18) M(C),M3(C7),M(C) 3,3,3 F1 Reaming(Oper19) Boring (Oper) M(C9),M3(C9),M(C9) M(C1),M3(C1),M(C1),M(C1) 1,1,9 1,1,9,1 Table 1. Process Data of Operations Machines No Loading Unloading Cutting tools No Time Drilling press M1 1 1 Drill 1 C1 Three-axis vertical milling M Drill 1 C 1 machine I Drill 1 C3 1 Three-axis vertical milling M3 Drill 1 C machine II Tapping tool C CNC three-axis vertical milling M Mill 1 C 3 machine Mill C7 Boring machine M 3 3 Mill 3 C8 Table. Loading and Unloading time in different machine Reaming tool C9 Boring tool C1 Table 3. Tool Changing Time Traditional approach M Tool Change Loading Oper1 Unloading Tool Change Loading Oper Unloading Separate consideration of set up time approach M Tool Change Loading Oper1 Oper Unloading Fig.3 Gantt Chart of Operation 1 and with machine M and Tool C It is common for parts in different job orders to have the same feature and hence the same operation. The chance of having a reduction on setup time between two consequential operations increased. In normal practice, repeating operations will be scheduled one by one to reduce the setup time. However, this practice only solves the problem locally. It may not optimize the overall makespan. IPPS with setup time consideration constructs a schedule which is able to achieve a global optimum with the setup time reduction and overall makespan minimization. 1

4 Proceedings of the 1st International Conference on Computers & Industrial Engineering Unloading of Operation 1 Tool Change for Current Operation Loading of Current Operation Operation M, C M3, C7 M, C8 Operation M, C7 M3, C7 M, C8 Operation M, C7 M3, C8 M, C8 Operation 11 M, C7 M3, C8 M, C7 Operation 18 M, C M3, C7 3 M, C Table. Setup Time Involved in Selecting the Next Operation after Operation 1 3. Proposed Ant Colony Optimization Approach The proposed ACO algorithm basically generates solution according to the standard ACO procedures (Dorigo, Maniezzo et al. 199). It is a modification of the MAS-ACO proposed by (Leung, Wong et al. 1). Fig. shows the ACO algorithm. Node Selection Procedure is modified to handle the consideration of setup time. Initialization () Step 1.1: For each node, set the initial pheromone trail Step 1.: Set algorithm parameters: maximum number of ants (k ), maximum iteration (maxnc), pheromone weight (α), desirability weight (β),setup time weight (γ), trail evaporation rate (ρ), C, Q, minimum trail (taumin) Step 1.3: set iteration counter (NC) = Iteration () Step.1: A colony of ants are initially positioned on node o; all the machine tool pre-set as tool 1 Step.: Construct a schedule for each ant k as follow: Loop Each ant repeatedly applies NodeSelectionProcedure to select the next processing operation Until (a feasible schedule is constructed) Step.3: For each ant k, report the schedule Xk to the supervisory agent Iteration Control () Step 3.1: Collect ants result Step 3.: Apply PheromoneUpdate Step 3.3: Go to Step.1 Termination () Step.1: Check if NC exceeds maxnc. If yes, go to Step.; Otherwise, go to Iteration () with NC: =NC+1 Step.: Terminate the algorithm. Record the best schedule Fig. Proposed ACO Algorithm 11

5 Proceedings of the 1st International Conference on Computers & Industrial Engineering With ant based algorithms, the ant paths are governed by the heuristic desirability η(v) and pheromone amount τ(v) along the different paths. The desirability is usually computed initially from a greedy problem-specific heuristic such as longest processing time or earliest completion time (Dorigo, Maniezzo et al. 199). In the traditional MAS-ACO for IPPS, process time is the only criterion for the amount of heuristic desirability (Leung, Wong et al. 1). In our approach, setup times are also included as the criteria of the heuristic desirability. It directly affects the process selection procedure in selecting the operation sequence with less setup time. The new desirability is calculated as follow: γ where C, γ are positive constants and and are the processing time and set up time of operation v on machine m. Therefore, the node with a smaller processing time and set up time has a higher desirability value, i.e. more attractive to ant. On the other hand, the pheromone amount reflects the quality of the preceding schedule for the subsequent ant paths. It will be updated according to the quality of makespan after an ant has completed a search. It reflects the attractiveness of the previous path. Setup times are included in the makespan which then affect the algorithm indirectly. With the autocatalytic process of ACO, the construction of the schedule is influenced by the direct and indirect effects of setup times. The pheromone is calculated as follow: ρ where ρ is the evaporation coefficient where Q is a positive constant and Lk is the makespan by the ant k. The probability of selecting from node v as the next visiting node for ant k is given as α β α β where α and β denote the weighting parameters controlling the relative importance of the pheromone amount or the desirability respectively. Sk is the set of nodes allowed to be visit in next step. The probability of the ant visit that node will increase with the amount of the pheromone or the heuristic desirability.. Experimental Studies To illustrate the effect of separated consideration of setup time, experiment of performing repeated job is performed. Table shows the schedule of repeating the production of part 1 three times. Ox,y represents the Operation y of job x. Fig. illustrates the Gantt Chart of the traditional approach and proposed approach. O,1, O,3, O,, O,7, O,11, O1,1, O3,1, O3,, O,18, O,8, O3,11, O,17, O,, O,9, O3,3, O,, O,, With setup O3,, O3,7, O3,8, O3,9, O,1, O3,1, O3,18, O,, O3,17, O3,, O,1, O,13, O1,1, O1,11, O1,, O1,, O1,18, time consideration O1,, O1,, O1,3, O1,17, O1,1, O1,13, O1,1, O1,19, O1,1, O1,1, O1,7, O3,1, O1,, O1,8, O1,9, O1,1, O3,13, O3,1, O,1, O,19, O,, O3,1, O,1, O3,19 O3,1, O,1 makespan 7 O,1, O,18, O,11, O,3, O1,1, O,, O,17, O,, O1,11, O,, O,, O1,3, O1,, O3,1, O1,18, O1,, O3,3, Traditional O3,8, O,7, O,1, O1,7, O1,, O3,17, O3,, O3,11, O3,, O,13, O,1, O3,, O1,8, O1,9, O3,7, O,8, O,9, approach O,19, O,, O3,, O1,17, O1,1, O,1, O3,8, O3,9, O,1, O3,1, O,1, O1,, O1,1, O1,13, O3,1, O3,13, O3,1, O3,19, O3,1, O1,1, O1,, O1,, O1,19, O1,, O3, O1,1, O1,1 makespan778 Table. Comparison of makespan of two approaches Fig. Gantt Chart of Frst Operation with Two Approaches 1

6 Proceedings of the 1st International Conference on Computers & Industrial Engineering It is indicated that the schedules of the two approaches are different. This may be caused by the consideration of setup time. In the traditional approach, setup time is included into the process time, the change of machines and tools will not be considered. In the proposed approach, the change of machines and tools are considered during the scheduling. The makespan is also reduced in the proposed approach. The reduction in the setup time should be one of the main reasons.. Conclusion This paper presents the importance of including setup time in the consideration when handling integrated process planning and scheduling problems. In order to have a feasible and effective schedule, there is a need to have setup time consideration when handling the sequent-dependent setup time in the operation. From the result of the experiment, we can observe the difference between the schedule of with and without setup time consideration. The result reflects the effectiveness of setup time consideration will be enlarged when the repeated jobs are performed. An ant colony optimization approach is developed for handling integrated process planning and scheduling problem with the consideration of setup time. Acknowledgements The work described in this paper is fully supported by a grant from the Research Grants Council of Hong Kong (Project Code HKU 71889E). References Allahverdi, A., J. N. D. Gupta, et al. (1999). "A review of scheduling research involving setup considerations." Omega-International Journal of Management Science 7(): Allahverdi, A., C. T. Ng, et al. (8). "A survey of scheduling problems with setup times or costs." European Journal of Operational Research 187(3): Cheng, T. C. E., J. N. D. Gupta, et al. (). "A review of flowshop scheduling research with setup times." Production and Operations Management 9(3): -8. Dorigo, M., V. Maniezzo, et al. (199). "Ant system: Optimization by a colony of cooperating agents." Ieee Transactions on Systems Man and Cybernetics Part B-Cybernetics (1): 9-1. Lasserre, J. B. (199). "An Integrated Model for Job-Shop Planning and Scheduling." Management Science 38(8): Lee, H. and S. S. Kim (1). "Integration of process planning and scheduling using simulation based genetic algorithms." International Journal of Advanced Manufacturing Technology 18(8): 8-9. Leung, C. W., T. N. Wong, et al. (1). "Integrated process planning and scheduling by an agent-based ant colony optimization." Computers & Industrial Engineering 9(1): Li, W. D. and C. A. McMahon (7). "A simulated annealing-based optimization approach for integrated process planning and scheduling." International Journal of Computer Integrated Manufacturing (1): 8-9. Li, W. D., S. K. Ong, et al. (). "Hybrid genetic algorithm and simulated annealing approach for the optimization of process plans for prismatic parts." International Journal of Production Research (8): Li, W. D., S. K. Ong, et al. (). "Optimization of process plans using a constraint-based tabu search approach." International Journal of Production Research (1): Moon, C., J. Kim, et al. (). "Integrated process planning and scheduling with minimizing total tardiness in multi-plants supply chain." Computers & Industrial Engineering 3(1-): Potts, C. N. and M. Y. Kovalyov (). "Scheduling with batching: A review." European Journal of Operational Research 1(): 8-9. Shang, W. L. and Y. S. Fan (). "Integrated optimization model of production planning and scheduling for batch production." Shaping Business Strategy in a Networked World, Vols 1 and, Proceedings: Yang, W. H. and C. J. Liao (1999). "Survey of scheduling research involving setup times." International Journal of Systems Science 3():