Approaches to Line Balancing COMSOAL & RPWActive Learning Module 2 Dr. César O. Malavé Texas A&M University Background Material Modeling and Analysis of Manufacturing Systems by Ronald G. Askin , Charles R. Standridge, John Wiley & Sons, 1993, Chapter 2. Manufacturing Systems Engineering by Stanley B. Gershwin, Prentice ± Hall,1994, Chapter 2. Any good manufacturing systems textbook which has detailed explanation on reliable serial systems. Lecture Objectives At the end of this module, the students should be able to Explain the approaches to line balancing COMSOAL Random Sequence Generation Ranked Positional Weight Heuristics Solve and find the optimal solutions to line balancing problems using the above techniques Time Management Introduction Readiness Assessment Test (RAT) COMSOAL Procedure Spot Exercise RPW Procedure Team Exercise Assignment Total Time 5 5 12 5 15 5 3 50 Mins . Which of the following characteristics is associated with process layout? a) stable demand b) less skilled workers c) specialized machinery d) low volume e) product for general market . work stations are arranged according to the general function they perform without regard to any particular product. a) True. b) False 5. work-in-process inventory is large for a product layout and small for a process layout. b) False 4. b) process.Readiness Assessment Test (RAT) 1. In a layout. b) False 3. Fixed position layouts are used in projects where the product cannot be moved. c) fixed position. a) product. and therefore equipment. a) True. In general. a) True. d) storage 2. A product layout is more suited to situations where product demand is stable than when it is fluctuating. and materials are brought to it. workers. Fixed position layouts are used in projects where the product cannot be moved. A product layout is more suited to situations where product demand is stable than when it is fluctuating. True. 3. Low Volume is associated with process layout. and therefore equipment. 2. and materials are brought to it. workers. . work-in-process inventory is large for a process layout and small for a product layout. In a Process layout. 5.RAT Solution 1. False. True. 4. In general. work stations are arranged according to the general function they perform without regard to any particular product. Approaches to Line Balancing Three Basic Approaches for finding a solution COMSOAL ± Basic random solution generation method Ranked Positional Weight Heuristic ± Good solutions found quickly Implicit Enumeration Scheme Assumptions Required cycle time. sequencing restrictions and task times are known . Sequence discarded as soon as it exceeds the upper bound. Sequence saved if it is better than the previous upper bound and the bound is updated. Efficiency depends on the data storage and processing structure .COMSOAL Random Sequence Generation A simple record-keeping approach that allows a large number of possible sequences to be examined quickly Only tasks that satisfy all the constraints are considered at each step. List of unassigned tasks (A) Tasks from A with all immediate predecessors (B) Tasks from B with task times not exceeding remaining cycle time in the workstation (F ± Fit List) During each sequence generation.COMSOAL Cont COMSOAL uses several list for speed computation. WIP(i) Indicates for which other tasks i is an immediate predecessor. NIP(i) Number of immediate predecessors for each task i. are updated. TK Consists of N tasks. . UB = w. c = C. NIPW(i) = NIP(i). Step 5. Time Feasibility : For all i B. Otherwise Step 3. if ti c. 5. Precedence Feasibility : For all.COMSOAL Procedure 1. Start the new sequence : Set x = x+1. otherwise Step 6. 4. C = Cycle Time. Open new station : IDLE = IDLE + c. If F empty. Set x = 0. add i to F. If IDLE > UB go to Step 2. . 3. 2. if NIPW(i) = 0. c = C. A = TK. add i to B. otherwise go to Step 3. Schedule completion : IDLE = IDLE + c. If IDLE UB. For all i WIP(i*). NIPW(i) = NIPW(i) ± 1. 7. UB = IDLE and store schedule. B. If A empty. .1). otherwise go to Step 2. Let i* = [m. Select Task : Set m = card {F}. go to Step 7. Randomly generate RN U(0. c = c ± ti*. F. If x = X.COMSOAL Procedure Cont 6.RN]th task from F. stop. Remove i* from A. . Basic idea can be applied to many decision problems. the better the expected solution .COMSOAL Advantages The technique is relatively easy to program. Greater the computational effort expended. the only requirement being that we can build solutions sequentially and a function evaluation can be performed to rank candidate solutions. Feasible solutions are found quickly. COMSOAL Task a b c d e f g h i j k l Activity Insert Front Axle / Wheels Insert Fan Rod Insert Fan Rod Cover Insert Rear Axle / Wheels Insert Hood to Wheel Frame Glue Windows to top Insert Gear Assembly Insert Gear Spacers Secure Front Wheel Frame Insert Engine Attach Top Add Decals Example Assembly Time 20 6 5 21 8 35 15 10 15 5 46 16 Immediate Predecessor a b c. d g e. h c f. j k . i. . Each shift receives two 10 minute breaks. 4 days a week will be used for assembly.COMSOAL Example Data Known : Two 4 hour-shifts. Planned production rate of 1500 units/week. No Zoning constraints exist. Example Solution Model Car Precedence Structure 20 6 5 5 a 21 b c 15 j 10 d 8 g h 15 46 16 e 35 i k l f . 17 1500 Units week day shift unit To meet demand C = 70 Seconds. Say outcome in our case is 0. d.Example Solution Cont 1 Week days shifts minutes minutes C! v4 v2 v 220 ! 1. Quick check of lower bound K ! 0 ? § l r !a r t C ! ?202 70 A! 3 A Thus Better Solutions may exist . Initially four potential tasks a.34 R is in second quadrant so keep d as first task. e. Continue the random generation. or f Generate random number between 0 and 1. l i. i. k. l i. c. i.1) 0. e a a b c g. b. j. g. j. k. j h. e. j j i k l U (0. g. b. k. l a. d. e. j. k. l h. l l l List B a. j i i k l l List F a. k. l c. j. c. l b. f a.21 0. k. -d a. h i. c. h. k. i. h.Single COMSOAL Sequence Results Step 1 2 3 4 4 5 6 7 8 9 10 10 11 12 12 List A a through l a through l. g. k. h. c. i.34 0. l k. j. e. g. k. l a. h. d. f e a b c g. i. h. j. i. l i. l g. j. b. e. k.83 Open Station 0. f a. h. g. i. e. f a. j. j j.42 Open Station Open Station l 4(54) i k 3(55) 3(9) a b c g h j 2(50) 2(44) 2(39) 2(24) 2(14) 2(9) Selected Tasks d f e Station (Idle Time) 1(49) 1(14) 1(6) . c d e . Assume demand is 100/day.Spot Exercise Solve the following line balancing problem using COMSOAL procedure. Task a b c d e f Time 2 1 2 3 1 3 Immediate Predecessor a a b. 8 Minutes a d e f c K ! 0 ? § l r !a r t C ! ? / 4.8A! 2.Exercise Solution 1 2 b 2 3 1 3 Production time available C! Desired units of output 8 Hours v 60 Minutes/hour ! 100 ! 4.5 } 3 12 A . Exercise Solution Step List A List B List F Cont U(0.8) 3(3. -c d to f e.8) 1(0.8) 3(0. f f a b.8) 2(0. c b d e f a b.1) Selected Task a c b d e f Station (Idle Time) 1(2.8) 2(3.8) 1 2 3 4 5 6 a to f b to f b to f. c b d e f 0.68 - . Cumulative remaining assembly time constrains the number of workstations required. . Tasks are assigned in this order to the lowest numbered feasible workstation. single pass heuristics. Procedure requires computation of positional weight PW(i) of each task.Ranked Positional Weight Heuristic A task is prioritized based on the cumulative assembly time associated with itself and its successors. Illustrates the greedy. Example. Compute PWi = ti + rS ( i ) t r § Tasks ordered such that i < r implies i not S(r). Task r is then a member of S(i) only if there exists an immediate successor relationship from i to r. . j S(i) means j cannot begin until i is complete. Immediate successors IS(i) are known from the inverse of the IP(i) relationships.RPW Procedure Let S(i) Set of successors of tasks i. «. Precedence Constraints : assignment to any workstation at least as large as that to which its predecessors are assigned Zoning & Time Restrictions : Checked on placement.«. .N assign task i to first feasible workstation. Order (rank) tasks by nonincreasing PW(i) Task Assignment : For ranked tasks i = .N compute 2. Task Ordering : For all tasks i = 1.RPW Procedure Cont 1. PW(i). RPW Procedure . j k . i.Example Task a b c d e f g h i j k l Activity Insert Front Axle / Wheels Insert Fan Rod Insert Fan Rod Cover Insert Rear Axle / Wheels Insert Hood to Wheel Frame Glue Windows to top Insert Gear Assembly Insert Gear Spacers Secure Front Wheel Frame Insert Engine Attach Top Add Decals Assembly Time 20 6 5 21 8 35 15 10 15 5 46 16 Immediate Predecessor a b c. h c f. d g e. Example Solution Model Car Precedence Structure 20 6 5 5 a 21 b c 15 j 10 d 8 g h 15 46 16 e 35 i k l f . Task a b c d e f g h i j k l PW 138 118 112 123 85 97 102 87 77 67 62 16 Ranked PW 1 3 4 2 8 6 5 7 9 10 11 12 PWl = its task time = 16 PWk = tk + PWl = 46+16 = 62 PWj = tj + PWk = 5+62 = 67 .RPW Procedure .Solution Positional Weight calculated based on the precedence structure (previous slide). 19. 35. 65. Task a assigned to station 1. 18. 2 70. 25. e. 17.RPW Solution Cont Assignment order is given by the rankings. 3 Tasks a. b. 3 70. c. c . i j. 29. 23. k.ta = 70 ± 20 = 50 seconds left in Station 1. g f. Station 1 2 3 Time Remaining 70. l Next Assign task d . d. h. 50. 50 ± 21 = 29 seconds left in Station 1. Solve by RPW Procedure Task a b c d e f g h Time 20 18 6 10 6 7 6 14 Immediate Predecessors a a b c. Task times and constraints are given below. f g . d e.Team Exercise Assembly of a product has been divided into elemental tasks suitable for assignment to unskilled workers. 0 30. 0 30. d b.Exercise Solution Task 6 c PWi 63 44 33 37 26 27 20 14 Rank 1 2 4 3 6 5 7 8 a 7 f 6 14 h b c d e f 20 a 18 b 10 d g 6 e Workstation 1 2 3 Assigned Tasks a. g. 6. c. e f. 23. 3 g h . h Remaining Time 30. 10. 12. 17. Assignment Write a flowchart for COMSOAL using the decision rule that feasible tasks are selected with probability proportional to their positional weight. .