EXAMPLE 8.2: Assembly-Line Balancing The Model J Wagon is to be assembled on a conveyor belt. Five hundred wagons are required per day. Production time per day is 420 minutes, and the assembly steps and times for the wagon are given in Exhibit 8.9A. Assignment: Find the balance that minimizes the number of workstations, subject to cycle time and precedence constraints. SOLUTION 1. Draw a precedence diagram. Exhibit 8.9B illustrates the sequential relationships iden- tified in Exhibit 8.9A. (The length of the arrows has no meaning.) 2. Determine workstation cycle time. Here we have to convert to seconds because our task times are in seconds. C= Production time per day 60 sec. x 420 min. Output per day 500 wagons 25,200 500 50.4 3. Determine the theoretical minimum number of workstations required (the actual number may be greater): 195 seconds = 3.87 = 4 (rounded up) N = G = 50.4 seconds 4. Select assignment rules. In general, the strategy is to use a rule assigning tasks that either have many followers or are of long duration because they effectively limit the balance achievable. In this case, we use the following as our primary rule. a. Prioritize tasks in order of the largest number of following tasks. Task Number of Following Tasks 6 A Bor D Cor E F, G, H, or 5 4 2 -- . K 0 Our secondary rule, to be invoked where ties exist from our primary rule, is: b. Prioritize tasks in order of longest task time (shown in Exhibit 8.10). Note that D should be assigned before B, and E assigned before C due to this tiebreaking rule. exhibit 8.9 | A. Assembly Steps and Times for Model J Wagon Task Task Time (in seconds) Tasks That Must Precede A 45 11 A 9 B D 50 E 15 Description Position rear axle support and hand fosten four screws to nuts. Insert rear axde. Tighten rear axle support screws to nuts. Position front axle assembly and hand fasten with four screws to nuts. Tighten front axle assembly screws Position rear wheel #1 and fasten hubcap. Position rear wheel #2 and fasten hubcap. Position front wheel #1 and fasten hubcap. Position front wheel #2 and fasten hubcap. Position wagon handle shaft on front axle assembly and hand fasten bolt and nut. Tighten bolt and nut F 12 C G 12 H 12 E 12 E 8 F, G, H, 2 K J 195 B. Precedence Graph for Model J Wagon exhibit 8.9 A. Assembly Steps and Times for Model J Wagon Task Time (In seconds) Tasks That Must Precede Task Description A 45 Position rear axde support and hand fasten four screws to nuts. B. 11 Insert rear axde. A 9 B D 50 E 15 D F 12 G 12 Tighten rear axle support screws to nuts. Position front axle assembly and hand fasten with four screws to nuts. Tighten front axle assembly screws. Position rear wheel #1 and fasten hubcap. Position rear wheel #2 and fasten hubcap. Position front wheel #1 and fasten hubcap. Position front wheel #2 and fasten hubcap. Position wagon handle shaft on front axle assembly and hand fasten bolt and nut. Tighten bolt and nut C H 12 E 1 12 E 8 F, G, H, I K 9 195 B. Precedence Graph for Model J Wagon 12 sec F 9 sec B 45 oC 12 sec A G SO 12 sec 8 sec 15 sec E D H 12 sec - 5. Make task assignments to form Workstation 1. Workstation 2, and so forth, un tasks are assigned. The actual assignment is given in Exhibit 8.10A and is shown graphically in Exhibit 8.10B. To understand this, it is best to trace through the task assignments in sequence in Exhibit 8.10A. See that when an assignment is made, the feasible remaining assignments are updated along with the priority rules. It is impor- tant to meet precedence and cycle time requirements as the assignments are made. 6. Calculate the efficiency. This is shown in Exhibit 8.10C. 7. Evaluate the solution. An efficiency of 77 percent indicates an imbalance or idle time of 23 percent (1.0-77) across the entire line. From Exhibit 8.10A we can see that there are 57 total seconds of idle time, and the choice" job is at Workstation 5. Is a better balance possible? In this case, yes. Try balancing the line with rule (b) and breaking ties with rule (a). (This will give you a feasible four-station balance.) exhibit 8.10 A. Balance Made According to Largest-Number-of-Following-Tasks Rule Task Time (in seconds) Task with Most Followers Remaining Unassigned Time (in seconds) 5.4 ide Feasible Remaining Tasks Task Task with Longest Operation Time Station 1 A 45 None Station 2 D 50 0.4 die None CE E Station 3 B E P 11 15 9 12 39.4 24.4 15.4 3.4 Ide CH, I EGHI None FGHI FGHI HI H HI G H Station 4 12 12 12 8 38.4 26.4 14.4 6.4 idle 1 None Station 5 K 9 41.4 idle None "Denotes task arbitrarily selected where there is a tie between longest operation times. B. Precedence Graph for Model J Wagon breaking ties with rule (a). give you exhibit 8.10 A. Balance Made According to Largest-Number-of-Following-Tasks Rule Task Time (in seconds) Remaining Unassigned Time (in seconds) 5.4 Ide Feasible Remaining Tasks Task Task with Most Followers Task with Longest Operation Time Station 1 A 45 None Station 2 D 50 0.4 de None E Station 3 B E P 11 15 9 12 39.4 24.4 15.4 3.4 Idle CE CHI FGH, None CE FGHI FGHI G H HI HI HI Station 4 12 12 12 8 38.4 26.4 14.4 6.4 idle - J None Station 5 K 9 41.4 idle None "Denotes task arbitrarily selected where there is a tle between longest operation times B. Precedence Graph for Model J Wagon WS WS 9 cc B 45 sec 12 WSS SO D 12 c. 15 E 8. H K WS2 12 sec WS4 C. Efficiency Calculation Efficiency 195 (5X50.4) 77. or 77 Review the solution for Example 8.2 on page 175. For this example, we use two assignment rules: a. Prioritize tasks in order of the largest number of following tasks, and b. Prioritize tasks in order of longest task time when we have tles from the primary rule (rule a). As the result shows, this balancing process yields the efficiency of 77%. How can we improve the balancing process? With the given constraints, Is there a better approach to reduce the idle times in workstations? Try balancing the assembly line by rule b first and break ties with rule a. 1. Show the sequential relationships among tasks using a precedent diagram 2. Calculate the required workstation cycle time. 3. Determine the theoretical number of workstations. 4. Assign tasks by ruleb and break ties by rule a 5. Calculate the efficiency of the balance Post a photo of your hand-written answer that includes the precedent diagram, balancing table, and calculations. Make comments on others'. Do not follow the EXAMPLE 8.2: Assembly-Line Balancing The Model J Wagon is to be assembled on a conveyor belt. Five hundred wagons are required per day. Production time per day is 420 minutes, and the assembly steps and times for the wagon are given in Exhibit 8.9A. Assignment: Find the balance that minimizes the number of workstations, subject to cycle time and precedence constraints. SOLUTION 1. Draw a precedence diagram. Exhibit 8.9B illustrates the sequential relationships iden- tified in Exhibit 8.9A. (The length of the arrows has no meaning.) 2. Determine workstation cycle time. Here we have to convert to seconds because our task times are in seconds. C= Production time per day 60 sec. x 420 min. Output per day 500 wagons 25,200 500 50.4 3. Determine the theoretical minimum number of workstations required (the actual number may be greater): 195 seconds = 3.87 = 4 (rounded up) N = G = 50.4 seconds 4. Select assignment rules. In general, the strategy is to use a rule assigning tasks that either have many followers or are of long duration because they effectively limit the balance achievable. In this case, we use the following as our primary rule. a. Prioritize tasks in order of the largest number of following tasks. Task Number of Following Tasks 6 A Bor D Cor E F, G, H, or 5 4 2 -- . K 0 Our secondary rule, to be invoked where ties exist from our primary rule, is: b. Prioritize tasks in order of longest task time (shown in Exhibit 8.10). Note that D should be assigned before B, and E assigned before C due to this tiebreaking rule. exhibit 8.9 | A. Assembly Steps and Times for Model J Wagon Task Task Time (in seconds) Tasks That Must Precede A 45 11 A 9 B D 50 E 15 Description Position rear axle support and hand fosten four screws to nuts. Insert rear axde. Tighten rear axle support screws to nuts. Position front axle assembly and hand fasten with four screws to nuts. Tighten front axle assembly screws Position rear wheel #1 and fasten hubcap. Position rear wheel #2 and fasten hubcap. Position front wheel #1 and fasten hubcap. Position front wheel #2 and fasten hubcap. Position wagon handle shaft on front axle assembly and hand fasten bolt and nut. Tighten bolt and nut F 12 C G 12 H 12 E 12 E 8 F, G, H, 2 K J 195 B. Precedence Graph for Model J Wagon exhibit 8.9 A. Assembly Steps and Times for Model J Wagon Task Time (In seconds) Tasks That Must Precede Task Description A 45 Position rear axde support and hand fasten four screws to nuts. B. 11 Insert rear axde. A 9 B D 50 E 15 D F 12 G 12 Tighten rear axle support screws to nuts. Position front axle assembly and hand fasten with four screws to nuts. Tighten front axle assembly screws. Position rear wheel #1 and fasten hubcap. Position rear wheel #2 and fasten hubcap. Position front wheel #1 and fasten hubcap. Position front wheel #2 and fasten hubcap. Position wagon handle shaft on front axle assembly and hand fasten bolt and nut. Tighten bolt and nut C H 12 E 1 12 E 8 F, G, H, I K 9 195 B. Precedence Graph for Model J Wagon 12 sec F 9 sec B 45 oC 12 sec A G SO 12 sec 8 sec 15 sec E D H 12 sec - 5. Make task assignments to form Workstation 1. Workstation 2, and so forth, un tasks are assigned. The actual assignment is given in Exhibit 8.10A and is shown graphically in Exhibit 8.10B. To understand this, it is best to trace through the task assignments in sequence in Exhibit 8.10A. See that when an assignment is made, the feasible remaining assignments are updated along with the priority rules. It is impor- tant to meet precedence and cycle time requirements as the assignments are made. 6. Calculate the efficiency. This is shown in Exhibit 8.10C. 7. Evaluate the solution. An efficiency of 77 percent indicates an imbalance or idle time of 23 percent (1.0-77) across the entire line. From Exhibit 8.10A we can see that there are 57 total seconds of idle time, and the choice" job is at Workstation 5. Is a better balance possible? In this case, yes. Try balancing the line with rule (b) and breaking ties with rule (a). (This will give you a feasible four-station balance.) exhibit 8.10 A. Balance Made According to Largest-Number-of-Following-Tasks Rule Task Time (in seconds) Task with Most Followers Remaining Unassigned Time (in seconds) 5.4 ide Feasible Remaining Tasks Task Task with Longest Operation Time Station 1 A 45 None Station 2 D 50 0.4 die None CE E Station 3 B E P 11 15 9 12 39.4 24.4 15.4 3.4 Ide CH, I EGHI None FGHI FGHI HI H HI G H Station 4 12 12 12 8 38.4 26.4 14.4 6.4 idle 1 None Station 5 K 9 41.4 idle None "Denotes task arbitrarily selected where there is a tie between longest operation times. B. Precedence Graph for Model J Wagon breaking ties with rule (a). give you exhibit 8.10 A. Balance Made According to Largest-Number-of-Following-Tasks Rule Task Time (in seconds) Remaining Unassigned Time (in seconds) 5.4 Ide Feasible Remaining Tasks Task Task with Most Followers Task with Longest Operation Time Station 1 A 45 None Station 2 D 50 0.4 de None E Station 3 B E P 11 15 9 12 39.4 24.4 15.4 3.4 Idle CE CHI FGH, None CE FGHI FGHI G H HI HI HI Station 4 12 12 12 8 38.4 26.4 14.4 6.4 idle - J None Station 5 K 9 41.4 idle None "Denotes task arbitrarily selected where there is a tle between longest operation times B. Precedence Graph for Model J Wagon WS WS 9 cc B 45 sec 12 WSS SO D 12 c. 15 E 8. H K WS2 12 sec WS4 C. Efficiency Calculation Efficiency 195 (5X50.4) 77. or 77 Review the solution for Example 8.2 on page 175. For this example, we use two assignment rules: a. Prioritize tasks in order of the largest number of following tasks, and b. Prioritize tasks in order of longest task time when we have tles from the primary rule (rule a). As the result shows, this balancing process yields the efficiency of 77%. How can we improve the balancing process? With the given constraints, Is there a better approach to reduce the idle times in workstations? Try balancing the assembly line by rule b first and break ties with rule a. 1. Show the sequential relationships among tasks using a precedent diagram 2. Calculate the required workstation cycle time. 3. Determine the theoretical number of workstations. 4. Assign tasks by ruleb and break ties by rule a 5. Calculate the efficiency of the balance Post a photo of your hand-written answer that includes the precedent diagram, balancing table, and calculations. Make comments on others'. Do not follow the