Production Planning Control Operations Scheduling Dr.Na genG Prof.Zhibin JIANG Department of Industrial Engineering Management Shanghai Jiao Tong University
Production Planning & Control Dr. Na GENG Prof. Zhibin JIANG Department of Industrial Engineering & Management Shanghai Jiao Tong University Operations Scheduling
Operations Scheduling Contents Introduction Job Shop Scheduling Terminology ·Sequencing Rules Sequencing Theory for a Single Machine Sequencing Theory for Multiple Machines Stochastic Scheduling:Static Analysis Assembly Line Balancing 。Summary 国上泽充鱼大皇
Operations Scheduling Contents • Introduction • Job Shop Scheduling Terminology • Sequencing Rules • Sequencing Theory for a Single Machine • Sequencing Theory for Multiple Machines • Stochastic Scheduling: Static Analysis • Assembly Line Balancing • Summary
Assembly Line Balancing Example 8.11 The Final assembly of Noname personal computers,a generic mail-order PC clone,requires a total of 12 tasks.The assembly is done at the Lubbock,Texas, plant using various components imported from the Far East.The network representation of this particular problem is given in the following figure. 3 8 6 10
Example 8.11 The Final assembly of Noname personal computers, a generic mail-order PC clone, requires a total of 12 tasks. The assembly is done at the Lubbock, Texas, plant using various components imported from the Far East. The network representation of this particular problem is given in the following figure. Assembly Line Balancing
Assembly Line Balancing Precondition The job times and precedence Task Immediate Time relationships for this problem are Predecessors 1 12 summarized in the table below. 2 i 6 3 2 6 Question 4 2 2 Suppose that the company iS 2 2 6 2 12 willing to hire enough workers to 7 3,4 7 produce one assembled machine 8 7 5 9 5 1 every 15 minutes. 10 9,6 4 T/C=4.67 11 8,10 6 12 11 7 Five-station OK? Sum 70
Task Immediate Predecessors Time 1 _ 12 21 6 32 6 42 2 52 2 6 2 12 7 3, 4 7 87 5 95 1 10 9, 6 4 11 8, 10 6 12 11 7 Sum 70 Precondition The job times and precedence relationships for this problem are summarized in the table below. Question Suppose that the company is willing to hire enough workers to produce one assembled machine every 15 minutes. T/C=4.67 Five-station OK? Assembly Line Balancing
Assembly Line Balancing The solution precedence requires determining the positional weight of each task.The positional weight of task i is defined as the time required to perform task i plus the times required to perform all tasks having task i as a predecessor. t3+t+ts+tu+t2=31 Task Positional Weight 1 7 目 2 3 3 4 27 5 6 29 7 25 8 18 9 18 The ranking 10 17 1,2,3,6,4,7,5,8,9,10,11,12 11 13 12 7
Task Positional Weight 1 70 2 58 3 31 4 27 5 20 6 29 7 25 8 18 9 18 10 17 11 13 12 7 The solution precedence requires determining the positional weight of each task. The positional weight of task i is defined as the time required to perform task i plus the times required to perform all tasks having task i as a predecessor. Assembly Line Balancing t3+t7+t8+t11+t12=31 The ranking 1, 2, 3, 6, 4, 7, 5, 8, 9, 10, 11, 12
Assembly Line Balancing Profile 1 C=15 Station 2 3 4 5 6 Tasks 12,3,4 5,6,9 7,8 10,11 12 Processing time 12 14 15 12 10 7 Idle time 3 1 0 3 5 8 Task Immediate Time Predecessors 12 2 1 6 3 2 6 4 2 2 5 2 2 6 2 12 7 3,4 7 8 7 5 The ranking 9 5 1 1,2,3,6,4,7,5,8,9,10,11,12 10 9,6 4 11 8,10 6 12 11 7
Profile 1 C=15 Assembly Line Balancing Station 1 2 3 4 5 6 Tasks 1 2, 3, 4 5, 6, 9 7, 8 10, 11 12 Processing time 12 14 15 12 10 7 Idle time 3 1 0 3 5 8 The ranking 1, 2, 3, 6, 4, 7, 5, 8, 9, 10, 11, 12 Task Immediate Predecessors Time 1 _ 12 21 6 32 6 42 2 52 2 6 2 12 7 3, 4 7 87 5 95 1 10 9, 6 4 11 8, 10 6 12 11 7
Assembly Line Balancing Profile 1 C=15 Station 1 2 3 4 5 6 Tasks 1 23,4 5,6,9 7,8 10,11 12 Processing time 12 14 15 2 10 7 Idle time 3 1 0 3 15 The ranking 1,2,3,6,4,7,5,8,9,10,11,12 Cycle Time=15 T1=12 T26 T2=6 T3=6 T4=2 T5=入 *Evaluate the T6=12 T5=2 T9=1 balancing results by T7=7 T8=5 T10=4 the efficiency Et/NC; T10=4 T11=6 T12=7 *The efficiencies T12=7 for Profiles 1 is 77.7%
T2=6 Profile 1 C=15 Assembly Line Balancing Station 1 2 3 4 5 6 Tasks 1 2,3,4 5,6,9 7,8 10,11 12 Processing time 12 14 15 2 10 7 Idle time 3 1 0 3 5 8 Cycle Time=15 T1=12 T2=6 T3=6 T4=2 T6=12 T5=2 T9=1 T5=2 T7=7 T8=5 T10=4 T10=4 T11=6 T12=7 T12=7 15 Evaluate the balancing results by the efficiency ti/NC; The efficiencies for Profiles 1 is 77.7%. The ranking 1, 2, 3, 6, 4, 7, 5, 8, 9, 10, 11, 12
Assembly Line Balancing Alternative 1:Change cycle time to ensure 5 station balance Profile 2:Increasing cycle time from 15 to 16 Station 2 3 4 5 Tasks 2,3,4,5 6,9 7,8,10 11,12 Idle time 4 0 3 0 3 Increasing the cycle time from 15 to 16,the total idle time has been cut down from 20 min/units to 10;resulting in a substantial improvement in balancing rate. However,the production rate has to be reduced from one unit/15 minutes to one unit/16minute;
Profile 2: Increasing cycle time from 15 to 16 Station 1 2 3 4 5 Tasks 1 2,3,4,5 6,9 7,8,10 11,12 Idle time 4 0 3 0 3 • Increasing the cycle time from 15 to 16, the total idle time has been cut down from 20 min/units to 10; resulting in a substantial improvement in balancing rate. • However, the production rate has to be reduced from one unit/15 minutes to one unit/16minute; Assembly Line Balancing Alternative 1: Change cycle time to ensure 5 station balance
Assembly Line Balancing Alternative 2:Staying with 6 stations,see if a six-station balance could be obtained by cycle time less that 15 minutes The efficiencies for profile 1~3 are 77.7%, Profile 2 C=13 87.5%,and 89.7%.Thus the profile 3 is the best one. Station 2 3 4 5 6 Tasks 1 2,3 6 4,5,7,9 8,10 11,12 Idle time 1 1 1 4 0 13 minutes appear to be the minimum cycle time with six station balance. Increasing the number of stations from 5 to 6 results in a great improvement in production rate;
Profile 2 C=13 Station 1 2 3 4 5 6 Tasks 1 2,3 6 4,5,7,9 8,10 11,12 Idle time 1 1 1140 Assembly Line Balancing Alternative 2: Staying with 6 stations, see if a six-station balance could be obtained by cycle time less that 15 minutes • 13 minutes appear to be the minimum cycle time with six station balance. • Increasing the number of stations from 5 to 6 results in a great improvement in production rate; The efficiencies for profile 1~ 3 are 77.7%, 87.5%, and 89.7%. Thus the profile 3 is the best one
Operations Scheduling Contents Introduction Job Shop Scheduling Terminology ·Sequencing Rules Sequencing Theory for a Single Machine Sequencing Theory for Multiple Machines Stochastic Scheduling:Static Analysis Assembly Line Balancing ·Summary 国上泽充鱼大皇
Operations Scheduling Contents • Introduction • Job Shop Scheduling Terminology • Sequencing Rules • Sequencing Theory for a Single Machine • Sequencing Theory for Multiple Machines • Stochastic Scheduling: Static Analysis • Assembly Line Balancing • Summary
