Perancangan Sistem Manufaktur D0394 Perancangan Sistem Manufaktur Kuliah Ke XXIII - XXVI

Introduction to Assembly Systems Definition of the term assembly The aggregation of all processes by which various parts and subassemblies are built together to form a complete, geometrically designed assembly or product either by an individual, batch, or continuous process. Assembly of manufactured goods accounts for: over 50% of total production time, 20% of the total unit production cost, and 33%-50% of labor costs

Product Assembly Virtually all end products go through some assembly process. Approaches Craftsman approach Output =  parts/unit time     Output = 3  parts/unit time

Product Assembly 3 3    3 Virtually all end products go through some assembly process. Approaches Craftsman approach Assembly line 3 3    3 Output = 3  parts/unit time Output = 3  parts/unit time

Product Assembly    3  = 2 part/hour each  = 2 part/hour each 3 1 2 3 v1    3  = 2 part/hour each 3  = 6 parts/hour v = 1/3  = 1/6 hour v2  = 2 part/hour each 3  = 6 parts/hour  = 1/  = 1/2 hour 3 v3 3 Assume = 1 = 2 = 3 =  Assume = v1 = v2 = v3 = v

Assembly Line • Each part moves sequentially down the line, visiting each workstation. • Assembly (or inspection) tasks are performed at each station. • C is defined as the cycle time. At steady state, one unit is produced every C time units (i.e., C = 1/required number of assemblies per unit time). • Paced lines vs. unpaced lines. • Single product vs. mixed lines. • Flexible flow line.

Assembly Line Balancing Assembly line balancing problems: ALB-1 - Assign tasks to the minimum number of stations such that the workload assigned to each station does not exceed the cycle time, C. ALB-2 - Assign tasks to a fixed number of stations such that the cycle time, C, is minimized. An assembly consists of a set of tasks. Task precedence relationships are described by a graph G = (N, A) where nj  N represents task j, and aijA indicates that task i is an immediate predecessor of task j.

Example Problem d Task Ti Predecessor a 3 - b 2 c a,b d e 1 a c e b

Assembly Line Balancing Problem (ALB-1): Assign tasks to workstations Objective: Minimize assembly cost f(labor cost while performing tasks, idle time cost) Constraints: Total time for all tasks assigned to a workstation can not exceed C. Precedence constraints between individual tasks. Zoning constraints Same workstation Different workstation

Parameter/Input Parameters / Inputs P parts/unit time are required m parallel lines are to be designed (usually 1) C = m/P is the required cycle time ti is the assembly time required by task i, i = 1,…,N IP = {(u,v) | task u must preceed task v} ZS = {(u,v) | tasks u and v must be assigned to the samen workstation} ZD = {(u,v) | tasks u and v can not be assigned to the same workstation} S(i) is the set of successors for task i.

Parameter / Decision Variables (cont.) k is the number of workstations required (unknown). cik is a set of cost coefficients such that:

ALB-1 Problem Formulation

Solving Problem Very difficult to solve optimally Heuristic Solutions Integer variables Non-linear constraints Heuristic Solutions COMSOAL Ranked positional weight Enumeration Methods Tree Generation Naive approach Fathoming rules

Example Problem 1 2 3 4 5 6 7 8 11 10 9 C = 72 j Tj Pj 1 5 - 2 35 3 25 60 30 6 10 2,3 7 8 4,5 9 70 7,9 11 1 2 3 4 5 6 7 8 11 10 9 C = 72

COMSOAL Random sequence generation procedure Benefits Sequentially generates solutions by randomly selecting from a set of “fittable” tasks at each stage. Stops the current solution when: a) a complete solution is generated, or b) an upper bound is violated Continues until the user says “stop.” Benefits Easy to implement Improvement method - Quickly generates feasible solutions and continues to improve with additional computer time. General solution procedure is very useful for similar problem

COMSOAL Procedure Form a list A of tasks. Set the trial station s=1 and remaining cycle time τ=C Promote all tasks from list A that have no immediate predecessors to list B, the “candidate list.” Scan list B, promoting each task, j, with tj <= τ to list C, the “fit list.” If C is empty, increment the trial station s = s+1, set τ=C, and goto step 3. Select task j from list C and assign it to station s. Set τ=τ-tj. Eliminate task j from all lists. If all lists are empty, STOP. Update the immediate successors of task j on list A and goto step 2.

Example Problem 1 2 3 4 5 6 7 8 11 10 9 C = 72 j Tj Pj All Pred, 1 5 - 35 3 25 4 60 1,2 30 6 10 2,3 1,2,3 7 1,2,3.6 8 4,5 1,2,4,5 9 1,2,4,5,8 70 7,9 1,2,3,4,5,6,7,8,9 11 1,2,3,4,5,6,7,8,9,10,11 1 2 3 4 5 6 7 8 11 10 9 C = 72

Ranked Positional Weight (RPW) Ranks tasks according to their positional weight and assigns tasks to workstations sequentially according to the ranking. The positional weight of a task is a measure of the total time required for the task and all succeeding tasks. where: ti is the time required for task i , and S(i) is the set tasks which follow task

Ranked Positional Weight Example j Tj Pj All Pred, S(j) PW(j) Rank Sts 1 5 - 2,3,4,5,6,7,8,9,10,11 385 2 35 4,5,6,7,8,9,10,11 355 3 25 6,7,10,11 195 4 60 1,2 8,9,10,11 220 30 190 6 10 2,3 1,2,3 7,10,11 170 7 1,2,3.6 10,11 160 8 4,5 1,2,4,5 9,10,11 9 1,2,4,5,8 135 70 7,9 1,2,3,4,5,6,7,8,9 11 100 1,2,3,4,5,6,7,8,9,10,11

Tree Generation Generate a decision tree containing all possible sequences of tasks that obey the precedence constraints (this version doesn’t consider zoning constraints). Askin and Standridge describe a general tree generation procedure that examines all N! sequences of N tasks. FABLE - Fast Algorithm for Balancing Lines Effectively Uses tree generation with a set of fathoming rules to reduce the solution space and speed evaluation.

FABLE Preprocessing – Task renumbering Renumber a task only after all of it’s predecessors have been renumbered Break ties in favor of tasks with the largest tj. Break second level ties in favor of the task with the largest number of successors Break third level ties arbitrarily Increase task times where possible to facilitate fathoming.

Example Tree Generation 2 3 4 5 Task Tj Pred. a 3 - b 2 c a,b d e 1 1 6 7 8 9 10 11 12 13 14 a d e 15 16 17 18 19 b c 20 21 22 C = 4