Assembly Systems And Assembly Line Balancing

MEng6106- Manufacturing Systems Modeling & Performance Analysis

Lecture II - Assembly Systems and Line Balancing Dr. Tafesse Gebresenbet AAU, Technology Faculty Mechanical Engineering Department Email [email protected]

References : Mikel Groover, Automation, production systems and CIM Askin, Standridge, Modelling and analysis of Manufacturing systems

Assembly Systems and Line Balancing  Assembly involves the joining together of two or

more separate parts to form a new entity, called a subassembly, an assembly or some similar name.  Three major categories of processes used to

accomplish the assembly of the components: 1. Mechanical fastening 2. Joining methods 3. Adhesive bounding

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Manufacturing systems modeling & perofrmance analysis (TGS)

Assembly Systems and Line Balancing

1.

Mechanical fastening:A mechanical action to hold the components together. Includes:

Threaded fasteners: Screw, nuts, bolts, etc.

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Very common in industry. Allow to be taken apart if necessary. Rivets, crimping, and other methods: he fastener or one of the components is mechanically deformed. Press fits: The two parts are joined together by pressing one into the other. Once fitted, the parts are not easily separated. Snap fits: One or both of the parts elastically deform when pressed together. Commercial hardware such as retainers, C-rings, and snap rings may be used. Manufacturing systems modeling & Used to assemble soft, Sewing and stitching: perofrmance analysis (TGS)

Assembly Systems and Line Balancing

2. Joining methods: Includes welding, brazing, and soldering. Molten metal is used to join two or more components together. Common feature of welding techniques is that fusing and melting occur in the metal parts being joined. In brazing and soldering, only the filler metal becomes molten for joining. The metal components do not melt. Not as strong as welding.

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3. Adhesive bonding: Involves the use of an adhesive material to join components. Two types of adhesives: thermoplastic and thermosetting. Thermosetting adhesives are more complicated to apply, but are stronger capable of withstanding Manufacturing systems modeling and & perofrmance analysis (TGS)

Assembly systems The methods used to accomplish assembly processes: 1. Manual single-station assembly: Generally used on a product that is complex and produced in small quantities. One or more workers are required depending on the size of the product. Ex: machine tools, industrial equipment, aircraft, ships, etc. 2. Manual assembly line: Consist of multiple workstations. One or more workers perform a portion of the total assembly work on the product. 3. Automated assembly system: Uses automated methods at the workstations rather than human beings. Manual Assembly Lines  Used in high-production situations where the work can be divided into small tasks (work elements) and the tasks assigned to the workstations on the line.  By giving each worker a limited set of tasks repeatedly, the worker becomes a specialist in those tasks and perform more quickly. (Division of labor) 5

Manufacturing systems modeling & perofrmance analysis (TGS)

Assembly systems Transfer of Work Between Workstations 1. Non mechanical Lines: Parts are passed from station to station by hand. Problems are:  Starving at stations  Blocking of stations

As a result, cycle times vary. Buffer stocks are used to overcome. 2. Moving Conveyor Lines: Use a moving conveyor (ex. A moving belt, conveyor, etc.) to move the subassemblies between workstations. The system can be continuous, intermittent (synchronous), or asynchronous. Problems of continuously moving conveyor: Starving Producing incomplete items

In the moving conveyor line, production rate may be controlled by means ofq feed rate. = feed rate = conveyor speed (feet per minute or meters per second) = spacing between parts 6

Manufacturing systems modeling & perofrmance analysis (TGS)

Assembly systems

Raw work parts are launched onto the line at regular intervals. The operator has a certain time period during which he/she must begin work before the part flows past the station. This time period is called the tolerance time. = tolerance time = length of the station

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Model Variations It is highly desirable to assign appropriate amount of work to the stations to equalize the process or assembly times at the workstations. This brings thesystems line modeling balancing problem and the three Manufacturing & perofrmance analysis (TGS)

Assembly systems 1. Single Model Line: Specialized line dedicated to the production of a single product. 2. Batch-model Line (Multiple parallel lines): Used for the production of two or more models with similar sequence of processing or assembly operations. 3. Mixed-model Line: Several models are intermixed on the line and are processed simultaneously.

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These cases may be applied to both manual flow lines and automated flow lines. Type 2 and 3 are easier to apply to manual flow-lines. The problem of line balancing becomes more complicated when going from type 1 to type 3. Manufacturing systems modeling & perofrmance analysis (TGS)

Multiple parallel lines  ADVANTAGES

 DISSADVANTAGES

 easy work load balancing

 higher setup costs

 increasing scheduling

 higher equipment costs

flexibility  higher skill requirements  job enrichment  slower learning  higher line availability  complex supervision  more accountability As with most problems, multiple objectives exist. By far the most commonly used objective for analytical models is minimization of idle time. However, in practice, real world issues of minimizing tooling investment, minimizing the maximum lift or strain by any worker, grouping tasks requiring similar skills, minimizing movement of existing equipment, and meeting production targets cannot be overlooked. 9

Manufacturing systems modeling & perofrmance analysis (TGS)

Workstation cycle time  PACED LINES  Each work station is given exactly the same amount of time to operate on each unit of product. At the conclusion of this cycle time TC, the handling system automatically indexes each unit to the next station  ROLE OF BUFFERS  Usually small buffers may be needed in non-automatic assembly to avoid starving. Without buffers if task times vary, un paced (asynchronous) lines may be preferable.  UNPACED LINES (ASYNCHRONOUS)  The station removes a new unit from the handling system as soon as it has completed the previous unit, performs the required tasks, and then forwards the unit on to the next station.  PARALLEL WORKSTATIONS IN SERIAL SYSTEMS  In many serial systems, each station along the line is usually a 10

Manufacturing systems modeling & perofrmance analysis (TGS)

The Line Balancing Problems It is to arrange the individual processing and assembly tasks at the workstations so that the total time required at each station is approximately the same. Very difficult to achieve perfect balance in most practical situations. If workstation times are unequal, the slowest station determines the overall production rate of the line. TERMINOLOGY Minimum Rational Work Element. The smallest practical indivisible tasks into which the job can be divided. = Time required to carry out this rational work element. Considered to be constant. In fact it varies in a manual station. Assumed that they are additive. In fact it changes when two are Manufacturing systems modeling &

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perofrmance analysis (TGS)

Total Work Content. ( ) Sum of the time of all the work elements to be done on the line. = Number of work elements that make up the total work or job. Workstation Process Time. ( ) The sum of the times of the work elements done at the station. n= number of stations Cycle Time. ( ) Ideal or theoretical cycle time of the flow line. The time interval between parts coming off the line. 12

Manufacturing systems modeling & perofrmance analysis (TGS)

Balance Delay. (balancing loss) (d) Measure of the line inefficiency.

The balance delay d will be zero for any values n and that satisfies the relationship Minimum number of workstations required to optimize the balance delay for a specified may be found by

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Manufacturing systems modeling & perofrmance analysis (TGS)

Line Balancing

The Basic objective of Line Balancing problem To assign work elements to workstations such that assembly cost is minimized Total assembly cost includes:  Labor cost (while performing tasks)  Idle time cost  Focus: minimize idle time  Limits: production constraints

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Manufacturing systems modeling & perofrmance analysis (TGS)

Line Balancing Problem formulation  production rate P (units/time)  number of parallel lines m  number of tasks N  time to perform task i : ti  total task time T = ∑i=1N ti  to meet demand: cycle time Tc =m/p  no worker must be assigned a set of tasks of duration longer

than m/p =Tc

Some Features of the Task order partially determined  assembly order constraints IP =(u,v) (i.e. task u must precede task v)

zoning restrictions  task pairs to same station ZS  taskManufacturing pairs not systems performed modelingin & same workstation ZD

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Line Balancing

Objective function features  lowered number stations fill up first  only stations with at least one task are constructed  benchmarking gage: proportion of idle time  idle time = (paid -productive)

BALANCE DELAY (measures proportion of idle time) D = (K* Tc -  ti)/(K* Tc) = idle time/paid time where K* is the number of stations required by the solution 16

Manufacturing systems modeling & perofrmance analysis (TGS)

Line Balancing Decision variables  task i assigned to station k ?  total number of tasks N

Cost coefficient Cik NCik≤ Ci, K+1, k =1,2,3, …., K-1  K is the number of maximum workstations allowed. This allows forcing tasks onto the lowest numbered stations so that unused stations may be discarded.  Xik= {1,0} , 1- if task is assigned to station k; 0- otherwise  total number of stations k

Problem Formulation  Minimize  (Cik Xik)  Subject to:  ti Xik < Tc (all stations k)

[the sum of the tasks assigned doesn’t exceed cycle time}  Xik = 1 (all tasks i) [the task is assigned to exactly one workstation]

Xvh < Xuj (all k) & (u,v) in IP restriction]

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Manufacturing systems modeling & perofrmance analysis (TGS)

[ adherence to the precedence

Line Balancing Comments  D is idle time over paid time  objective does not allocate idle time equally among stns  best solutions: good work load balancing  total task time T =  ti  Maximum time per station is Tc  minimum stations (lower bound)

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Manufacturing systems modeling & perofrmance analysis (TGS)

Ko = | T/TC |

LINE BALANCING APPROACHES  Largest Candidate rule  Kilbridge and Wester’s method  RPWH  COMSOAL  OPTIMAL SOLUTIONS TREE GENERATION & EXPLORATION PROBLEM STRUCTURE RULES FATHOMING RULES

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Manufacturing systems modeling & perofrmance analysis (TGS)

Line Balancing They are heuristic approaches - based on logic and common sense rather than on mathematical proof. They do not guarantee an optimal solution, but result in good solutions which approach the true optimum. 1. Largest-candidate rule: PROCEDURE Step 1:List all elements in descending order of . Step 2:Start from the top and select an element that satisfies the precedence requirements and does not cause the sum of the values at the station to exceed the cycle time . Step 3:Continue to apply Step 2 until no further elements can be added without exceeding . Step 4: Repeat steps 2 and 3 for the other stations until all the elements have been assigned. The practical realities of the line balancing problem may not permit the realization of the most desirable number of stations. 20

Manufacturing systems modeling & perofrmance analysis (TGS)

2. Kilbridge and Wester’s method: PROCEDURE Step 1: Construct the precedence diagram so that the nodes with identical precedence are arranged vertically in columns. Step 2: List the elements in order of their columns. If an element can be located in more than one column, list all the columns by the element to show the transferability of the element. Step 3: To assign elements to workstations, start with the column I elements. Continue to the assignment procedure in order of column number until the cycle time is reached. Go on until all elements are allocated. In general, this method provides a superior line balancing solution when compared with the largest-candidate rule. 21

Manufacturing systems modeling & perofrmance analysis (TGS)

3. Ranked positional weights method:  Ranked Positional Weight Heuristic  A single sequence is constructed  A task is prioritized by cumulative assembly time associated with itself and its successors  Tasks are then assigned to the lowest numbered feasible workstation PROCEDURE Step 1: Calculate the ranked positional weight value (RPW) for each element by summing the element’s Te together with the Te values for all the elements that follow it in the arrow chain of the precedence diagram. Step 2: List the elements in descending order of their RPW. Step 3: Assign elements to stations according to RPW, avoiding precedence constraint and time-cycle violations. S(i) successor tasks to task i

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Manufacturing systems modeling & perofrmance analysis (TGS)

Ranked positional weights method Let tasks be ordered, then Let PW(i) be the positional weight of taks i and let S(i) be the set of its successors. Thus

PW(i) = ti + ∑ tj

; j in S(i)

Task r Є S(i) if and only if there is a path of immediate successor relations from i to r. Let the Immediate Successors be IS(i) and the Immediate Predecessors be IP(i) The RPWH procedure as follows 9. Task ordering: For all i=1,2, …. N compute PW(i) and order the tasks by increasing values of PW (i) 10. Task assignment: For ranked tasks i, assign them in sequence to the first feasible station 23

Manufacturing systems modeling & perofrmance analysis (TGS)

COMSOAL 4. COMSOAL - A Computerized Line Balancing Method PROCEDURE : Computer Method for Sequencing Operations for Assembly Lines  Simple record keeping to allow examination of many possible sequences  Sequences are generated by random picking a task and constructing subsequent tasks  New stations are opened when needed  Sequences that exceed the best solution are discarded  Better sequences become upper bounds Step 1: Construct list A, showing all work elements in one column and the total number of elements that immediately precede each element in an adjacent column. 24

Manufacturing systems modeling & perofrmance analysis (TGS)

COMSOAL (for generation X trial) Array of Number of Immediate Predecessors for each task i NIP(i) Array of for which other tasks is i an immediate predecessor WIP(i) Array of N tasks TK, c- available time remaining in current workstation List of unassigned tasks A List of tasks from A with all immediate predecessors assigned B List of tasks from B with tasks times not exceeding remaining cycle time in the current workstation F 1.- SET x=0, UB=∞, cycle time, c=Tc 2.- Start new sequence: SET x=x+1, A=TK, NIPW(i) = NIP(i) 3.- Precedence feasibility FOR all i ЄA, IF NIPW(i) = 0 , ADD i TO B 4. Time feasibility FOR i ЄB, IF ti< c ADD i TO F . If F empty , 5 , otherwise 6 5.- Open new station IDLE=IDLE + c , c = TC If IDLE > UB , 2, otherwise 3      

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Manufacturing systems modeling & perofrmance analysis (TGS)

COMSOAL (contd’) 6.- Select task: SET m = card{F} Random generate RN Є U(0,1) LET i* = [m*RN] th TASK from F Remove i* from A,B,F c = c - ti FOR ALL i Є WIP(i*), NIPW=NIPW-1 IF A EMPTY Go to 7, OTHERWISE Go to 3 7.- Schedule completion IDLE = IDLE + c IF IDLE < UB , UB = IDLE Go to STORE SCHEDULE IF x = X , STOP, OTHERWISE Go to 2

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Manufacturing systems modeling & perofrmance analysis (TGS)

Optimization of Line Balancing Consider the construction of a decision tree with all possible sequences obeying precedence constraints. The tree starts at the root and evolves to the first branches; the tasks without predecessors. Form there, the next level of possible task evolve. The process continues until we reach the leaves. The path from the root to each leaf constitutes a complete sequence.  The optimal sequence is the one of the leaves but which one? Optimization procedures are based on searching decision trees for the optimal leaf.

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Manufacturing systems modeling & perofrmance analysis (TGS)

Optimization of Line Balancing Depth first Backtracking In the depth first backtracking we first generate the tree. Then we start with a leaf and backtrack towards the root of the tree.

Assume the number of decision to be made is N. The choices available at stage n depend on earlier decisions. The tree is generated considering only the ordering of the tasks. At any stage, eligible tasks are those whose predecessors have already been included in the partially completed sequence. Sequences thus created necessarily satisfy precedence constraints. One proceeds depth first by growing the tree by selecting first alternative at each stage until a terminal leaf is reached. Next we backtrack from the leaf towards the root until unexplored branch is reached. Then we Manufacturing systems modeling &

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perofrmance analysis (TGS)

Optimization of Line Balancing To solve the problem, a sequence is selected and divided into workstations fulfilling the cycle time constraint and starting new stations only when absolutely necessary. This requires the concept of fittable task, i.e., a task if fittable into a station if  it fits into the remaining idle time of the station  It is still unassigned, and  All its predecessors have been assigned

The procedure is then as follows: 5. Input bound and task data 6. Setup; k=1; p=0; Ck=Tc; B=0 7. Select new task: Find i’= lowest i; i fittabel i>N. Does i’ exists?. If yes got to 6; otherwise go to 3. 8. Assign task: Ai=k; p=p+1; Ck = Ck-ti*; B=0. Is p=N? If yes got to 6; otherwise go to 3. 9. Open new station: k=k+1; Ck=TC 10.Sequence complete; Save it if best solution 11.Backtrack to B (remove B from station K) If Ck=Tc, k=K-1, B=Tap; AB=0; Ck-Ck+tB; p=P-1; i*= go to 3. 29

Manufacturing systems modeling & perofrmance analysis (TGS)

Optimization of Line Balancing The problem can be simplified by “pruning” the tree i.e., only creating those new nodes required for the search of a better solution. Fathoming rules are introduced such that if a node satisfies one of the rules all paths from that node can be discarded. This process is called fathoming the node. Once all remaining nodes are either fathomed or are leaves we are alone. The following optimality principles need always be invoked.  Never close a station while fittabel tasks remain  If a task makes all others unfittabel, make it a work station. The list of fathoming rules is as follows  Task dominance  Station dominance  Solution dominance 30

Manufacturing systems modeling & perofrmance analysis (TGS)

Mixed Model lines The objective function is the same to spread the work load among stations as evenly as possible can be expressed as follows. In mixed assembly model assembly line balancing, total work element times per shift or per hour are used. and Minimize (wAT-WL) or minimize Where w-number of workers or stations ( we are assuming the Mi =1, so that n=w, w=WL/AT WL-work load to be accomplished by the workers in the scheduled time period (min/hr) AT =available time in the period of interest (min/hr/worker) TTs= total service time at station i to perform its assigned portion of the work 31

Work load can be calculated

The total time to perform each element in the work load is calculated

Where TTk– the total time within the workload that must be allocated to element k for all products (min) Total service times at each stations are computed

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Measures of balance efficiency for mixed assembly line balancing corresponds to those in single model line balancing:

Where Eb- balance efficiency WL-work load w – number of workers(stations) max{TTsi}- maximum value of total service time among all stations in the solution

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Manufacturing systems modeling & perofrmance analysis (TGS)

SEQUENCING MIXED MODELS We assume qj– the proportion of the product type j, j=1,….P to be produced The first step is to develop an assembly line balance for the weighted average product. Let tij be the time to perform the task i on product type j and sk the set of tasks assigned to the workstation k We can state an average feasibility condition ∑iЄSk ∑j=1 p qj tij ≤ Tc k=1,….K In solving this problem we use ti =∑j=1

p

qj tij

1.- Initialization: create list of all products to be assigned (A) 2.- Assign a product (List A)  FOR n from list A, create list B of all product types assignable without violating constraints  from list B select product which minimizes the function | ∑j=1 n ∑iЄSkb ti,j(n) - n Ckb |  Add product type j* to the nth position  Remove a product type j* from A IF n < N  GO TO 1 34

Manufacturing systems modeling & perofrmance analysis (TGS)

SEQUENCING MIXED MODELS Subject to the following constraints ∑j=1 N = Nj j=1,…., p (to ensure that all items are produced during the cycle) nNj – s1 ≤ ∑j=1 n Xjb ≤ nNj/N + s1 n=1,…., N j= 1, ….P (to restrict the production rate of each product to be within s1 of its average rate at all times) ∑b=1 n ∑j=1 P ∑iЄsk tiXjb ≤ (n+s2)Ck n= 1,….N k=1,….K (limit the maximum overutilization at all times) Xjn = 0 or 1 The constraints attempt to restrict unplanned station 35

Manufacturing systems modeling & perofrmance analysis (TGS)

UNPACED LINES  Paced line with K stations and cycle time TC, the Each time spends KTC in system (throughput

time) Production rate is 1/ TC

 In a deterministic unpaced line Production rate is 1/ TC Time in system is maybe not KTC  WIP is smaller for unpaced lines

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Manufacturing systems modeling & perofrmance analysis (TGS)

Other Ways to Improve the Line Balance  Dividing work elements  Changing work head speeds at automatic stations  Methods analysis  Preassembly of components  Inventory buffers between stations  Parallel stations

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Manufacturing systems modeling & perofrmance analysis (TGS)