Sequencing Mixed Models

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Sequencing Mixed Models Unpaced Lines
Active Learning Module 4
Dr. César O. Malavé Texas AM University
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Background Material

• Modeling and Analysis of Manufacturing Systemsby
  Ronald G. Askin , Charles R. Standridge, John
  Wiley Sons,
• Manufacturing Systems Engineering by Stanley B.
  Gershwin, Prentice Hall,1994, Chapter 2.
• Any good manufacturing systems textbook which
  has detailed explanation on mixed models and
  unpaced lines.

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Lecture Objectives

• At the end of this module, the students would be
• able to
• Explain the fundamentals of sequencing mixed
  models.
• Explain the basics of unpaced lines.
• Solve various problems related to these topics.

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Time Management
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Readiness Assessment Test (RAT)

• Discuss the basic features of Group Technology
  Layout and Just-In-Time Layout

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RAT Solution

• Group technology (GT) layout
• Dissimilar machines are grouped into work
  centers or cells
• Similar to process layout in that cells are
  designed to perform a specific set of processes
• Similar to product layout in that cells are
  dedicated to a limited range of products
• Just-in-Time layout
• Flow line similar to an assembly line
• Equipment and workstations arranged in
  sequence
• Job shop or process layout
• Focus on simplifying material handling

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Sequencing Mixed Models

• Several different products can be assembled
  simultaneously on the line.
• Products are generally classified as
• Type 1 Products with constant ratio of item
  task time to average item task time.
• Type 2 Products with independent station
  requirements.

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Sequencing Mixed Models

• Let qj ? Proportion of product type j, j1,,P
• tij ? Time to perform task I on product type
  j
• Sk ? Set of tasks assigned to workstation k
  
• An average feasibility is

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Sequencing Mixed Models

• For each item j, Qj items to be produced
• r be the greatest common denominator of all Qj.
  Cycle repeats for r times to satisfy demand.
• Repeated cycle consists of Nj Qj / r
• Bottleneck station kb is the station with maximum
  total work. kb argmaxkCk
• Xjn be 1 if item j is placed in nth position 0
  otherwise
• j(n) denotes the type of item placed nth

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Sequencing Mixed Models

• Selecting the nth item to be entered in the line
  is to optimize the following problem

Subject to
j 1,.., p
1
n 1,.., N j 1 ,, P ...
2
n 1,.., N k 1 ,, K
3
0 or 1
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Sequencing Constraints

• Constraints
• 1 ? Ensures that all the products are produced.
• 2 ? Restricts the production rate of each product
  to be within s1 of its average time at all times.
  This controls production rate to suitably match
  utilization.
• 3 ? Limits maximum utilization at all times.

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Sequencing Heuristics

• Step 0 Initialization. Create a list of all
  products to be assigned during the cycle. This
  is List A
• Step 1 Assign a Product. For n 1,.,N from
  List A, create a List B of all product types
  that could be assigned without violating any
  constraint. From List B select the product type (
  j) that minimizes
• Add product type j to the nth position. Remove
  a product type j from A and if n lt N, go to 1.

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Sequencing Example

• Bottleneck station is assigned with workload of
  68 seconds/cycle. Actual workload by model type
  for that station is provided in the table.

Model Sales Time
Red Z 250 16.7 72
Blue Q 250 16.7 68
Black R 500 33.3 68
RWB American 500 33.3 66
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Example Solution

• 1 Red, 1 Blue, 2 Black, 2RWB per cycle.
• Set s1 s2 0.9

Stage Red Z Blue Q Black R RWB American Assigned
1 1/6, 4 1/6, 0 1/3, 0 1/3, 2 Black
2 1/3, 4 1/3, 0 -1/3, 0 2/3, 2 Blue
3 1/2, 4 - 0, 0 1, 2 RWB
4 2/3, 2 - 1/3, 2 1/3, 4 Red
5 - - 2/3, 2 2/3, 0 RWB
6 - - 1, 0 - Black
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Team Exercise

• Three products are produced on the same line. One
  half of the demand is for A, the other half is
  evenly split between B C. Find a repeating
  cycle without building unnecessary inventories or
  shortages. The following table gives the
  bottleneck machine times.

Model Time
A 100
B 95
C 105
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Exercise Solution

• Repeating Cycle NA 2, NB 1, NC 1, N 4
• Let Max Inventory() lt 1

Stage A B C Cum.Time (Excess) Assignment
1 0.5, 0 0.75, -5 0.75, 5 100 (0) A
2 1.0, 0 0.5, -5 0.5, 5 195 (-5) B
3 0.5, -5 - 0.25, 0 300 (0) C
4 0, 0 - - 100 (0) A
Assume A undesirable due to inventory
accumulation
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Unpaced Lines

• Let
• K - number of stations
• C - Cycle times
• Sk - the sum of task times for tasks assigned to
  station k.
• kb - bottleneck machine
• All the times are deterministic

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Unpaced Lines

• Let us divide the line into 2 lines as 1 to kb
  kb1 to K
• Station 1 to k-1 work faster than kb
• Each item has to spend skb to avoid the inventory
  pile at each machine
• Throughput time for Line 2 is sum of all station
  times.
• Combining the lines, production time in system is

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Unpaced Line - Illustration

• Let S1 2, S2 4, S3 3

Item Enter 1 Leave 1 Enter 2 Leave 2 Enter 3 Leave 3 Flow Time
1 0 2 2 6 6 9 9
2 5 7 7 11 11 14 9
3 10 12 12 16 16 19 9
4 15 17 17 21 21 24 9
5 20 22 22 26 26 29 9
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Assignment

• Find a repeating cycle for entering product onto
  the mixed model line. Demand and the bottleneck
  process times are shown below.

Product Demand Time
A 1000 45
B 500 40
C 750 45
D 500 50
E 250 55
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Summary

• Assembly lines have greatly enhanced production
  because one objective Producing good product
• Advances in computational speed makes it possible
  to find optimal solutions for many problems.
• Mixed model cases are handled by unpaced lines,
  has advantage of allowing variability in assembly
  times.
• Paced lines avoid need to remove and replace the
  products on the transport mechanism.
• Little work has been done on modeling the full
  range of practical consideration in assembly line
  design.