Sequencing Mixed Models & Unpaced Lines

Active Learning Module 4

Dr. César O. Malavé

Texas A&M University

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.

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.

Time Management

3Assignment

9Unpaced Lines

5Summary

50 MinsTotal Time

10Team Exercise

15Sequencing Mixed Models

5Readiness Assessment Test (RAT)

3 Introduction

Readiness Assessment Test (RAT)

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

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

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.

Sequencing Mixed Models

Let qj → Proportion of product type j, j=1,…,P

tij → Time to perform task I on product type j

Sk → Set of tasks assigned to workstation k

An average feasibility is

kSi

P

jijj Ctq

1

Kk ,....,1

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

Sequencing Mixed Models

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

Sequencing Mixed Models

n

j Siknji

Nnbk

bnCt1

)(,1maxmin

k

n

h

P

j Sijhij

jn

hjh

j

N

njjn

CSnXt

SN

nNXS

N

nN

NX

k

1 12

11

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Subject to j = 1,.., p ………

n = 1,.., N & j = 1 ,…, P ...

n = 1,.., N & k = 1 ,…, K …

jnX 0 or 1

1

2

3

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 < N, go to 1.

Sequencing Heuristics

n

j Siknji

bk

bnCt1

)(,

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

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

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

Exercise – Solution

Repeating Cycle : NA = 2, NB = 1, NC = 1, N = 4

Let Max Inventory(±) < 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

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

Unpaced Lines

Let us divide the line into 2 lines as 1 to kb & kb+1 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

K

kk kbkbbssk

1

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

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

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.