General Flow Pattern

University of Southern California
Department of Industrial and Systems Engineering
ISE 310L Production I; Facilities and Logistics
Spring 2000

February Lecture Handouts (Part 2)

General Flow Pattern

Flow Distance Calculations

Dr. Ardavan Asef-Vaziri

General Flow Pattern

After completing

Product design

Market Research

Break-Even analysis

Make / Buy decision

Process design

Schedule design

Machine fraction calculations

Now we have

-Parts list of each product

-Production routing of each part

-Machine of each operation

-Total material & parts inflow

-Number of machines

The next step in facilities planning process is to imagine the overall flow pattern in the factory. The general flow pattern is the back bone of the production system. Four well know general flow patterns are Straight line, U shaped, Zigzag, and Loop. However, no real world general flow pattern is so simple. There are many factors which do not allow the general flow pattern to remain so simple. Among these factors are # of parts, # of processes, # of machines, special requirements of machines and processes, # of assemblies and subassemblies, location of external infrastructure facilities, building restrictions, and material handling system characteristics. Examples of the simple back bones, and their augmented forms are shown on the next page.

Signs of a good general flow pattern

1-A back bone for flow which emanate from receiving and terminate at shipping.

2-Well grouped flow lines with hierarchical densities which orderly join the main stream.

3-Straight lines, short lines of flow, which indicates that the relative activities are located close to each others.

4-Minimum back-tracking.

5-Material are moved directly to point of use, not first to an intermediate storage and then to the next activity.

6-Minimum WIP.

7-Flow pattern is easily expandable, new processes can easily be merged in.

After the initial design of the general flow pattern, we should also design the arrangement of machines with respect to each others. We should also design the arrangement of machines with respect to aisles. Some example are shown on the next page, operators are shown by small circles, represent operators.

Flow within product department (a) End-to-end (b) Back-to-end (c) Front-to-end (d)Circular (e) Odd-angle

(a) (b) (c)

Flow within process departments (a)Parallel (b)Perpendicular (c)Diagonal

Graphical Tools for Analysis and design of material flow system

We have already discussed:

Assembly chart

Operations process chart

Some others are:

Flow process chart

Flow diagram

Composite flow diagram

From-To chart

Flow Process chart is quite similar to Operations Process Chart, its format is similar, and it shows assemblies, operations, and inspections. However, it also shows material handling and storage.

Flow Diagram is a flow process chart spread over the layout of the corresponding area.

Composite flow diagram shows the over all material flow.

The main difference between flow diagram and composite flow diagram is in their application. Flow diagram is used for analysis of material flow in micro level. Composite flow diagram does the same task in macro level.

From-To chart

Recall our discussion on

Material flow is the most important factor in determining the location of production activities. From To chart is the most popular tool for material flow analysis.

Suppose we manufacture 5 parts and their production routings are as follows. A, B, C,….are manufacturing departments or manufacturing cells, or manufacturing machinery.

We assume they are machinery.

Part Production Routing

1A-B-D-J-M-K-L

2A-B-D-H-J-D-G-K-L

3A-B-H-J-G-K-L

4A-B-C-F-J-G-L

5A-B-D-M-K-L

To make the model simple, suppose all machines are of equal size and we want to arrange the in a row, i.e. a straight line layout. Now suppose we either have a physical layout on the shop floor or the image of a proposed layout in our mind. Therefore, our machines are physically or logically arranged on a straight line. Write them in the same order both in the first row and the first column of a table.

Production routing of Part 1 is

A-B-D-J-M-K-L

It goes from machine A to machine B

Go to Row A and Column B and put a “ “ in the corresponding element of the matrix.

Part 1 then goes from B to D

Go to Row B and Column D and put a “ “ in the corresponding element of the matrix.

It then goes from D to J

Go to Row D and Column J and put a “ “ in the corresponding element of the matrix.

Part 1 then goes from J to M

Go to Row J and Column M and put a “ “ in the corresponding element of the matrix.

Part 1 then goes from M to K

Go to Row M and Column K and put a “ “ in the corresponding element of the matrix.

Part 1 then goes from K to L

Go to Row K and Column L and put a “ “ in the corresponding element of the matrix.

For Part 1

/ A / B / C / D / F / G / H / M / J / K / L
A / /
B / /
C
D / /
F
G
H
M / /
J / /
K / /
L

An element just one block above the diagonal means a part goes from one machine directly to its next adjacent machine.

An element two blocks above the diagonal means a part passes the next adjacent machine and goes to a machine which is one machine away from the current machine. \

An element one block below the diagonal means a part backtracks to the previous machine. The best layout is a layout where all marks are in the boxes just above the diagonal. This may be possible for one part, but it is not possible for all parts.

Continue the process on the same table for all parts. You should get the following table

/ A / B / C / D / F / G / H / M / J / K / L
A / ///// / 5
B / / / /// / / / 5
C / / / 1
D / / / / / / / / / 4
F / / / 1
G / // / / / 3
H / // / 2
M / // / 2
J / / / // / / / 4
K / ///// / 5
L
5 / 1 / 4 / 1 / 3 / 2 / 2 / 4 / 4 / 5

But, production of all parts are not equal. Suppose we have the following product mix in each production run.

Part Part Mix Routing

1 20 A-B-D-J-M-K-L

2 40 A-B-D-H-J-D-G-K-L

3 30 A-B-H-J-G-K-L

4 60 A-B-C-F-J-G-L

5 40 A-B-D-M-K-L

In other words, 20 units of part 1 is one module of production. If we produce 20 units of part 1 then we produce 40 units of part 2 and part 5, 30 units of part 3, and 60 units of part 4.

Therefore, each movement of part 1 has an impact of 20, while that of part 2 has an impact of 40.

/ A / B / C / D / F / G / H / M / J / K / L
A / 20/
40
B / 20/
40
C
D
F
G
H
M
J
K
L

But except in very rare cases, parts are not moved one by one. They are moved in unit loads. One of our duties is to define and design unit load for each and every part.

Unit load

Unit load is a set of items (raw material, semi finished parts, finished product) to be move together, like:

-A set of cartons on a pallet

-A set of products in an intermodal container

-A car

In a unit load, parts are

-In something (In a carton)

-On something (On a pallet)

-Grouped by something (wrapped, strapped)

In your term project, have a schematic drawing for one of your unit loads.

An example of arranging items in a unit load is given on the next page.

Stacking patterns for different pallet sizes. (a)Block pattern (b)Row pattern (c)Pinwheel pattern (d) Honeycomb pattern (e) Split-row pattern (f) Split-pinwheel pattern (g)Split-pinwheel pattern for narrow boxes (h)Brick pattern.

Moving more items at one time reduces the No. of movements, loading, unloading. Therefore having more items in a unit load reduces material handling cost per unit of items. However, it is true up to some points, after that point, we need more expensive material handling equipment and a building with heavier foundation and stronger structure.

Optimal unit load size

No. of items in the unit load

Suppose we have the following information regarding the unit loads of our parts.

For example, 4 units of part 1 form a unit load, while 10 units of part 4 form a unit load.

Part Product Mix Parts per Unit load No of unit loads Routing

1 20 4 5 A-B-D-J-M-K-L

2 40 5 8 A-B-D-H-J-D-G-K-L

3 30 6 5 A-B-H-J-G-K-L

4 60 10 6 A-B-C-F-J-G-L

5 40 10 4 A-B-D-M-K-L

Our new F-T chart for part 1 and a couple of operations of part 2 are given below

/ A / B / C / D / F / G / H / M / J / K / L
A / 5+8
B / 5+8
C
D / 8 / 5
F
G
H
M / 5
J / 5
K / 5
L

The F-T chart for all parts is as follows

/ A / B / C / D / F / G / H / M / J / K / L
A / 5+8
5+6
4 / 28
B / 6 / 5+8
4 / 5 / 28
C / 6 / 6
D / 8 / 8 / 4 / 5 / 25
F / 6 / 6
G / 8+5 / 6 / 19
H / 8+5 / 13
M / 5+4 / 9
J / 8 / 5+6 / 5 / 24
K / 5+8
5+4 / 22
L / 2
28 / 6 / 25 / 6 / 19 / 13 / 9 / 24 / 22 / 28

Now let's solve the layout problem for a very simplified situation. Suppose

We want to arrange these machines in a straight line
All machines are of the same size
Our objective is to minimize material handling. In the other words we want to minimize flow X distance
The distance between the working points of each pair of adjacent machines is 1
The current layout is as follows

Let's go back to our From-To chart and see what is the value of the measure of effectiveness for this layout. Since we assumed the distance between two adjacent machines is 1 then our objective function is to minimize the momentum of the FT chart

Min Z = |j-i|

123456

2817845 61+53*2+19*3+23*4+24*5=436

661165

228136

5138

Total: 6153192324

9 / A / B / C / D / F / G / H / M / J / K / L
A / 28 / 28
B / 6 / 17 / 5 / 28
C / 6 / 6
D / 8 / 8 / 4 / 5 / 25
F / 6 / 6
G / 13 / 6 / 19
H / 13 / 13
M / 9 / 9
J / 8 / 11 / 5 / 24
K / 22 / 22
L
28 / 6 / 25 / 6 / 19 / 13 / 9 / 24 / 22 / 28

How can I improve this layout:

/ A / B / C / D / F / G / H / M / J / K / L
A / 28 / 28
B / 6 / 17 / 5 / 28
C / 6 / 6
D / 8 / 8 / 4 / 5 / 25
F / 6 / 6
G / 13 / 6 / 19
H / 13 / 13
M / 9 / 9
J / 8 / 11 / 5 / 24
K / 22 / 22
L
28 / 6 / 25 / 6 / 19 / 13 / 9 / 24 / 22 / 28
10 / A / B / D / C / F / M / H / J / G / K / L
A / 5+8
5+6
4
B / 5+8
4 / 6 / 5
D / 4 / 8 / 5 / 8
C / 6
F / 6
M / 5+4
H / 8+5
J / 8 / 5 / 5+6
G / 8 / 5+6
K / 5+8
4
L

Momentom=380

This is a better layout but we do not know whether it is the best layout or not.

Flow * Distance calculations

Suppose we have the following FT chart and layout.

The objective function is flow times distance

Z=

fij is flow from cell i to cell j,

It is given in the FT chart. It is not dependent to the layout.

dij is layout dependent and can be measured in many different ways. We look at some of them

-Rectilinear material handling

-Material handling on flow pattern

-Material handling on aisle network

1)Rectilinear

Distance between point A and point B is the rectilinear distant between them

Obviously the above distance is equal to any other rectilinear distance between A and B .

For example

Rectilinear distance between A, B

dA,B = | XA - XB | + | YA - YB |

In facilities layout, when we talk about rectilinear distance between two cells, we assume that the pick-up and delivery point (Input / Output point) of each cell is on the centroid of that cell. Therefore, distance between two cells i j is the distance between their centroids.

Let's find centroids of the cells in over layout.

dA,B= |0.5-2.5| + | 1.5-1.5 | = 2

dA,C= |0.5-1| + | 1.5-0.5 | = 1.5

dA,D= |0.5-3| + | 1.5-0.5 | = 3.5

Therefore we will have the following distance matrix

Now we can calculate the total Flow * Distance of our proposed layout.

We simply multiply each element of FT the distance chart and sum them up.

chart by corresponding element in

Z=1*2 + 1*1.5 + 2*3.5 +1*2.5 +1*1.5 + 1*1.5 + 1*1.5 + 1*3.5 +

1*1.5 + 2*1.5 = 25.5

Note that in rectilinear movement the distance from A to B is equal to the distance from B to A.

dij = dji

Can I use this property and simplify my calculation.

First I can get rid of the below diagonal portion of my distance matrix. The information on the upper diagonal by itself represents all I need.

Now I can develop a new FT chart in which

New(fij) =Old(fij) + Old(fji)

For example

fAC= fAC + fCA

fAC =1+1=2

fAD=2+1=3

I define this new chart only for ij where j>i , because it already have fij for j<i . Therefore my new flow matrix is:

Again, if I multiply each element of the flow matrix by the corresponding element in the distance matrix, I get the same Flow * Distance of 25.5 .

We could do this simplification only because

dij = dji

Material handling on flow pattern

Now suppose the FT chart is the same , but material moves on the following bi-directional U shaped general flow pattern.

In this flow network, we assume the pick-up and delivery station of each cell is on the middle of the portion of flow pattern covering the corresponding cell under this assumption,

Cell / Length of flow pattern on this cell / Location of PID station
A
B
C
D / 1
2.5
2
1.5 / 0.5
1.25
1
0.75

dAB = dBA= 0.5+1.25 =1.75

dAC = dCA= 0.5+2.5+1.5+1=2.5=5.5 = dCA

dAD = dDA= 0.5+2.5+.75= 3.75 = dDA

dBC = dAC - dAB = 5.5-1.75 = 3.75 = dCB

dBD = dAD - dAB= 3.75-1.75 = 2.25

dCD = dDC = 1+.75=1.75

Total Flow * Distance = 1.75 + 11 + 11.25 + 3.75 + 4 + 5.25 = 37

Now suppose flow is on a unidirectional loop on the aisle system

For simplicity of calculation, suppose P/D station of each cell is on the middle of the longest edge of that cell on the flow network.

For example, cell B has edges on the flow network, namely 1-2, 2-3, 3-4, 4-5, 5-1. Among them, 1-2 is the longest.

Length of the loop is = 8

dAB = 0.5+1.5 =2

dBA= 1.5+1+1+1+0.5+0.5+0.5 =6

dBA= 8-2=6

dAC =7

dAD = 5.5

dBC = 5

dBD= 3.5

dCD= 6.5

The lower diagonal elements are complements of a upper diagonal elements and 8.

8 is the length of the loop.

Z = Flow * Distance = 46

Highest but must realistic.