The document discusses layout planning at various levels including plant location, department location, and machine location. It focuses on department location planning and describes the criteria of minimizing material handling costs. The document outlines the systematic layout planning methodology including data collection, flow analysis, quantitative analysis, relationship diagrams, and consideration of space requirements and constraints to develop an optimal layout. The methodology uses a greedy algorithm and 2-opt heuristic to iteratively improve the layout design based on minimizing material handling costs.

1. Layout Planning
The term 'layout planning' can be applied at various levels of planning:
Plant location planning (where you are concerned with location of a factory or a warehouse or
other facility.) This is of some importance in design of multi-nationally cooperating, Global-
supply Chain systems.
Department location Planning: This deals with the location of different departments or sections
within a plant/factory. This is the problem we shall study in a little more detail, below.
Machine location problems: which deal with the location of separate machine tools, desks,
offices, and other facilities within each cell or department.
Detailed planning: The final stage of a facility planning is the generation, using CAD tools or
detailed engineering drawings, of scaled models of the entire floor plans, including details such
as the location of power supplies, cabling for computer networks and phone lines, etc.
The Department Location Problem: A department is defined as any single, large resource, with a
well defined set of operations, and fixed material entry and exit points. Examples range from a
large machine tool, or a design department. The aim is to develop a BLOCK PLAN showing the
relative locations of the departments.
Criteria: The primary criteria for evaluating any layout will be the:
MINIMIZATION of material handling costs.
MH cost components: depreciation of MH equipment, variable operating costs, labor expenses.
Also, MH costs are typically directly proportional to (a) the frequency of movement of material,
and (b) The length over which material is moved.

2. Advantages of these criteria (reduced material movements):
1. Reduction of Aisle space required.
2. Lower WIP levels
3. Lower throughput times
4. Less product damage and lower obsolescence
5. Reduced storage space
6. Simplified material control and scheduling
7. Less congestion in system.
Consider the following:
Location of next operation Material Handled per move
adjacent machine single part
across the aisle unit load
across the plant lot size of over 1 hour of production
another plant one day's production
At each stage, the WIP is increasing by as much as 10 times.
The most popular layout for complex systems is the SPINE LAYOUT. Examples are shown in
the following figure.

3. The spine defines a central channel of material flow for the entire facility. Each department
branches out of this central core. Ideally, each department has its own input/output area along the
spine. This departmental point of usage concept reduces material flow.
We shall now look at some details of how to locate departments along a spine to optimize the
flow of materials. Let us first try to see if we can evaluate whether there is a dominant flow
pattern in a manufacturing system or not.
fij = flow volume (trips/time) between department I and j.
hij = cost/unit distance for the material handling system.
The cost = unit fixed cost + unit variable cost.
We define the weight of the cost of moving material between departments i and j as:
wij = fij.hij
Given the values of all the wij's, one measure of flow dominance is the coefficient of variation,
defined as:

4. What do different computed values of f mean ?
Clearly, f=0 implies that there is no significant variation of flow volumes between different pairs
of departments. In such cases, almost any solution for layouts will be close to optimal.
Similarly, if f is large (>2), it implies that some flows in the system are very low, while others are
extremely dominant. This is typical for assembly lines types of systems. It is easy to design the
layout for such systems (Why?).
However, if the value of f is close to 1, then it is difficult to see dominant flows, and other
techniques of layout design need to be employed.
One such technique is the manual design methodology developed by Muther, called:
Systematic Layout Planning
The figure below shows the steps of this methodology.

5. The method can be described in terms of the basic steps:
1. Data Collection: A study of the Product Mix, Quantity of each product to be produced,
Routing for each product, Support services needed, and the Schedule (or the timing and
transport issues related to production schedules of the products types).
2. Flow Analysis: whence we identify what each department will be, what its inputs and
outputs are likely to be, specification of physical workstations required to do the tasks (in
the process plan) etc.
At the early stages, this involves considerations of quantity of material flow, as well as
overall flow lines that could be better in the implementation of departments.
Examples include straight-line flow, S-shaped flow, U-shaped flow, or W-shaped flows.
Further, even for a spine shaped system, the spine geometry can be straight line, or U-
shaped (the latter case is useful if a single material receiving/delivery point is preferred.)
3. Quantitative analysis: Some factors, such as flow costs, can be quantified. Several others
are not so easy to quantify. For example
a. MH receiving and delivery stations to be kept together.
b. Delicate testing equipment should be placed far from high vibration areas, etc.

6. Such relationships can be quantified by using REL diagrams, as shown in the
figure below. The relative importance of each factor is expressed in terms of
subjective evaluations, ranging from A (absolutely necessary) to U (unnecessary),
and X (necessary to keep apart).
The diagram can also give reasons for such decisions. An example is shown
below.
4. Relationship Diagram: The quantitative and qualitative analysis is combined into a
relationship diagram. One way to do this is to assign some numerical values to the A-X
ratings, (typically, large integer for A-rating, 0 for U-rating, and large -ve integer for X-
rating).
These ratings can then be used to determine the closeness rating for each department as
the sum of all the rating-values of all links coming into it. Usually, a department with a
large rating value should have significant links will many other departments, and should
therefore be at the center of the layout (to be close to all other departments.)
We can now use these ratings (or their numerical values) to define the total closeness
rating of different departments. If V(X) is a function which defines the value of
achieving closeness between two departments, the total closeness rating of a department
can be defined as the sum of its closeness rating values for all its sister departments.

7. To give a numerical example, assume that we allow: V(A) = 81, V(E) = 27, V(I) =9,
V(O) = 3 and V(U) = 1. Then the closeness ratings corresponding to each department in
the example figure above are:
Department Total
Closeness
Rating
SR 9+3+9+3+81
= 105
PC 9+0+1+1+27
= 38
PS 58
IC 39
XT 35
AT 165
In the above, the X-ratings were ignored in order to allow each department to have a fair
chance in placement in the initial design of the layout. The real value of this rating will be
used later, when we put some effort into modification on the first-guess solution.
Forming the first guess solution (greedy algorithm):
Step 1. Notice that AT has the highest rating, and so is placed in the center of the layout
(why ?)
Step 2. The next highest ranked department is SR, which may be placed adjacent to AT
due to their mutual A-rating. We put it on top of AT.
Step 3. Next up is PS, which should go adjacent to AT (since V(AT,PS) is the highest
rated closeness value for PS.
Step 4. Next comes XT, which should be close to PS.
Step 5. Next is IC, which should be close to AT and is placed below it.
Step 6. Finally, we have PC, which must stay away from PS.

8. Using these directions, we have a first attempt at the layout as follows:
Notice the odd shape of the final layout. This does not matter, since we still have not
considered the relative sizes of the departments. But before considering that, we must
also attempt to improve upon our greedy solution.
One heuristic to do so is called the 2-Opt method. A k-opt method is said to have
converged when any switching between k variables (in this case, locations of
departments) cannot improve upon the objective (in our case, minimization of the total
MH cost).
The 2-Opt procedure to improve on the greedy solution is pretty straightforward, and
described rather well in your text (Askin and Standridge, pp 219). In summary, it is a hill-
climbing heuristic, in which, starting from the initial solution, at each step we compute
the reduction (if any) in cost associated with switching the positions of each pair of
departments.
The pair which yields the maximum reduction in costs (steepest local benefit) is selected
at this step. The switch is made, and the procedure continues, until at some stage, we are
unable to find any pair-switch which improves on the MH cost.
In the above, the MH cost associated with any pair of departments is often based on the
estimated MH cost factor, wij that we computed earlier, multiplied by an estimate of the
distance between the two cells.
5. Space requirements: these are determined based on industrial standards, equipment
required, shelf space required, etc.
6. Space availability: this is determined based on the economic analysis, as well as on other
constraints that may arise (especially if the system is to be housed in an existing facility).
The last two considerations will give an estimate of total space for each department, and
sometimes also the shape of each department (based on flow type within the department).

9. 7. Space relationship diagram: In this part, we substitute in the actual area on each
department, and fit the departments into the available space. Usually, the solution
methods may be computer-assisted heuristics, or just direct visual methods.
8. Putting in the constraints: Finally, other existing constraints are employed to cut down the
number of feasible solutions, to result in a small set of solutions. from among these,
direct comparison can be used to rank, eliminate, or select the optimum design.
These notes are based largely on material from the text (Askin and Standridge, as well as some
material from the text on Facilities Planning, by James Tompkins and John White (pub. John
Wiley).