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.
Advantages of these criteria (reduced material movements):
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.
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.
f_{ij} = flow volume (trips/time) between department I and j.
h_{ij} = 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:
w_{ij} = f_{ij}.h_{ij}
Given the values of all the w_{ij}'s, one measure of flow dominance is the coefficient of variation, defined as:
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.
The method can be described in terms of the basic steps:
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.)
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.
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.
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.
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, w_{ij} that we computed earlier, multiplied by an estimate of the distance between the two cells.