Quantitative & Qualitative
Formulation of Facility Layout Problems
Module 5
Facility Layout Problems
The facility layout problem is one of the optimization problems which arises in
a variety of issues such as placing machines on a factory floor, very large-scale
integration (VLSI) design systems, layout design of hospitals, schools etc.
Facility layout formulation approaches can generally be classified into many
groups such as quantitative, qualitative, and multi-objective.
Facility Layout Problems
Facility layout problem (FLP) is defined as the placement of facilities in a
plant area, with the aim of determining the most effective arrangement in
accordance with some criteria or objectives under certain constraints, such
as shape, size, orientation, and pick-up/drop-off point of the facilities.
These layout problems fall into two basic categories
Those involving quantitative decision criteria
Those involving qualitative criteria.
Facility Layout Problems
• Layout problems are found in several types of manufacturing systems.
Typically
• Layout problems are related to the location of facilities (e. g.
machines, departments) in a plant.
• Have great impact on the system performance.
Facility Layout Problems
Facility layout problem (FLP) is defined as the placement of facilities in a
plant area, with the aim of determining the most effective arrangement in
accordance with some criteria or objectives under certain constraints, such
as shape, size, orientation, and pick-up/drop-off point of the facilities.
These layout problems fall into two basic categories
Those involving quantitative decision criteria
Those involving qualitative criteria.
Quantitative Criteria
Various types of process layout problem can be formulated with quantitative
criteria ( mainly related to cost and time).
These include the
minimization of material-handling costs in factories and warehouses
minimization of employee or customer traveling time in service operations.
A choice of criteria, of course, always requires a decision on the objectives of the
operations for example;
Is it more important to minimize doctor or patient traveling time in a hospital,
or should the sum of both times be minimized?
Quantitative Criteria
Many quantitative-criteria problems concerning the location of facilities
can be expressed in the flowing form
• Tij: trips between department I and department j
• Cij: cost Per unit distance Per trip traveled
• Dij: distance from I to j
• C: Total cost
• N: number of department.
Quantitative Criteria - Example
• A facility that will be used to produce a single product has three departments (A,B,C) that
must be housed in the configuration shown in figure. The inter departmental centers are
given in Table. In addition two trial-and error optional layouts are shown. Assume that the
cost to transport this product is $1 Per load food.
Qualitative Criteria
• Layout problems involving qualitative criteria occur when relationships
between in qualitative terms. In some cases, these qualitative criteria may be
more readily available or more appropriate than quantitative criteria.
• The qualitative location problem has been studied in depth by Muther
(1962) who has proposed a method of formulation and solution called
SLP (systematic Layout Planning).
Qualitative Criteria - Example
• According to Muther’s approach, the desirability of locating a given
department next to any other department is rated by one of the
following terms: Absolutely necessary, Especially important,
important, Ordinary closeness okay, Unimportant, undesirable.
• These qualitative ratings may be based on safety considerations, customer
convenience, or approximate flows between departments.
Qualitative Criteria - Example
• It might be desirable to locate the baby food department near the milk department in a
supermarket for convenience of shopping.
• In these example it is shown for a typical supermarket. The solution is not necessarily
an optimal solution but simply a good solution chosen for purposes of illustration.
• Qualitative layout problems are frequently encountered in the service industries,
where customers interact with the facilities.
Qualitative Criteria - Example
• Several computerized approaches are available for developing and analyzing process
layouts.
• Computerized Relative Allocation of Facilities Technique CRAFT (Soft ware)
packages program attempts to minimize material handling costs by calculating cost a
exchanging department.
• ALDEP and CORELAP programs attempt to maximize a nearness rating within the
facility dimension constraints. None of the methods guarantees optimality.
end
Multi Objective Formulation of
Layout Problems
Facility Layout Problems
The facility layout problem is one of the optimization
problems which arises in a variety of issues normally
addressing multi objective.
Multi Objective Formulation
Facility layout problem :
Determining the most efficient arrangement of physical
departments within a facility
complex and are generally NP-Hard
Classical approach is to minimize material handling cost
Actual problem has several conflicting objectives hence multi
objective formulation
Multi Objective Formulation
Flexible bay structure is considered
a rectangular area of assigned dimension H (height) and W (width)
subdivided in vertical bays, each containing one or more
rectangular departments
Here three bays are considered
Multi Objective Formulation
Bay structure representation:
There are three bays with 3, 2, 3 departments per bay
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Multi Objective Formulation
The following objectives are therefore considered:
1. minimization of material handling cost
2. maximization of the satisfaction of weighted adjacency
3. maximization of the satisfaction of distance requests
4. maximization of the satisfaction of aspect ratio requests
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Multi Objective Formulation
Solving using genetic algorithm:
Step 1. An initial population P0 of N individuals is randomly generated
Step 2. At each generation j, all the individuals are randomly coupled
to form N/2 couples. From each couple, two children are generated by
crossover operator and then an offspring population of N individuals is
obtained
Step 3. The two populations are combined together to form a unique
population Tj of size 2N
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Multi Objective Formulation
Solving using genetic algorithm:
Step 4. The number of clones is detected and kept below a fixed
value by means of recursive mutations.
Step 5. From the population Tj, the best N individuals are selected
employing the Selection Procedure (described apart). These
individuals constitute the new parent population Pj+1.
Step 6. Mutation operator is applied to the individuals with a fixed
probability
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end
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Limitations of Computerized
Layout Planning
Layout Planning
• Layout planning is deciding on the best physical arrangement of all resources that
consume space within a facility.
• These resources might include a work desk, a work center, a cabinet, a person, an
entire office, or even a department. Decisions about the arrangement of resources
in a business are not made only when a new facility is being designed.
• Layout can change any time there is a change in the arrangement of resources,
such as a new worker being added, a machine being moved, or a change in
procedure being implemented.
• Also, layout planning is performed any time there is an expansion in the facility or
a space reduction.
Computerized Layout Planning
• C omputerized layout planning can improve the search phase of the systematic
layout design process.
• By using computer programme, the layout analyst can quickly generate a number
of alternative layouts.
• In some plants, the cost of repeated handling constitute a very high proportion of
the total cost of the end product and in some others the distance materials have to
move is not the sole criterion and often is not even the primary concern for
locating an area or an operation.
• Hence, more realistic value assessment of the factors that truly affect total cost in
different kinds of layout planning situations is needed. The available computer
aided layout algorithms fall into either improvement or construction of
routine categories.
Computerized Methods of Layout Design
Constructive algorithms are of following types:
1. Automated Layout Design Program (ALDEP)
2. Computerized Relationship Planning (CORELAP)
• The most famous type in Improvement types Algorithms is;
1. Computerized Relative Allocation of Facilities Technique (CRAFT).
ALDEP
• ALDEP is “Automated Layout Design Program”.
• While CRAFT is an improvement procedure,ALDEP is a construction procedure.
• CRAFT requires an initial layout, which is improved by CRAFT. ALDEP does not need any initial
layout. ALDEP constructs a layout when there is none.
• ALDEP is basically a construction algorithm, but it can also be used to evaluate two layouts.
• It uses basic data on facilities & builds a layout by successively placing the layout using
relationship information b/w the departments.
• Basic inputs to ALDEP:
Length & width of facility
Area of each department
Minimum Closeness Preference (MCP) Value
Sweep width
Relationship chart showing the closeness rating
Location & size of any restricted area
Limitations of ALDEP
• ALDEP is that it randomly picks departments for consideration in the layout
process.
• ALDEP should be executed several times to assure that the layouts generated are
the “best” layouts.
The “best” layout will eventually generated will be presented to the facility
designer for selecting the most appropriate and feasible layout .
CORELAP
• CORELAP is “Computerized Relationship Layout Planning”
• CORELAP constructs layouts by locating rectangular shaped departments
• The relationship chart provides the basis for the order in which different
departments are placed
• The input requirements of CORELAP consists of:
• Relationship chart with weights for the depts
• Number & area of departments
Limitations of CORELAP
• CORELAP is that it has problems when an attempt is made to fix departments in
a certain location.
• CORELAP does not take into account the building and is dependent on the layout
arrangement. It is useful for new plants where the objective is to determine new
building design and not for buildings that are already in existence
CRAFT
• CRAFT is “Computerized Relative Allocation of Facilities Technique”.
• CRAFT is more popular than the other computer based layout procedures.
• It is improvement algorithm & starts with an initial layout & proceeds to improve
the layout by interchanging the departments pair wise to reduce the total
material transportation cost
• It does not give the Optimal Layout; but the results are good & near optimal,
which can be later corrected to suit the need of the layout planner
Limitations of CRAFT
1. Because the basis is the cost of materials handling, only production departments
are considered.
2. An initial idea of the layout is required. Therefore the technique only applies to
the modification of an existing layout or new layouts where the outline shape is
known
3. The Distance b/w the departments is taken as straight lines where as in practice
movement is usually rectangular along orthogonal lines
end
Flow Dominance, Complexity Rating and
Solution Efficiency
Flow Dominance
• The concept of flow dominance was introduced by Vollmann and Buffa (1966) as
a measure of the extent to which the flow matrix (from-to chart or travel chart)
shows "dominant" flow patterns.
Flow Dominance can be defined or measured in different ways
• Flow dominance was defined as the coefficient of variation of the flow data,
computed from the flow matrix elements as (100 x standard deviation/mean).
Flow Dominance
The measure f of flow dominance is a number between 0 and 1 that indicates
whether no dominant flows occur in a from-to matrix (the case where f = 1)
or whether there are dominant flows (the case where f = 0).
If there are M processes, the from-to matrix is of order M × M and each
entry is denoted by wij where i = 1...
Complexity Rating
Block provided a definitive method to evaluate the complexity of facilities
layout problems.
He proposed a complexity rating factor that is based on flow dominance and
the number of facilities.
Mathematically, the rating factor suffers from the use of an incorrect upper
bound for flow dominance.
Also, there is a problem with regard to its interpretability. The sensitivities of
flow dominance and the rating factor to changes in a single element of the
flow matrix can be examined.
Solution Efficiency
• Efficiency of the current & proposed plant layout are calculated
using different scoring mechanisms.
• the best layout design has to be selected and finally the preferred
solution should be implemented.
end
