Facility layout

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Facility layout

• Activity relationship analysis

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REL chart

• Flow analysis tends to relate various activities
  on some quantitative basis (refer Travel chart).
• Typically, the relationship is expressed as a
  function of transport cost or material handling
  cost.
• There might be other qualitative aspects of
  layout design that might be important.
• The activity relationship chart (REL chart) was
  developed to facilitate the consideration of
  qualitative factors analytically!
• The REL chart replaces the numbers in the Travel
  chart by a qualitative closeness rating.

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REL chart

• All pairs of relationships are evaluated, and a
  closeness rating (A, E, I, O, U, and X) is
  assigned to each pair.
• When evaluating activity relationships for N
  activities, there are N(N-1)/2 such evaluations.
• With the exception of U rating, the reason for
  the assigned rating is indicated using a numeric
  code.
• Closeness ratings represent an ordered preference
  for closeness.
• Specifically, A and X ratings are considered to
  be most important ratings.
• Hence, any layout must satisfy A and X ratings.
• Thus, A and X gt E gt I gt O gt U , where gt means
  more important or higher ranking than.

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REL chart

• A Absolutely necessary
• E Especially important
• I Important
• O Ordinary closeness OK
• U Unimportant
• X Undesirable

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REL chart

• Assignment of the closeness rating is subjective.
• Rule of thumb
• Very few A and X relationships should be
  assigned. (no more than 5 of the closeness
  ratings to be an A and X).
• No more than 10 should be an E.
• No more than 15 to be an I.
• No more than 20 to be an O.
• Which means that about 50 of the relationships
  should be U.

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Hierarchical approach

• Block plans, or block layouts are developed first
  by determining the sizes, shapes and relative
  locations of departments or other designated
  activities.
• Next, detailed layouts are designed for each
  department.
• Thus different REL charts are needed for
  designing block plans and detailed layouts.
• The process of constructing an activity
  relationship chart can be complicated by the
  presence of multiple relationships that will
  influence the design of the layout.

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REL chart example
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REL chart REL diagram

• From REL chart, we construct activity
  relationship diagram (REL diagram).
• The purpose is to depict spatially the
  relationships of the activities.
• The basic premise is that geographic proximity
  can be used to satisfy particular relationships.
• For example, when the activity relationships
  reflect the magnitudes of material flows, pairs
  of activities having the greatest pair wise flow
  are located next to each other.
• Similarly, pairs of activities having an A rating
  are located adjacently.

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Activity relationship diagram
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Activity relationship diagram
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Graph based process

• Each activity is represented by a circle, node or
  vertex.
• Activities that must be adjacent are denoted by
  connecting the respective nodes or vertices with
  lines, links or edges.
• The resulting representation of the activities
  and relationships is the activity relationship
  diagram or graph.
• A graph is planar if it can be drawn so that its
  vertices are points in the space and each edge
  can be drawn such that it intersects no other
  edges and passes through no other vertices.
• A requirement for the existence of a layout
  satisfying the activity relationships depicted in
  the graph is that the graph be planar.

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Graph based process

• Regions defined by a graph are referred to as
  faces with the unbounded outside region is the
  exterior face.
• Two faces are said to be adjacent if they share a
  common edge.
• An additional aspect of a graph is its dual.
• To construct the dual of a planar graph, place a
  dual node in each face of the primal graph.
• Whenever two faces are adjacent in primal,
  connect the corresponding dual nodes by an edge
  such that it crosses the edge that divides the
  primal faces.
• If the REL diagram is a planar graph, its dual
  graph will be planar.

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Graph based process

• It is not a simple matter to establish the
  planarity of a graph for a reasonably large
  layout problem.
• Computer codes do exist for establishing the same
  though.
• More importantly, upper bound exists on the
  number of pairs of adjacent activities.
• If there are N activities, no more than 3N-6
  pairs of activities can be adjacent.
• That is, if the graph of adjacency relationships
  has more than 3N-6 edges, it cannot be planar.
• However, this is an upper bound. Examples can be
  constructed such that non-planarity results with
  less number of adjacent activities considered.

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Graph based process

• If at least half of the relationships are U
  ratings, then for planarity to exist, the upper
  bound places the following limitations on the
  number of activities
• Hence if more than 10 departments are involved,
  planarity will not exist if all A, E, I, and O
  relationships must be satisfied via adjacency.

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Graph based process

• Therefore, for large problems, if adjacency is
  the basis of satisfying closeness requirements,
  it might be that only A, or A and E,
  relationships can be satisfied.
• If the distribution of closeness rating is 5 A,
  10 E, 15 I, and 20 O, then as many as 118
  departments can be accommodated if only A
  relationships must be satisfied via adjacency.
• However, if A and E relationships are to be
  satisfied via adjacency, no more than 38
  departments can be accommodated.
• Similarly, to include A, E, and I relationships,
  only 18 departments can be fit.

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Graph based process

• In summary,
• The graph based approach provides a structured
  approach for developing the REL diagram.
• Graph based approach is widely used in
  activity-based block layouts.
• It emphasizes the importance of constructing a
  planar graph of the REL chart if the block
  diagram is to be constructed to satisfy the
  relationships.

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Graph based process

• Limitations
• Interpretation of closeness to mean adjacency.
  This, at times, results in peculiar shapes of
  departments to satisfy adjacency requirements.
• There is no well-defined algorithm to draw a
  planar graph.
• Planarity requirement is a limitation Just
  because a set of requirements can not be
  satisfied via a planar graph does not mean that a
  block layout cannot be developed. It only means
  that it is not possible to satisfy all
  relationships with adjacency.

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Relationship diagram process
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Designing a layout

• After the block layout is ready, estimate is made
  of the space requirements.
• This includes space required for machines,
  equipments, products.
• Estimation of human resources needed is made
  based on the number of machines operated and
  production rate.
• Then, space relationship diagrams are made.

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Sample Space relationship table
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Example Alternate block diagram
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Example Alternate block diagram
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Use of computers in layout design

• Many Systematic Layout Planning (SLP) commercial
  software packages available.
• Examples
• CRAFT
• CORELAP
• ALDEP
• PLANET
• Originally developed in late 60s, many of these
  packages are still around.. with latest additions
  to the features!

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Layout design

• It has to be noted that if the favorable
  factors dont lend themselves for quantification,
  it is very difficult to calculate the utility of
  a layout using a computer software.
• How do you measure flexibility of a layout
  against another?
• So some form of quantifiable function is used in
  most of the algorithms.

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Adjacency-based rating

• The layout score is computed as
• where,
• Xi is the number of adjacencies in class i, and
• wi is the weighting factor for class i.
• Typical weights A (64), E(16), I(4), O(1), U(0)
  and X(-1024)
• Larger the score, better is the layout.

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Distance-based scoring

• The scoring model for m activities
• Cij is the cost per unit distance of flow between
  activities i and j. (same as i-to-j and j-to-i)
• Dij is the distance between activities i and j.

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Process layout and relative location problem

• Arrangement by similar processes grouping.
• Can simultaneously handle a wide variety of
  services.
• Give flexibility in equipment use and in employee
  assignment.
• Downside customer has to travel more than in
  product layout.
• e.g. Law offices, banks, amusement parks etc.
• Key to a good layout arrange departments or
  service center depending the flow of customers
  and travel time between the pair of departments.
• Pair-wise switching algorithm is one of the
  methods to solve this problem.

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Objective of process layout algorithm

• Objective function
• Instead of distance, it could be time taken or
  cost of movement.

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Example pair-wise switching algorithm
Transportation cost of Re. 1 for adjacent
departments and Cost of Rs. 2 for nonadjacent
departments
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Pair-wise switching algorithm

• Cost of the default layout 50210022030501
  022010050 Rs. 570
• Cost of new layout 50100202305010220100
  50 Rs. 480