Layout design: CRAFT and systematic layout planning

Why it matters

Once the layout type is chosen, departments still have to be placed relative to each other, and the number of possible arrangements explodes (10 departments can be arranged in over 3.6 million ways). Systematic Layout Planning gives a structured, people-friendly procedure that captures qualitative closeness needs, while CRAFT and similar algorithms search for arrangements that cut material-handling cost. Real projects use both.

Key ideas

Systematic Layout Planning (SLP), developed by Richard Muther, is a step-by-step procedure:

1. Input data and activities. P (product), Q (quantity), R (routing), S (supporting services), T (timing): the "PQRST" key data.
2. Flow of materials. Quantify movements between activities with a from–to chart (loads or trips per period).
3. Activity relationships. Build an activity relationship chart: for every pair of activities, a closeness rating with a reason code (shared equipment, flow, supervision, safety, noise).
   • A = absolutely necessary
   • E = especially important
   • I = important
   • O = ordinary closeness okay
   • U = unimportant
   • X = undesirable (keep apart, e.g. a paint shop and welding)
4. Relationship diagram. Place activities so that A and E pairs are adjacent and X pairs are separated; lines of different number show strength.
5. Space requirements and space available. Estimate the area for each activity from machines, operators, WIP and aisles; reconcile with the building.
6. Space relationship diagram. Redraw the relationship diagram with each block sized to its area.
7. Modifying considerations and practical limitations. Material-handling method, building columns, utilities, safety codes, cost limits.
8. Develop alternative layouts and evaluate them (weighted factor analysis, cost comparison), then select and detail.

Computerised layout algorithms

• Construction algorithms build a layout from scratch: ALDEP (uses closeness ratings and randomised placement), CORELAP (places the activity with the highest total closeness rating first and adds others by closeness), PLANET.
• Improvement algorithms start from an existing layout and improve it: CRAFT (Computerised Relative Allocation of Facilities Technique, Armour and Buffa, 1963).

CRAFT in detail

• Inputs: an initial block layout; a flow matrix f_ij (loads per period between departments); a cost matrix c_ij (cost per load per unit distance); any fixed departments.
• Distance d_ij is the rectilinear distance between department centroids.
• Objective: minimise total handling cost Σ f_ij · c_ij · d_ij.
• Procedure: consider all pairwise (or three-way) exchanges of departments that are adjacent or have equal areas; estimate the cost change for each; make the exchange giving the largest reduction; recompute centroids; repeat until no exchange reduces cost.
• Character: a steepest-descent heuristic. It finds a local, not necessarily global, optimum, so the result depends on the initial layout; it can produce odd department shapes that must be cleaned up; it uses only quantitative flow data, so qualitative closeness needs must be checked separately.

SLP vs CRAFT. SLP handles qualitative relationships, services and people issues and is used early when flow data are rough. CRAFT handles quantified flows precisely for an existing or proposed layout. In practice SLP gives the concept and CRAFT refines it.

Formulas

Total handling cost TC = Σ_i Σ_j f_ij · c_ij · d_ij

• f_ij = loads or trips per period between departments i and j; c_ij = cost per load per metre (₹/load·m); d_ij = distance between centroids (m).

Rectilinear distance d_ij = |x_i − x_j| + |y_i − y_j|

• (x, y) = centroid coordinates (m).

Centroid of a department: x̄ = Σ A_k x_k / Σ A_k, ȳ = Σ A_k y_k / Σ A_k

• A_k = area of rectangle k making up the department; (x_k, y_k) = its centre.

Worked examples

Example 1 (standard). Four equal-area departments A, B, C, D sit in a row with centroids at 0, 10, 20 and 30 m. Loads per day between them: A–B 10, A–C 15, A–D 40, B–C 30, B–D 5, C–D 25. Handling costs ₹1 per load per metre. Find the total daily handling cost.

1. Distances: A–B 10, A–C 20, A–D 30, B–C 10, B–D 20, C–D 10 m.
2. f × d: 100, 300, 1,200, 300, 100, 250.
3. TC = 100 + 300 + 1,200 + 300 + 100 + 250 = ₹2,250 per day.

Example 2 (GATE level). Apply one CRAFT iteration with pairwise exchanges to the layout of Example 1 and give the improved layout and cost.

1. Evaluate each exchange (new order, cost in ₹/day):
   • A↔B: B A C D, 2,050
   • A↔C: C B A D, 1,950
   • A↔D: D B C A, 2,400
   • B↔C: A C B D, 2,400
   • B↔D: A D C B, 1,650
   • C↔D: A B D C, 2,250
2. Largest reduction: exchange B and D.
3. Check A D C B: A–D 40 × 10 = 400; A–C 15 × 20 = 300; A–B 10 × 30 = 300; D–C 25 × 10 = 250; D–B 5 × 20 = 100; C–B 30 × 10 = 300. Total = 1,650.
4. New layout A D C B, cost ₹1,650 per day (27 % lower). A second iteration finds no exchange that reduces cost, so CRAFT stops. Here this happens to be the global optimum (its mirror image B C D A costs the same), but in general CRAFT only guarantees a local optimum.

Common mistakes

• Using straight-line distances when the question specifies rectilinear (aisle) distances.
• Counting each pair twice when the flow matrix already gives total two-way loads (or once when it gives one-way flows in both directions).
• Calling CRAFT a construction algorithm; it improves an existing layout.
• Believing CRAFT gives the global optimum.
• Mixing up the closeness codes: X means keep apart, U means it does not matter.

For GATE PI

Expect NAT questions on total handling cost for a given layout, the cost after a specified exchange, or the best pairwise exchange in a small CRAFT problem, and one-mark questions on SLP closeness codes and on construction vs improvement algorithms. Practise laying out a from–to table and computing rectilinear distances quickly.

Quick check

1. What does the closeness rating X mean?
2. Is CRAFT a construction or an improvement algorithm?
3. Centroids at (0, 0) and (20, 15) m: rectilinear distance?
4. Why might two runs of CRAFT on the same data give different final layouts?

Answers: 1. Undesirable to be close; 2. Improvement; 3. 35 m; 4. It is a local-search heuristic, so the result depends on the initial layout.