The document introduces aldep++, a constructive heuristic algorithm designed to improve upon the original aldep method by batching departments for placement to address its shortcomings. It highlights the efficiency of aldep++ in yielding lower cost layouts and maintaining high total closeness ratings (TCR) compared to both aldep and microcraft algorithms. Overall, aldep++ effectively balances adjacency scoring and cost considerations, making it a practical option for facility layout design.

1. A N I M P R O V E M E N T O N T H E A L D E P H E U R I S T I C
V I A D E P A R T M E N T B A T C H I N G
ALDEP++

2. BACKGROUND & MOTIVATION
Introduction to ALDEP –
• Construction algorithm that randomly chooses the first department
• Successively adds more on the basis of closeness ratings of the relationship chart following S
pattern
Advantages of ALDEP –
• simple and not time consuming.
• does not need any initial Layout
• Since the S-flow method is used in ALDEP, resulting in practical layouts
• A greater variety of good options are exposed as compared to other methods

3. BACKGROUND & MOTIVATION
Shortcomings of ALDEP -
• Shortsightedness - Only considers relationship between immediate previously placed department
and each of remaining departments.
• Each individual department is Considered for one subsequent department decision
• Leads to generation of many suboptimal layouts, not necessarily the most optimal layout.
• Blind to constraints (such as disallowing departments with X relation)
• Only considers adjacent departments for comparing different layouts via total closeness ratings,
there is information lost regarding the total costs.
Motivation –
• The ALDEP adds one department at a time resulting in blindness to many department
relationships
• Adding all departments at once makes it a quadratic assignment problem which is
computationally difficult as the problem size increases.
• ALDEP++ is a method which functions between these two extremes by adding departments in
small batches.
• ALDEP provides a good starting point for designing a new constructive heuristic algorithm.
• New algorithm “ALDEP++” will attempt to counter the shortcomings of ALDEP without
abandoning these advantages.

4. EVOLUTION OF ALDEP++
ALDEP++ : The General Approach
• Addition of departments in batches
• Use of flow * distance as our measurement for what order to place the departments from each batch
in the ALDEP++ algorithm.
• Slightly modified input compared to ALDEP.
• In-between flow matrix is required
Benefits of ALDEP++
• Addition of department in batches overcomes the shortsightedness of ALDEP and produce more
optimized solutions
• Use of flow * distance as a measure , it allows us to obtain total costs of comparable to layouts
produced with the MicroCRAFT algorithm while still obtaining high TCR’s (maintaining some of the
simplicity of the ALDEP algorithm)

5. MODEL FORMULATION :ALDEP++
Assumptions –
• The area of departments is a multiple of sweep width.
• The length and width of the building is a multiple of sweep width.
• The floor space should be amenable to the serpentine flow.
• If there is a tie, departments are chosen/placed randomly.
• The shape of department can be changed.
• The next department starts where the previous one ends.
Batching -
• Uses relationship categories with respective scoring weights to determine which departments to
add next.
• Takes the sum of the relationships to all departments from the previous batch.
• Ranks the remaining departments by this relationship sum, the top scoring departments can be
determined as the subset to be included in the next batch.

6. MODEL FORMULATION :ALDEP++
Order Determination
• Batch of n departments analyze all n! possible orders of placement along the serpentine sweep pattern
• Resulting combinations are compared using a flow*distance calculation for the subset of departments
consisting of the current batch and the previous batch
• The placement order resulting in the lowest total flow*distance is selected and applied
• Distances can be measured as either E-DIST or centroid distances, depending on the preferences and
limitations of the user
Initialization
• First n departments are to be placed following the ALDEP algorithm.
• The first department is chosen at random, and each successive department is chosen based on the highest
relationships with the previously placed department. This process introduces the randomness of the ALDEP
process.
Iterations
• ALDEP++ makes random decisions whenever there are ties.
• At the very least, the starting department will be random.
• If multiple layouts are tied in the end for highest TCR, total flow * distance is used as the tiebreaker.

7. EXAMPLE MODEL: ALDEP++
Flow-Between Matrix
A B C D E F
A 0 8 0 4 0
B 0 5 0 2
C 0 1 0
D 6 0
E 4
F
Department Size (sq units)
A 400
B 800
C 600
D 600
E 800
F 400
Total Facility Size = 60 x 60 units
Sweep Width = 20 units
Relationship Categories
A = 8
E = 6, 5
I = 4
O = 1, 2
U = 0
Scoring Weights
A = 64
E = 16
I = 4
O = 1
U = 0
STEP 1 –
• Department F randomly selected for the start, and
the ALDEP algorithm selected E as the next
department as it has the strongest relationship with
F
• Using a batch size of 2
Initial two departments (first batch)
F
E

8. EXAMPLE MODEL: ALDEP++
Flow-Between Matrix
A B C D E F
A 0 8 0 4 0
B 0 5 0 2
C 0 1 0
D 6 0
E 4
F
Department Size (sq units)
A 400
B 800
C 600
D 600
E 800
F 400
STEP 2 – Second batch:
• Calculating the relationship ratings based on the scoring weights, it is determined that A
and D are the departments for the second batch.
• Because n=2, there are 2!=2 order combinations
Department Relationship Rating
A 4+0 = 4
B 0+1 = 1
C 1+0 = 1
D 16+0 = 16
F
A
E
D
F
D
E
A
Alternative 1 Alternative 2

9. EXAMPLE MODEL: ALDEP++
Flow-Between Matrix
A B C D E F
A 0 8 0 4 0
B 0 5 0 2
C 0 1 0
D 6 0
E 4
F
F
A
E
D
Alternative 1 Alternative 2
Calculating the sum-product of the E-DIST matrices with the flow matrix gives 490 for
order 1 and 364 for order 2. Because we want the minimum flow*distance, we select
alternative 2.

10. EXAMPLE MODEL: ALDEP++
Flow-Between Matrix
A B C D E F
A 0 8 0 4 0
B 0 5 0 2
C 0 1 0
D 6 0
E 4
F
F B
A
E
D C
Alternative 1 Alternative 2
• This is the last batch, so we can immediately skip to testing the 2 order combinations.
• Calculating the sum products gives 603.75 for order 1 and 371.68 for order 2. Therefore we
choose order 2, and that is the completed layout.
Third Batch:
F C
A
E
D B
Alternative 1 Alternative 2

11. EXAMPLE MODEL: ALDEP++
• This final layout has a total flow*distance of 1066.7 as compared to the results from the standard ALDEP
procedure which results in a higher total of 1132.9.
• Under the adjacency scoring method, the ALDEP++ layout receives a total weighted score of 104 as
compared to the ALDEP layout which scores only 101.
• In this example, ALDEP++ has outperformed ALDEP under both methods of comparison.
F B
A
E
D C
F C
A
E
D B
ALDEP LAYOUT
total weighted score – 101
Flow*dist = 1132.9
ALDEP++ LAYOUT
Total weighted score – 104
Flow*dist = 1132.9

12. IMPLEMENTATION & RESULTS
IMPLEMENTATION –
• ALDEP++ was compared with the original ALDEP and MicroCRAFT
• All three heuristic algorithms implanted with Matlab code
• ALDEP++ was coded using centroid distances primary reason for this decision being making a fair
comparison in total cost with the results from MicroCRAFT, which also is based on centroid
distance.
• Layout problems with appropriate variability generated and the run in these three codes
RESULTS :
For all cases, our outputs were TCR (total closeness rating) for adjacency based scoring, and
centroid distance * flows for the cost based scoring.

13. IMPLEMENTATION & RESULTS
Interpretation :
• TCR results for the ALDEP++ layouts are generally very close to the TCR results from ALDEP
• Comparing case-by-case, it can be seen that ALDEP++ works better when:
• The layout is square or close to square.
• Department sizes are not highly variable.
• Each batch roughly fills one column of the serpentine flow pattern.
Total Material Handling Cost Comparison
ALDEP++ yields lower costs on average because ALDEP does not consider flow * distance in it’s algorithm, while
ALDEP++ does.
ALDEP++ gives significantly better TCR than MicroCRAFT. As a result, while ALDEP++ consistently has high
TCR, MicroCRAFT results in highly variable TCR’s

14. BENEFITS & CONCLUSIONS
Benefits -
• ALDEP++ procedure improves on the performance of the layouts generated through adding departments
in batches.
• In general, we have found that the ALDEP++ algorithm is producing lower cost layouts when compared
to the total costs obtained from the ALDEP algorithm.
• The layout TCR’s obtained from the ALDEP++ algorithm are not significantly lower than the TCR’s seen
from the ALDEP algorithm.
• ALDEP++ has the best properties of both MicroCRAFT and ALDEP algorithms.
• ALDEP++ also has the advantage of covering one of ALDEP’s flaws, in avoiding undesirable X-
relationships.
• Batch-approach of ALDEP++ allows it to avoid X-relationships more effectively
Conclusions –
• ALDEP++ is a feasible heuristic algorithm for generating new layouts
• Provides balance between adjacency based TCR scoring and distance * flow total cost scoring
• ALDEP++ performs similarly to ALDEP with respect to TCR, and also obtains low-cost layouts similar to
the results from MicroCRAFT.
• Generally, ALDEP++ works best when the factors allow single batches to fit in one pass of the serpentine
flow pattern
• As total cost is an important realistic consideration for comparing layouts, ALDEP++ offers facility layouts
that are more practically optimal as compared to ALDEP.