Download SSA Focus

SSA Decisions
• how much shelf space
to allocate to a product
category
• how much shelf space
to allocate to a product
within each product
category.
SSA Focus
• which products to
include in the
assortment
• how much space to
allocate
• at what price to sell
1
Multiplicative-Additive Demand Structure
•
•
UMDi Unmodied Demand of product i, UMDi = i (unit/day)
MDi
Modified Demand of product i (unit/day)
Di =
MDi + ADi
Di = UMDi*GDi + ADi
Di =
2
Enhanced Model for the Demand
• Reyes and Frazier (2007)
– Price sensitivity factor
Demand Model
– Our sensitivity factor
3
Optimization Model
• The gross profit for a product i under brand b
At least one shelf allocation
Can be allocated to a limited number of shelves
Logical brand and product relations
Defining top and bottom shelf for brands
4
Defining top and bottom shelf for products
Logical product-shelf allocations
Logical product-shelf allocations
Ensuring same number of products on adjacent shelves
Ensuring total space allocation of a shelf
Min and max shelf height policy
Relation between the sum of the shelf heights with the section height
Shelf height allocation considering stackability conditions
Defining total number of facing allocation
Min and max number of facing policy
5
Max and min allowable percentage of price change policy
6
Numerical Analysis
Parameter
Range
width-length (w)
[4, 9]
height-length (h)
[7, 13]
purchasing cost (c)
[5, 8]
suggested selling price (p)
[9, 13]
market share-strength (¼)
[40, 100]
own-space elasticity (®)
[0.3, 0.5]
cross-space elasticity (¯)
[0.005, 0.03]
own-price change elasticity (¾’)
[-1, -4]
cross-price change elasticity (¹’)
[0, 0.2]
bounds for allocations (Xmin, Xmax)
[2, 16]
bounds for price change (PC)
[-0.4, 0.4]
total shelf section height (TH)
(60, 180)
total shelf width-length (L)
(30, 120)
7
Example Shelf Space Allocation
• Results of a 10 products -3 shelves test problem
pisuggested
pinew
raise
9.442
13.2188
-0.4
raise
11.010
15.414
1
-0.4
raise
9.641
13.4974
3
3
0.4
discount
12.490
7.494
1*2=2
1
1
-0.4
raise
10.060
14.84
6
2*2 +
2*4=12
2
1
0.236
discount
10.143
7.749
7
1*2=2
1
1
-0.4
raise
11.376
15.9264
8
4*4=16
2
2
0.273
discount
11.891
8.6447
9
1*4=4
2
2
-0.4
raise
11.513
16.1182
10
1*2=2
3
3
-0.4
raise
10.855
15.197
Item
xi (w*h)
topi
bottomi
PCi
1
3*2=6
1
1
-0.4
2
1*2=2
3
3
3
1*2=2
1
4
5*3=15
5
8