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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