Hyper-local sustainable assortment planning Nupur Aggarwal, Abhishek Bansal, Kushagra Manglik, Kedar Kulkarni, Vikas Raykar IBM Research
Sustainability The fashion industry is considered to be the world’s second largest polluter, after oil and gas. Reducing unsold inventory is one step into this direction.
Assortment planning Assortment planning, an important seasonal activity for any retailer, involves choosing the right subset of products to stock in each store.
current practices Heavily spreadsheet driven and relies on ü the expertise and intuition of the merchandisers. Not scalable when a merchandiser has to ü do planning for hundreds of stores. Typically stores are grouped into store ü clusters and an assortment is planned for each cluster rather than store. A sub-optimal assortment results in ü excess leftover inventory for the unpopular items, increasing the inventory costs, and stock outs of popular items, resulting in lost demand and unsatisfied customers. Existing approaches only maximize the ü expected revenue under certain store and budget constraints. Along with the revenue the choice of the final assortment has also an environmental cost associated with it.
store-wise hyper-local sustainable assortment planning What set of products to stock at each store ? Determine the optimal subset of products to be stocked in each store so that the assortment is ü localized to the preferences of the customers shopping in that store ü diverse ü sustainable The concept generalizes from store to ü distribution centre/warehouse ü region/state/country ü physical/online/omni channel
Literature Survey Broadly there are three aspects to assortment planning, • the choice of the demand model • estimating the parameters of the chosen demand model • using the demand estimates in an assortment optimization setup. • Demand Models • Independent Demand Models - The simplest approach is to assume product demand to be independent of the offer set or the assortment, that is, the demand for a product does not depend on other available products. • Choice models – Models demand for product j at store s when the assortment offered at the store was q. In practice the demand for a product is heavily influenced by the assortment that is under offer mainly due to product substitution (cannibalization) and product complementarity (halo effect)
Estimate sales using matrix factorization 1) 1) Product ct bias as: • E.g. special promotions being carried (re-train model every season) for Blue denim shirt will lead to higher sales 10 20 5 50 34 2) 2) St Stor ore bias as: • E.g. Stores more accessible to the society will show high overall sales 31 5 6 4 1 23 43 3) Var ariab able predict ction interval als: • Observed values in the sparse matrix 16 12 11 2 might have different confidence levels i.e. some might have tighter UB / LB 3 45 46 5 than others: Case 1: Observed 4 th week STR for an • 3 61 42 entry might be 0.4 but the upper and lower bounds can be 0.48 and 0.36, respectively. Case 2 : Observed 4 th week STR for an • entry might be 0.6 but the upper and lower bounds can be 0.73 and 0.4, respectively. Given a a spar arse Product ct X Store mat atrix : Clearly, we need to have differential • The objective is to estimate the unobserved entries in it These entries can be 4 th week / 8 th week STR, sales per month etc. treatment for such values. •
Lat at 1 Lat at 2 Lat at 3 Lat at 4 Lat at 1 Lat at 2 Lat at 3 Lat at 4 Method deployed for 0.2 0.3 0.1 0.6 Prod 1 estimating the missed • 0.2 0.3 0.1 0.6 The underlying hidden Store 1 opportunities : structure (latent feature 0.1 0.4 0.3 0.2 Store 2 0.1 0.4 0.3 0.2 Prod 2 matrix) influencing the 1) 1) Al Alternat ating 0.6 0.8 0.7 0.3 sales of products are Store 3 0.6 0.8 0.7 0.3 Prod 3 Leas ast Squar ares learnt 0.9 0.6 0.1 0.5 optimizat ation Store 4 0.9 0.6 0.1 0.5 Prod 4 Coupled 0.3 0.3 0.4 0.8 Store 5 • Product / store bias with 0.3 0.3 0.4 0.8 Prod 5 features are also learnt 0.2 0.7 0.6 0.1 Store 6 2) Lear 2) arning Latent matrix for products Latent matrix for stores vect ctors • To overcome the problem of variable prediction Coupled e : In red = Estimated intervals the estimated with No Note errors are penalized values for missing entries 3) Differential 3) al according to width of the St Stor ore 1 St Stor ore 2 St Stor ore 3 St Stor ore 4 St Stor ore 5 St Stor ore 6 treat atment confidence band 0.24 0.32 0.17 0.64 0.59 0.66 Product 1 0.14 0.43 0.72 0.11 0.76 0.23 Product 2 • Finally, the completed 0.87 0.83 0.86 0.51 0.41 0.88 Product 3 matrix is fed to the 0.91 0.34 0.67 0.54 0.77 0.12 Product 4 Assortment Planner 0.33 0.11 0.43 0.91 0.44 0.86 Product 5
Sustainability Scores ü Sustainability in a product can be related to social, economical or environmental. Even within environmental impact, it can be further measured using its affect on climate change, eutrophication, resource depletion, water scarcity, chemistry . ü Higg Index is one such index that gives sustainability scores by taking input information about various stages that were involved in fabric manufacturing. ü Higg Index is available for 1 Kg of the fabric. ü Since many garments are blended fabrics, we take a weighted average of the Higg index of fabrics present in the blended fabric and normalize it by the weight of the garment. ü To calculate sustainability score for an assortment, we take a weighted average of the Higg Index of the products in the assortment.
Cardinality The number of products to be included in an assortment Diversity Ensure that the selected assortment is diverse . Without the diversity constraints the assortment tends to prefer products that are similar to each other. Similar products might cannibalize each others’ sales. Sustainability We would like to include those products that are sustainable from an environmental perspective. A particular jeans might be trendy and have a high demand but may not be environment friendly. Complementarity A good assortment has products that are frequently bought together
Multi-objective optimization formulation Assortment optimization is solved 𝑦 !" : binary variable indicating presence of product j from the assortment at as a stochastic subset selection the store 𝑡 . optimization problem. 𝜌 !" : revenue generated of product j from the assortment at the store 𝑡 . 𝑒 𝑘𝑡 : the demand for product 𝑘 at store 𝑡 ℎ 𝑘 : the weighted Higg MSI score for that product 𝜇 : a parameter through which the user can specify the relative importance of each objective.
Multi-objective optimization An optimal assortment must that have: • Quality Infeasible region A high sustainability-score (or a low Higg MSI score) • Score x x A high quality-score (or high sales / revenue) • x x To optimize these two conflicting objectives a multi- • x objective optimization (MOO) formulation is considered Convergence to the MOO problems have been solved using classical methods • x globally optimal and meta-heuristics in literature Pareto front We choose the weighted sum method here due to its • x simplicity in configuration and use. Coefficients of different objective functions are continually • x changed; and for each coefficient-realization of these, a Feasible region single-objective optimization problem is solved yielding an optimal assortment. Solving these single-objective optimization problems for • Sustainability Score multiple coefficient realizations yields a family of Pareto- optimal assortments that are non-dominated with respect Pareto-front to each other x Solution on Pareto-front
Solve multiple single-objective optimization problems ü Solve the optimization problem for different values of 𝜇 and 𝛽 At each iteration, select the product ü with highest marginal gain. Update the marginal gains of ü products similar and complementary to the selected product. Proven approximation guarantee if ü the objective function is submodular Our implementation: ü Heap-based Approach ü Time Complexity O(klog(n)) instead of O(kn) ü Inference time 7secs for 50000 products on a CPU ü Empirically approx. ratio in range (1.01 to 1.03).
Product Quality and Higg MSI score distribution • 3 peaks corresponding to Quality distribution evenly • • 100% cotton, 100% viscose, 100% polyester spread across products • Cotton has highest Higg MSI (least sustainable) • Polyester has least Higg MSI (most sustainable)
Pareto Optimal Fronts The 3 horizontal clusters correspond to the 3 peaks of 100% cotton, 100% viscose and 100% Pareto frontier and the assortment cluster shrinks relative to the polyester respectively. frontier. This is because as we aggregate the scores of more products, the consolidated scores move closer to their mean.
Pareto Optimal Fabric composition for different lambda Looking at 𝜇 = 0.0 and 𝜇 = 0.5 plots • we see that viscose fabric is dominant since its Higg MSI is lower than cotton and it has the best quality score in terms of quality scores as well. For 𝜇 = 1 (maximum importance to • sustainability), the fabric composition in the assortment products comprises mostly of polyester .
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