Intelligent Warehouse Allocator for Optimal Regional Utilization - PowerPoint PPT Presentation

Intelligent Warehouse Allocator for Optimal Regional Utilization Girish Sathayanarayana Arun Patro girish.sathyanarayana@myntra.com arun.patro@myntra.com Myntra Designs Myntra Designs

Introduction • Buying and Replenishment is a major, throughout the year activity in large fashion e-commerce firms. • Hundreds of Purchase Orders (POs) are raised every day to procure styles of di ff erent article types from vendors. • The task is to distribute the procured inventory optimally between the principal warehouses. • Goal is to reduce logistics cost and faster delivery times to customers.

Introduction SKU ID QUANTITY Vendor Partner 1 A0001 320 Vendor Partner 2 A0002 234 …. A0003 124 …. … … …. … … … … …. … … Vendor Partner N A1000 1034 3. Optimally distribute the stock 1. Raise a Purchase Order 2. Vendors deliver the products among warehouses

Caveats of Allocation • The quantity of the product (SKU) that gets located in a warehouse must be in proportion to the regional (areas in the vicinity of the warehouse) demand of the product. • Warehouses have capacity constraints and old inventory which must be accounted while determining the new stocking quantities.

Problem Statement Input Output Optimal warehouse allocations Purchase Order {( 𝑡𝑙𝑣 𝑗 , 𝑂 𝑗 ) |1 ≤ 𝑗 ≤ 𝑁 } {( 𝑡𝑙𝑣 𝑗 , [ 𝑌 𝑗 1 , ... 𝑌 𝑗𝐿 , 𝑌 𝑗𝑚 ]) |1 ≤ 𝑗 ≤ 𝑁 } Compute 𝐿 warehouses with capacities [ 𝐷 1 , 𝐷 2 , … 𝐷 𝐿 ] where 𝑌 𝑗𝑘 is the number of 𝑡𝑙𝑣 𝑗 allocated to Existing inventory of the SKUs { 𝐹 𝑗𝑘 |1 ≤ 𝑗 ≤ 𝑁 ; 1 ≤ 𝑘 ≤ 𝐿 } warehouse 𝑘 . 𝑌 𝑗𝑚 denotes the number of 𝑡𝑙𝑣 𝑗 not assigned to any warehouse. Subject To Total Orders Constraint Warehouse Capacity Constraint

Problem Statement Output Non-assigned quantity Input K warehouses SKU ID QUANTITY X 11 X 12 … … X 1K X 1L SKU 1 N 1 X 21 X 22 … … X 2K X 2L SKU 2 N 2 M orders … … … … … … SKU 3 N 3 …. …. X M1 X M2 … … X MK X ML SKU M N M Optimal Warehouse Allocation Matrix Purchase Order X ∈ R M *( K +1) 𝑌 𝑗𝑘 is the number of 𝑡𝑙𝑣 𝑗 allocated to warehouse 𝑘 𝑌 𝑗 L denotes the number of 𝑡𝑙𝑣 𝑗 not assigned to any warehouse

Problem Statement Subject to Constraints sum ( X 11 X 12 … … X 1K X 1L X 21 X 22 … … X 2K X 2L sum ( ) <= N 2 Total Orders Constraint … … … … … … X ML X M1 X M2 … … X MK ) <= C 2 Warehouse Capacity Constraint

Solution 1. Ideal Splits Computation: Predicting the ideal split at the SKU level by a split prediction model and generating an ideal warehouse allocation given the order quantity from a demand model for every SKU assuming unlimited capacity in warehouses. 2. Optimal Feasible Allocations: Finding optimal feasible allocations considering warehouse capacity constraints by defining an allocation penalty matrix and solving the constrained optimization problem.

Step 1: Ideal Splits Computation • Given a purchase order of size M and K warehouses, we compute the Ideal Split Matrix by calculating the probability matrix I P • = Probability (Purchase event for is located in geographical cluster P ij sku i with associated nearest warehouse being warehouse ) j • Ideal splits are computed by: I ij [ I i 1 , I i 2 , . . . I ik ] = N i * [ P i 1 , P i 2 , . . . P ik ]

Step 1: Ideal Splits Computation • We estimate these probabilities by learning a classifier which predicts the warehouse probabilities using predictors like attributes of the style P 1 P 2 P 3 sku i ... … P K Feature Vector Probability Vector representing attributes like representing colour, brand, fabric, size, age group, price, regional demand of the product sleeve length, neck-type etc

Step 1: Ideal Splits Computation Log Loss for the three layer multi layer perceptron for various article types and genders

Step 2: Optimal Feasible Allocations • Given Ideal Split Matrix and Warehouse Capacity constraints, we can compute the Optimal Allocation Matrix using two formulations 1. Binary Integer Programming 2. Integer Programming

Step 2: Optimal Feasible Allocations Non-assignment Loss • Optimality is with regard to the inter warehouse redistribution task. We L 11 L 12 … … L 1K λ NA formalise this by defining a redistribution cost penalty matrix L 21 L 22 … … L 2K λ NA • Penalties mirror logistics cost involved in … … … … … … fulfilling an order from warehouse 𝑘 when … … … … … λ NA the nearest warehouse is warehouse 𝑗 . L K1 L K2 … … L KK λ NA • Non-assignment is allowed to handle cases where total number of items in the Redistribution Cost Penalty Matrix PO is greater than the combined capacity of all warehouses. L ∈ R K *( K +1) L i , K +1 = λ NA λ NA > > L ij

Step 2: Optimal Feasible Allocations Binary Integer Programming • Given a specification , we can define an exploded PO Specification {( sku i , N i ) | 1 ≤ i ≤ M } PO item set by repeating number of times represented as . PO ′ sku i N i item ij • We compute the warehouse allocation using a one-hot decision vector for each item of the exploded set. We define a Boolean Decision Variable Matrix Y 11 Y 12 … … Y 1K ITEM QUANTITY SKU ID QUANTITY item 1 1 N 1 Y 21 Y 22 … … Y 2K SKU 1 N 1 items of SKU 1 item 2 1 SKU 2 N 2 … 1 SKU 3 N 3 … … … … … … 1 …. …. … 1 N M items of SKU M SKU M N M Y N1 Y N2 … … Y NK item N 1 PO Exploded PO Decision Variable Matrix M ∑ N = N i Y ∈ {0,1} N * K i =1

Step 2: Optimal Feasible Allocations Binary Integer Programming Y opt Mapping from W = Ideal Allocation Matrix Item Allocation to SKU Allocation Z = 1 N − Y 1 K (Truncated Loss Matrix) L ′ = L [1 : K ][1 : K ] Solved using https://github.com/coin-or/Cbc

Step 2: Optimal Feasible Allocations Integer Programming • In the Integer Programming Case, we define Y 11 Y 12 … … Y 1K Y 1,K+1 an Integer Decision Variable Tensor Y ∈ Z M * K *( K +1) Y 21 Y 22 … … Y 2K Y 2,K+1 + … … … … … … • = number of ideally allocated to Y iuv sku i warehouse which is finally placed in u Y K1 Y K2 … … Y KK Y K,K+1 warehouse ( implies not v v = K + 1 assigned to any warehouse) Decision Variable Matrix Y i

Step 2: Optimal Feasible Allocations Integer Programming Y opt Solved using https://github.com/coin-or/Cbc

Evaluation and Results • We back-tested the model on purchase orders created during an entire month at Myntra using 2 scenarios • Tested for Apparel, Footwear and Personal Care, covering 23 di ff erent Article types. Around 8,000 purchase orders were created for 43,000 SKUs and a total quantity of 3.4 million.

Evaluation and Results RU: Regional Utilization which is the 2DD: Percentage Two-Day-Delivery which fraction of orders which are fulfilled by is the fraction of orders which are fulfilled the nearest warehouse within two days of placing the order.

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