For efficient delivery and better customer experience it is imperative that the supply chain at Myntra be optimised. We describe our inventory redistribution model here, an integral part of our supply chain and a fusion of probabilistic modelling, optimisation, historical data and heuristics.

### Redistribution Model:

#### 1. Problem Statement

At Myntra a section of our supply chain is organised as follows. The country is divided into clusters based on the zipcode. In each cluster a Forward Deployment Center (FDC) hosts a select group of products to cater to the customers of its region. An order of a product from the customer of a cluster first reaches the FDC of the cluster and gets delivered if it is available at the FDC. If the product is unavailable at the FDC the order is forwarded to the central warehouse.

For better customer satisfaction through faster fulfillment of orders and efficient delivery it is essential that an ordered product be available at the FDC of the cluster most of the time. One way to accomplish this task is to hold a diverse range and quantity of products at the FDC and replenish them every week from the central warehouse. We summarise the setup in the following block diagram

#### 2. Current Situation

The effectiveness of the weekly redistribution of inventory to the FDCs is measured by the metrics Fulfillment Index (FI) and Utilisation Index (UI). FI is defined as the ratio of number of products delivered from the FDC of the cluster to number of products ordered from the cluster in a week. UI is defined as the ratio of number of products made available at the FDC for sale by the model in a week to number of products delivered from the given FDC in the previous week. Note that, at a given FDC, FI measures efficient storage of high demand products and UI measures congestion. In summary a FI of 100% at 1 UI is an ideal situation where every week all the items moved to FDC are sold completely. For an earlier production model on the benchmark dataset the average FI stood at 31% with average UI at 1.35

#### 3. Solution

Our solution approach to the redistribution problem involves reformulation of FI and UI at the level of a Stock Keeping Units (SKUs) and a fusion of probabilistic modelling, optimisation, heuristics and historical data. To start we setup some notation.

Given a SKU and FDC pair, denote by

We reformulate the definitions of FI and UI at the level of a SKU as follows. FI of a given SKU is defined as the ratio of number of products of the SKU delivered from the FDC of the cluster to number of products of the SKU ordered from the cluster in a week. UI of a given SKU is defined as the ratio of number of products of the SKU made available/predicted at the FDC for sale by the model in a week to number of products of the SKU delivered from the given FDC in the previous week. In mathematical notation,

We define an allocation function for a given SKU at cluster and simplify it as follows.

Optimisation of allocation function via simple calculus, heuristic choice of Poisson distribution for demand and approximations to solve for optima show that the optimal quantity of movement for a given SKU is

We summarise our approach in the form of an algorithm here.

#### 4. Results

With this solution we obtained significant improvements in both FI and UI on benchmark dataset. The average FI and UI stood at 44% and 0.89 respectively. Further explanation of the model and detailed experimental results of the approach in comparison to earlier production models are available in our publication at

https://arxiv.org/abs/2007.02510

Vulcan: Inventory Redistribution at Myntra was originally published in Myntra Engineering on Medium, where people are continuing the conversation by highlighting and responding to this story.

Source: Myntra

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