An Application of Newsboy Problem in Supply Chain Optimisation of Online Fashion E-Commerce Chandramouli K, Gopinath A, Nachiappan Sundaram, T Ravindra Babu, Chaithanya Bandi Myntra Designs Pvt. Ltd. August 2020 Application of Newsboy Problem August 2020 1 / 18
Contents Motivation Business metrics and problem statement Our solution Algorithm Experiments and conclusion Application of Newsboy Problem August 2020 2 / 18
Motivation Online fashion e-commerce and Myntra Fast and efficient delivery of an order Clusters and placement of Forward Deployment Centers (FDCs) Periodic movement, say, weekly Application of Newsboy Problem August 2020 3 / 18
Business metrics Definition Fulfilment Index (FI): The ratio of number of SKUs delivered from the FDC of the cluster to number of SKUs ordered from the cluster in a week. FI ( cluster ) = #Delivered SKUs in the week #Ordered SKUs in the week Higher values of FI signify efficient storage of high demand products and better customer service for the customers of the FDC cluster Application of Newsboy Problem August 2020 4 / 18
Business metrics ctd. Definition Utilization Index (UI): The ratio of number of SKUs predicted for sale by the model for a given FDC in a week to number of SKUs delivered from the FDC in the previous week. #predicted SKUs for the week UI ( cluster ) = #SKUs sold in the previous week High UI for large number of weeks signify that the FDC is getting congested. Application of Newsboy Problem August 2020 5 / 18
Problem statement FI of 100% at 1 UI is an ideal situation where every week all the items moved to FDC are sold completely FI and UI are dependent metrics Our objective is to come up with a solution that maximizes FI and minimizes UI simultaneously. Application of Newsboy Problem August 2020 6 / 18
Solution Define approximations for the FI and UI of a cluster at the level of SKU and model the reduced problem as an instance of newsboy problem. Application of Newsboy Problem August 2020 7 / 18
Solution ctd. Notation. Given a SKU, denote by D : Demand random variable of the given SKU f : Probability density function of D with support in (0 , ∞ ) F : Cumulative distribution function of D q : Quantity of a given SKU to be transported to the FDC s : Last week sales of SKU r : Relative importance between FI and UI ❊ : Expectation with respect to F Application of Newsboy Problem August 2020 8 / 18
Solution ctd. Similar to FI/UI of a cluster we look into FI/UI of the given SKU. FI ( SKU ) :=#Deliveries of the SKU in the week = min { q , D } # Orders of the SKU in the week D UI ( SKU ) := #Predicted quantity of the SKU for the week #Quantity of the SKU sold in the previous week = q s Application of Newsboy Problem August 2020 9 / 18
Solution ctd. To achieve the objective consider the following allocation function of q , a ( q ). a ( q ) := ❊ [ FI ( SKU ) − r UI ( SKU )] � min { q , D } � − r q = ❊ D s � ∞ x f ( x ) dx − r q 1 = F ( q ) + q s q Application of Newsboy Problem August 2020 10 / 18
Solution ctd. Theorem � ∞ 1 x f ( x ) dx = r q ∗ given by s is the global maximizer of allocation q ∗ function a. Application of Newsboy Problem August 2020 11 / 18
Solution ctd. Heuristics: The demand of a SKU in the case of fashion e-commerce is a discrete distribution. We assume that each SKU follows a Poisson distribution. � ∞ � � k e − λ λ k λ k +1 1 1 k ! ≈ 1 e − λ x f ( x ) dx ≈ ( k + 1)! λ q k ≥ q k ≥ q = 1 − F Poisson ( q ) λ where λ is the parameter of the Poisson distribution. Application of Newsboy Problem August 2020 12 / 18
SKU allocation algorithm Algorithm Input: Historic weekly sales of each SKU Output: Quantity to allocate for each SKU 1: procedure ALLOCATE: for each SKU do 2: Estimate the parameter of F Poisson for the SKU utilizing historic weekly 3: sales of the SKU. Poisson (1 − r � SKU = F − 1 λ SKU Evaluate q ∗ s SKU ) for the SKU. 4: return q ∗ SKU for each SKU 5: Application of Newsboy Problem August 2020 13 / 18
Comments � � 1 − r � Observe that F − 1 λ SKU is well defined if and only if Poisson s SKU � � 1 − r � ⇒ r � λ SKU 0 < ⇐ λ SKU < s SKU . s SKU Hence there is a recommendation q ∗ SKU for the SKU only under the condition that the last week sales, s SKU , is larger than the relative importance, r , times the mean of sales � λ SKU of the SKU, a intuitive thing to do, and the quantity to recommend is obtained as a quantile of the demand distribution. Application of Newsboy Problem August 2020 14 / 18
Experiments We compare our algorithm with a ARMAX time series based earlier production model at Myntra. Our solution only utilizes a subset of the features utilized by the time series based model. Application of Newsboy Problem August 2020 15 / 18
Experiments ctd. Table: Comparison of cluster wise FI and UI metrics for both models Regression Model Our Algorithm Region FI UI FI UI FDC 1 25% 1.24 36% 0.85 FDC 2 47% 1.98 67% 0.97 FDC 3 18% 0.81 31% 0.83 FDC 4 54% 2.06 62% 0.98 FDC 5 21% 1.08 36% 0.88 FDC 6 41% 2.10 52% 0.98 FDC 7 21% 0.70 35% 0.83 FDC 8 21% 0.84 34% 0.83 FDC 9 32% 0.83 45% 0.90 FDC 10 15% 0.75 28% 0.75 FDC 11 48% 1.99 69% 0.98 FDC 12 33% 1.81 37% 0.86 Application of Newsboy Problem August 2020 16 / 18
Conclusion The boost in performance, unlike in time series based model where the objective is mean square error, is a result of direct optimization of an objective that depends on FI and UI. To conclude we have modeled our business problem as an instance of newsboy problem and efficiently solved it. Application of Newsboy Problem August 2020 17 / 18
Thanks Application of Newsboy Problem August 2020 18 / 18
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