Implementation of Artificial Intelligence for Cost Optimization in Inventory Storage and Order Prediction in the Fashion Industry

Chairman LUXONOMY™ Group

1. Introduction

The implementation of advanced Artificial Intelligence (AI) techniques in supply chain management in the fashion industry has the potential to generate significant operational cost reductions, particularly in merchandise storage and demand forecasting. This study focuses on the use of machine learning (ML) and deep learning (DL) algorithms to optimize these key areas, providing a technical approach aimed at AI experts.

The study will cover underlying mathematical models and algorithmic techniques, including time series analysis, mathematical optimization, recommendation models, and neural network techniques applied to forecasting and inventory optimization problems.

2. Cost Reduction in Storage through AI

2.1 Inventory Optimization using Stochastic Programming

The inventory optimization problem can be modeled as a stochastic programming problem. Using historical sales data and projected demand, we can model the optimal inventory level by using techniques such as the stochastic optimal control model. The objective is to minimize the total cost \(C\), which includes the inventory holding cost \(C_m\), the stockout cost \(C_r\), and the cost of ordering more stock \(C_o\):

        C = C_m + C_r + C_o

Where:

C_m = h · I, where h is the holding cost per unit and I is the inventory level.
C_r = p · B, where p is the cost of lost sales due to stockouts and B is the backorder or stock in waiting.
C_o = s · q, where s is the cost per order and q is the number of units ordered.

Using stochastic optimization algorithms such as Stochastic Dynamic Programming (SDP), we can optimize when and how much inventory to order. The Bellman method in SDP is based on the following recurrence equation:

        V_t(s) = min_q [C(s, q) + E[V_t+1(s')]]

Where V_t(s) is the expected value in state s at time t, and s' is the next state.

2.2 Physical Space Optimization using Routing and Placement Algorithms

The problem of warehouse organization can be modeled as a combinatorial optimization problem, in which the goal is to minimize picking time and maximize efficient space usage. Algorithms such as the optimized A* Search Algorithm and models based on Simulated Annealing can be used to optimize picking routes.

If we define a cost metric \(C_p\) as the sum of the distances traveled by operators in the warehouse, the objective is to minimize \(C_p\) under the spatial constraints of the warehouse:

        C_p = ∑ d(x_i, y_i)

Where d(x_i, y_i) is the distance between product i and the dispatch point y_i, and n is the total number of products in the order.

2.3 Supply Chain Optimization through Bayesian Networks

Supply chain disruption forecasting can be addressed using Bayesian networks. By modeling the supply chain as a network of stochastic variables \(X_i\) with conditional probabilities \(P(X_i | X_j)\), it is possible to calculate the probability of disruptions and adjust inventory decisions accordingly.

        P(X_i | X_j) = P(X_i, X_j) / P(X_j)

Where \(P(X_i, X_j)\) is the joint probability of a disruption at node i given an event at node j. These networks can be optimized using the Expectation Maximization (EM) algorithm to adjust the conditional distributions from historical data.

3. Order Prediction in the Fashion Industry through AI

3.1 Time Series Models for Trend Prediction

Demand forecasting in fashion exhibits high volatility, making it an ideal problem for advanced time series models such as ARIMA and recurrent neural networks (RNN) with Long Short-Term Memory (LSTM) cells.

The ARIMA (p, d, q) model is based on three parameters:

p: number of autoregressive lags.
d: degree of differencing to make the series stationary.
q: number of moving average terms.

The general model is represented as:

        Y_t = ϕ₁ Y_t-1 + … + ϕ_p Y_t-p + θ₁ ε_t-1 + … + θ_q ε_t-q + ε_t

To improve accuracy in fast trend prediction, LSTM networks are highly effective due to their ability to learn long-term dependencies in temporal data. The update of the LSTM cell state is given by:

        h_t = o_t · tanh(C_t)

Where C_t is the cell state and o_t is the output gate.

3.2 Recommendation Systems and Collaborative Learning

Recommendation systems in fashion are implemented using matrix factorization models and variational autoencoders. Matrix factorization decomposes the user-product interaction matrix \(R\) into two latent matrices \(P\) and \(Q\), such that:

        R ≈ PQ^T

The objective is to minimize the error function:

        min_{P, Q} ∑ (R_ij - P_i Q_j^T)² + λ (||P||² + ||Q||²)

Where λ is the regularization parameter.

3.3 Reducing Returns through Predictive Analytics

Return prediction in fashion can be modeled as a binary classification problem, where the probability of a product being returned is predicted based on characteristics such as the type of garment, customer behavior, and social media feedback. Algorithms such as decision trees and XGBoost are highly effective in this type of prediction.

The objective function for XGBoost is:

        ℒ(θ) = ∑ l(y_i, ŷ_i) + ∑ Ω(f_k)

Where \(l\) is the quadratic loss and \(\Omega(f_k)\) is the regularization term controlling the model's complexity.

4. Real Example of Savings through AI Implementation in Inventory Storage and Order Prediction

Let's consider a fashion company with the following characteristics:

Annual sales: €50 million
Storage cost per unit (h): €2 per unit per month
Average inventory volume: 100,000 units
Stockout cost (p): €50 for each unfulfilled order
Average monthly demand: 80,000 units
Overstock cost: Related to immobilized capital and inventory maintenance

4.1 Storage Cost Savings through Inventory Optimization

Before implementing AI-based inventory optimization, the company maintained a safety stock level 30% above average monthly demand, resulting in an average inventory of 104,000 units:

        Previous Average Inventory = 80,000 × (1 + 0.30) = 104,000 units

The monthly storage cost is calculated as:

        C_m = h × I = 2 € × 104,000 = 208,000 € per month

By implementing a stochastic optimization system with AI, we can reduce the safety stock level to 10% above average demand, as AI more accurately predicts demand fluctuations. The new inventory level is:

        New Average Inventory = 80,000 × (1 + 0.10) = 88,000 units

The new monthly storage cost becomes:

        C_m^new = 2 € × 88,000 = 176,000 €

The monthly storage savings are:

        Storage Savings = 208,000 - 176,000 = 32,000 €

Over a year, this results in:

        Annual Savings = 32,000 € × 12 = 384,000 €

4.2 Stockout Cost Savings

Before AI implementation, the company experienced an average of 1,000 unfulfilled orders per month, resulting in an estimated stockout cost of:

        C_r = p × B = 50 € × 1,000 = 50,000 € per month

With a predictive system based on recurrent neural networks (LSTM), the company reduces unfulfilled orders to only 200 per month, lowering the stockout cost to:

        C_r^new = 50 € × 200 = 10,000 € per month

The monthly stockout savings are:

        Stockout Savings = 50,000 - 10,000 = 40,000 €

Over a year, this translates to:

        Annual Stockout Savings = 40,000 € × 12 = 480,000 €

4.3 Total Annual Savings through AI Implementation

By adding the annual savings from storage and stockout reductions, we get the total annual savings:

        Total Annual Savings = 384,000 € + 480,000 € = 864,000 €

4.4 Impact on Immobilized Capital

Additionally, by reducing the average inventory from 104,000 units to 88,000 units, the immobilized capital in inventory is reduced. Assuming an average cost per unit of €30, the immobilized capital before and after optimization would be:

Before AI: €30 × 104,000 = €3,120,000
After AI: €30 × 88,000 = €2,640,000

This results in a release of €480,000 in immobilized capital, which can be reinvested in other operational areas or expansion projects, improving the company's liquidity and return on investment (ROI).

4.5 Return on Investment (ROI) from AI

The cost of implementing an advanced AI system (including software, infrastructure, and personnel) can be estimated at around €200,000 annually. Comparing this to the annual savings, we obtain a positive return on investment (ROI):

        ROI = (Total Annual Savings - AI Investment) / AI Investment × 100

        ROI = (864,000 - 200,000) / 200,000 × 100 = 332%

This calculation shows that AI implementation not only covers its costs but also generates a 332% ROI, highlighting the strategic and economic value of this technology in inventory optimization and demand prediction.

5. Conclusion

The use of advanced AI in fashion offers substantial improvements in storage efficiency and order forecasting. Implementing techniques such as stochastic optimization, neural networks, and advanced recommendation models can significantly reduce storage costs and improve demand prediction accuracy. This example demonstrates that adopting AI not only enhances efficiency but also provides substantial ROI, making it a highly profitable investment for the company.