SOLVING THE DATA-DRIVEN NEWSVENDOR WITH ATTENTION TO TIME

Inventory management systems support firms in planning for an uncertain future by using demand forecasts and optimization models to make restocking decisions. Recent work on the data-driven newsvendor found that incorporating machine learning (ML) can improve the success of inventory management by accounting for demand-driving information. However, ML methods are infamously hard to interpret, which may hinder their acceptance. To ameliorate this, we show how to apply an interpretable attention-based architecture, the Temporal Fusion Transformer (TFT), to the data-driven newsvendor problem. Our approach replicates and extends the original TFT time series forecasting method to the inventory management domain. We evaluate our method on two real-world retail datasets, each covering 260 perishable food items, and provide domain-specific benchmarks. The computational study illustrates TFT’s interpretable predictions and their comparatively high accuracy. Our work aims to lay the groundwork for further design science research on transparency in human-AI collaboration in this domain

Applying Deep Learning to the Ice Cream Vendor Problem: An Extension of the Newsvendor Problem

The Newsvendor problem is a classical supply chain problem used to develop strategies for inventory optimization. The goal of the newsvendor problem is to predict the optimal order quantity of a product to meet an uncertain demand in the future, given that the demand distribution itself is known. The Ice Cream Vendor Problem extends the classical newsvendor problem to an uncertain demand with unknown distribution, albeit a distribution that is known to depend on exogenous features. The goal is thus to estimate the order quantity that minimizes the total cost when demand does not follow any known statistical distribution. The problem is formulated as a mathematical programming problem and solved using a Deep Neural network approach. The feature-dependent demand data used to train and test the deep neural network is produced by a discrete event simulation based on actual daily temperature data, among other features

Integrated Optimization And Learning Methods Of Predictive And Prescriptive Analytics

A typical decision problem optimizes one or more objectives subject to a set of constraints on its decision variables. Most real-world decision problems contain uncertain parameters. The exponential growth of data availability, ease of accessibility in computational power, and more efficient optimization techniques have paved the way for machine learning tools to effectively predict these uncertain parameters. Traditional machine learning models measure the quality of predictions based on the closeness between true and predicted values and ignore decision problems involving uncertain parameters for which predicted values are treated as the true values.Standard approaches passing point estimates of machine learning models into decision problems as replacement of uncertain parameters lose the connection between predictive and prescriptive tasks. Recently developed methods to strengthen the bond between predictive and prescriptive tasks still rely on either first predict, then optimize strategy or use approximation techniques in integrating predictive and prescriptive tasks. We develop an integrated framework for performing predictive and prescriptive analytics concurrently to realize the best prescriptive performance under uncertainty. This framework is applicable to all prescriptive tasks involving uncertainty. Further, it is scalable to handle integrated predictive and prescriptive tasks with reasonable computational effort and enables users to apply decomposition algorithms for large-scale problems. The framework also accommodates prediction tasks ranging from simple regression to more complex black-box neural network models. The integrated optimization framework is composed of two integration approaches. The first approach integrates regression-based prediction and mathematical programming-based prescription tasks as a bilevel program. While the lower-level problem prescribes decisions based on the predicted outcome for a specific observation, the upper-level evaluates the quality of decisions with respect to true values. The upper-level problem can be considered as a prescriptive error, and the goal is to minimize this prescriptive error. In order to achieve the same performance in external data sets (test) compared to internal data sets (train), we offer different approaches to control the prescription generalization error associated with out-of-sample observation. We develop a decomposition algorithm for large-scale problems by leveraging a progressive hedging algorithm to solve the resulting bilevel formulation. The second approach integrates the learning of neural network-based prediction and optimization tasks as a nested neural network. While the predictive neural network promotes decisions based on predicted outcomes, the prescriptive neural network evaluates the quality of predicted decisions with respect to true values. We also propose a weight initialization process for nested neural networks and build a decomposition algorithm for large-scale problems. Our results for the example problems validate the performance of our proposed integrated predictive and prescriptive optimization and training frameworks. With customarily generated synthetic data sets, proposed methods surpass all of the first predict, then optimize approaches and recently developed approximate integration methods for both in-sample and out of sample data sets. We also observe how the proposed generalization error controlling approach improves results in out of sample data sets. Customarily generated synthetic data pairs at different levels of correlation and non-linearity graphically show us how different methods converge to each other

A Survey of Contextual Optimization Methods for Decision Making under Uncertainty

Recently there has been a surge of interest in operations research (OR) and the machine learning (ML) community in combining prediction algorithms and optimization techniques to solve decision-making problems in the face of uncertainty. This gave rise to the field of contextual optimization, under which data-driven procedures are developed to prescribe actions to the decision-maker that make the best use of the most recently updated information. A large variety of models and methods have been presented in both OR and ML literature under a variety of names, including data-driven optimization, prescriptive optimization, predictive stochastic programming, policy optimization, (smart) predict/estimate-then-optimize, decision-focused learning, (task-based) end-to-end learning/forecasting/optimization, etc. Focusing on single and two-stage stochastic programming problems, this review article identifies three main frameworks for learning policies from data and discusses their strengths and limitations. We present the existing models and methods under a uniform notation and terminology and classify them according to the three main frameworks identified. Our objective with this survey is to both strengthen the general understanding of this active field of research and stimulate further theoretical and algorithmic advancements in integrating ML and stochastic programming

Streamlined Framework for Agile Forecasting Model Development towards Efficient Inventory Management

This paper proposes a framework for developing forecasting models by streamlining the connections between core components of the developmental process. The proposed framework enables swift and robust integration of new datasets, experimentation on different algorithms, and selection of the best models. We start with the datasets of different issues and apply pre-processing steps to clean and engineer meaningful representations of time-series data. To identify robust training configurations, we introduce a novel mechanism of multiple cross-validation strategies. We apply different evaluation metrics to find the best-suited models for varying applications. One of the referent applications is our participation in the intelligent forecasting competition held by the United States Agency of International Development (USAID). Finally, we leverage the flexibility of the framework by applying different evaluation metrics to assess the performance of the models in inventory management settings

Applications of Machine Learning in Supply Chains

Advances in new technologies have resulted in increasing the speed of data generation and accessing larger data storage. The availability of huge datasets and massive computational power have resulted in the emergence of new algorithms in artificial intelligence and specifically machine learning, with significant research done in fields like computer vision. Although the same amount of data exists in most components of supply chains, there is not much research to utilize the power of raw data to improve efficiency in supply chains.In this dissertation our objective is to propose data-driven non-parametric machine learning algorithms to solve different supply chain problems in data-rich environments.Among wide range of supply chain problems, inventory management has been one of the main challenges in every supply chain. The ability to manage inventories to maximize the service level while minimizing holding costs is a goal of many company. An unbalanced inventory system can easily result in a stopped production line, back-ordered demands, lost sales, and huge extra costs. This dissertation studies three problems and proposes machine learning algorithms to help inventory managers reduce their inventory costs.In the first problem, we consider the newsvendor problem in which an inventory manager needs to determine the order quantity of a perishable product to minimize the sum of shortage and holding costs, while some feature information is available for each product. We propose a neural network approach with a specialized loss function to solve this problem. The neural network gets historical data and is trained to provide the order quantity. We show that our approach works better than the classical separated estimation and optimization approaches as well as other machine learning based algorithms. Especially when the historical data is noisy, and there is little data for each combination of features, our approach works much better than other approaches. Also, to show how this approach can be used in other common inventory policies, we apply it on an $(r,Q)$ policy and provide the results.This algorithm allows inventory managers to quickly determine an order quantity without obtaining the underling demand distribution.Now, assume the order quantities or safety stock levels are obtained for a single or multi-echelon system. Classical inventory optimization models work well in normal conditions, or in other words when all underlying assumptions are valid. Once one of the assumptions or the normal working conditions is violated, unplanned stock-outs or excess inventories arise.To address this issue, in the second problem, a multi-echelon supply network is considered, and the goal is to determine the nodes that might face a stock-out in the next period. Stock-outs are usually expensive and inventory managers try to avoid them, so stock-out prediction might results in averting stock-outs and the corresponding costs.In order to provide such predictions, we propose a neural network model and additionally three naive algorithms. We analyze the performance of the proposed algorithms by comparing them with classical forecasting algorithms and a linear regression model, over five network topologies. Numerical results show that the neural network model is quite accurate and obtains accuracies in $[0.92, 0.99]$ for the hardest to easiest network topologies, with average of 0.950 and standard deviation of 0.023, while the closest competitor, i.e., one of the proposed naive algorithms, obtains accuracies in $[0.91, 0.95]$ with average of 9.26 and standard deviation of .0136. Additionally, we suggest conditions under which each algorithm is the most reliable and additionally apply all algorithms to threshold and multi-period predictions.Although stock-out prediction can be very useful, any inventory manager would like to have a powerful model to optimize the inventory system and balance the holding and shortage costs. The literature on multi-echelon inventory models is quite rich, though it mostly relies on the assumption of accessing a known demand distribution. The demand distribution can be approximated, but even so, in some cases a globally optimal model is not available.In the third problem, we develop a machine learning algorithm to address this issue for multi-period inventory optimization problems in multi-echelon networks. We consider the well-known beer game problem and propose a reinforcement learning algorithm to efficiently learn ordering policies from data.The beer game is a serial supply chain with four agents, i.e. retailer, wholesaler, distributor, and manufacturer, in which each agent replenishes its stock by ordering beer from its predecessor. The retailer satisfies the demand of external customers, and the manufacturer orders from external suppliers. Each of the agents must decide its own order quantity to minimize the summation of holding and shortage cost of the system, while they are not allowed to share any information with other agents. For this setting, a base-stock policy is optimal, if the retailer is the only node with a positive shortage cost and a known demand distribution is available. Outside of this narrow condition, there is not a known optimal policy for this game. Also, from the game theory point of view, the beer game can be modeled as a decentralized multi-agent cooperative problem with partial observability, which is known as a NEXP-complete problem.We propose an extension of deep Q-network for making decisions about order quantities in a single node of the beer game. When the co-players follow a rational policy, it obtains a close-to-optimal solution, and it works much better than a base-stock policy if the other agents play irrationally. Additionally, to reduce the training time of the algorithm, we propose using transfer learning, which reduces the training time by one order of magnitude. This approach can be extended to other inventory optimization and supply chain problems