Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements

Constructive solution methodologies to the capacitated newsvendor problem and surrogate extension

The newsvendor problem is a single-period stochastic model used to determine the order quantity of perishable product that maximizes/minimizes the profit/cost of the vendor under uncertain demand. The goal is to fmd an initial order quantity that can offset the impact of backlog or shortage caused by mismatch between the procurement amount and uncertain demand. If there are multiple products and substitution between them is feasible, overstocking and understocking can be further reduced and hence, the vendor\u27s overall profit is improved compared to the standard problem. When there are one or more resource constraints, such as budget, volume or weight, it becomes a constrained newsvendor problem. In the past few decades, many researchers have proposed solution methods to solve the newsvendor problem. The literature is first reviewed where the performance of each of existing model is examined and its contribution is reported. To add to these works, it is complemented through developing constructive solution methods and extending the existing published works by introducing the product substitution models which so far has not received sufficient attention despite its importance to supply chain management decisions. To illustrate this dissertation provides an easy-to-use approach that utilizes the known network flow problem or knapsack problem. Then, a polynomial in fashion algorithm is developed to solve it. Extensive numerical experiments are conducted to compare the performance of the proposed method and some existing ones. Results show that the proposed approach though approximates, yet, it simplifies the solution steps without sacrificing accuracy. Further, this dissertation addresses the important arena of product substitute models. These models deal with two perishable products, a primary product and a surrogate one. The primary product yields higher profit than the surrogate. If the demand of the primary exceeds the available quantity and there is excess amount of the surrogate, this excess quantity can be utilized to fulfill the shortage. The objective is to find the optimal lot sizes of both products, that minimize the total cost (alternatively, maximize the profit). Simulation is utilized to validate the developed model. Since the analytical solutions are difficult to obtain, Mathematical software is employed to find the optimal results. Numerical experiments are also conducted to analyze the behavior of the optimal results versus the governing parameters. The results show the contribution of surrogate approach to the overall performance of the policy. From a practical perspective, this dissertation introduces the applications of the proposed models and methods in different industries such as inventory management, grocery retailing, fashion sector and hotel reservation

Approximating the Nonlinear Newsvendor and Single-Item Stochastic Lot-Sizing Problems When Data Is Given by an Oracle

The single-item stochastic lot-sizing problem is to find an inventory replenishment policy in the presence of discrete stochastic demands under periodic review and finite time horizon. A closely related problem is the single-period newsvendor model. It is well known that the newsvendor problem admits a closed formula for the optimal order quantity whenever the revenue and salvage values are linear increasing functions and the procurement (ordering) cost is fixed plus linear. The optimal policy for the single-item lot-sizing model is also well known under similar assumptions. In this paper we show that the classical (single-period) newsvendor model with fixed plus linear ordering cost cannot be approximated to any degree of accuracy when either the demand distribution or the cost functions are given by an oracle. We provide a fully polynomial time approximation scheme for the nonlinear single-item stochastic lot-sizing problem, when demand distribution is given by an oracle, procurement costs are provided as nondecreasing oracles, holding/backlogging/disposal costs are linear, and lead time is positive. Similar results exist for the nonlinear newsvendor problem. These approximation schemes are designed by extending the technique of K-approximation sets and functions.National Science Foundation (U.S.) (Contract CMMI-0758069)United States. Office of Naval Research (Grant N000141110056

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

The Big Data Newsvendor: Practical Insights from Machine Learning

This is a revision of previously published DSpace entry: http://hdl.handle.net/1721.1/81412.We investigate the newsvendor problem when one has n observations of p features related to the demand as well as past demands. Both small data (p=n = o(1)) and big data (p=n = O(1)) are considered. For both cases, we propose a machine learning algorithm to solve the problem and derive a tight generalization bound on the expected out-of-sample cost. The algorithms can be extended intuitively to other situations, such as having censored demand data, ordering for multiple, similar items and having a new item with limited data. We show analytically that our custom-designed, feature-based approach can be better than other data-driven approaches such as Sample Average Approximation (SAA) and separated estimation and optimization (SEO). Our method can also naturally incorporate the operational statistics method. We then apply the algorithms to nurse staffing in a hospital emergency room and show that (i) they can reduce the median out-of-sample cost by up to 46% and 16% compared to SAA and SEO respectively, with statistical significance at 0.01, and (ii) this is achieved either by carefully selecting a small number of features and applying the small data algorithm, or by using a large number of features and using the big data algorithm, which automates feature-selection

The Big Data Newsvendor: Practical Insights from Machine Learning Analysis

A 2/6/2014 revision to this paper is available at http://hdl.handle.net/1721.1/85658.We present a version of the newsvendor problem where one has n observations of p features as well as past demand. We consider both \big data" (p=n = O(1)) as well as small data (p=n = o(1)). For small data, we provide a linear programming machine learning algorithm that yields an asymptotically optimal order quantity. We also derive a generalization bound based on algorithmic stability, which is an upper bound on the expected out-of-sample cost. For big data, we propose a regularized version of the algorithm to address the curse of dimensionality. A generalization bound is derived for this case as well, bounding the out-of-sample cost with a quantity that depends on n and the amount of regularization. We apply the algorithm to analyze the newsvendor cost of nurse sta_ng using data from the emergency room of a large teaching hospital and show that (i) incorporating appropriate features can reduce the out-of-sample cost by up to 23% relative to the featureless Sample Average Approximation approach, and (ii) regularization can automate feature-selection while controlling the out-of-sample cost. By an appropriate choice of the newsvendor underage and overage costs, our results also apply to quantile regression