Single-period Inventory Problem Research Articles

An end-to-end deep learning model for solving data-driven newsvendor problem with accessibility to textual review data

We investigate a data-driven single-period inventory management problem with uncertain demand, where large amounts of textual online reviews and historical data are accessible. Unlike two-step frameworks (i.e., predict-then-optimization), we propose an end-to-end (E2E) framework that directly suggests the order quantity by leveraging a deep learning model that inputs textual online reviews and other demand-related feature data, without any intermediate steps such as text sentiment analysis. The E2E model does not require any prior assumptions about the demand distribution and can automatically determine the order quantity that minimizes the newsvendor cost by employing the information from real-world data. Our experiments, using publicly available real-world data, demonstrate that our method can significantly reduce the sum of overage and underage costs, outperforming other data-driven models proposed in recent years. Specifically, the inclusion of textual online review data improves ordering decisions by a 28.7% cost reduction.

Application of a Distributionally Robust Optimization Approach for Single-Period Stochastic Inventory Problems with Different Carbon Policies

While single-period stochastic inventory problems have been studied in academia and industry, the impacts of both carbon emissions reduction and partial distribution information have not been investigated. In this paper, we consider carbon emission reduction in a single-period inventory problem where both product price and demand are stochastic. When only partial information on the first and second moments of the two stochastic elements is specified, we use the max–min criterion to construct two optimization models under cap-and-trade and carbon tax policies. For each model, we prove the existence of the optimal robust decisions on production quantity and cleaning equipment investment. By comparing the profit and carbon emission between these two models, we identify certain conditions that improve the economic and environmental performance of the manufacturer. Finally, we conduct a numerical study to test the robustness of the optimal operational decisions under each carbon policy.

A Distributionally Robust Fuzzy Optimization Method for Single-Period Inventory Management Problems

This paper investigates single-period inventory management problems with uncertain market demand, where the exact possibility distribution of demand is unavailable. In this condition, it is important to order a reliable quantity which can immunize against distribution uncertainty. To model this type of single-period inventory management problem, this paper characterizes the uncertain demand by generalized interval-valued possibility distributions. We present a novel concept about an uncertain distribution set to describe distribution perturbation characterization. First, we introduce a lambda selection of the interval-valued fuzzy variable, and the uncertain distribution set is a collection of all generalized possibility distributions of lambda selection variables. According to the uncertain distribution set, a new distributionally robust fuzzy optimization method is developed for single-period inventory management problems. Under mild assumptions, the robust counterpart of the proposed fuzzy single-period inventory management model is formulated, which is an optimization program with certain linear objectives and infinitely many integral constraints. We discuss the computational issue of integral constraints and reformulate equivalently the robust counterpart as three deterministic inventory submodels under generalized interval-valued trapezoidal possibility distributions. According to the characteristics of three submodels, a domain decomposition method is designed to find the robust optimal solution that can immunize against uncertainty in our single-period inventory management problem. Finally, some computational results demonstrate the efficiency of the proposed distributionally robust fuzzy optimization method.

An integrated data-driven method using deep learning for a newsvendor problem with unobservable features

We consider a single-period inventory problem with random demand with both directly observable and unobservable features that impact the demand distribution. With the recent advances in data collection and analysis technologies, data-driven approaches to classical inventory management problems have gained traction. Specially, machine learning methods are increasingly being integrated into optimization problems. Although data-driven approaches have been developed for the newsvendor problem, they often consider learning from the available data and optimizing the system separate tasks to be performed in sequence. One of the setbacks of this approach is that in the learning phase, costly and cheap mistakes receive equal attention and, in the optimization phase, the optimizer is blind to the confidence of the learner in its estimates for different regions of the problem. To remedy this, we consider an integrated learning and optimization problem for optimizing a newsvendor’s strategy facing a complex correlated demand with additional information about the unobservable state of the system. We give an algorithm based on integrating optimization, neural networks and hidden Markov models and use numerical experiments to show the efficiency of our method. In an empirical experiment, the method outperforms the best competitor benchmark by more than 27%, on average, in terms of the system cost. We give further analyses of the performance of the method using a set of numerical experiments.

The loss-averse newsvendor problem with quantity-oriented reference point under CVaR criterion

<p style='text-indent:20px;'>This paper studies a single-period inventory problem with quantity-oriented reference point, where the newsvendor has loss-averse preferences and conditional value-at-risk (CVaR) measure is introduced to hedge against his risk. It is shown there exists a unique optimal order quantity maximizing the CVaR of utility. Moreover, it is decreasing in loss aversion level, confidence level and target unit profit, respectively. Then we establish the sufficient conditions under which the newsvendor's optimal order quantity may be larger than, equal to or less than the classical newsvendor solution. In particular, when the target unit profit is a convex combination of the maximum and minimum, the optimal order quantity is independent of price and cost parameters. Numerical experiments are conducted to illustrate our results and present some managerial insights.</p>

Modelling single-period inventory problem by distributionally robust fuzzy optimization method

Modelling single-period inventory problem by distributionally robust fuzzy optimization method

The risk averse and prudent newsboy: changes in risk and fixed costs

The classic single-period inventory problem (newsboy model) has been analysed to determine the qualitative effects of increases in the demand riskiness and of changes in fixed costs. This paper provides a sufficient condition for an increase in fixed costs to reduce orders. It has been shown that when the demand experiences a single spread around the optimal order or a restricted mean-preserving spread, the newsvendor reduces orders if he is risk averse, or prudent respectively. This paper advances such results by showing that the relation runs in both directions. That is, whenever the uncertain demand undergoes a risk increase characterised by a single spread, the newsboy will reduce orders if and only if he is risk averse; and that prudence is both necessary and sufficient condition for the newsboy to reduce orders whenever he is faced with a restricted mean-preserving spread of the random demand.

The risk averse and prudent newsboy: changes in risk and fixed costs

The classic single-period inventory problem (newsboy model) has been analysed to determine the qualitative effects of increases in the demand riskiness and of changes in fixed costs. This paper provides a sufficient condition for an increase in fixed costs to reduce orders. It has been shown that when the demand experiences a single spread around the optimal order or a restricted mean-preserving spread, the newsvendor reduces orders if he is risk averse, or prudent respectively. This paper advances such results by showing that the relation runs in both directions. That is, whenever the uncertain demand undergoes a risk increase characterised by a single spread, the newsboy will reduce orders if and only if he is risk averse; and that prudence is both necessary and sufficient condition for the newsboy to reduce orders whenever he is faced with a restricted mean-preserving spread of the random demand.

Procurement strategies with quantity-oriented reference point and loss aversion

This paper considers a single-product, single-period inventory management problem in which the retailer is loss averse with adaptive quantity-oriented reference points. The impact of the loss degree and the quantity-oriented reference point is investigated jointly on the optimal ordering quantity and the profit maximization of the retailer. It shows that there exists a unique optimal order quantity while maximizing the expected utility. The optimal solution can be readily determined via a numerical approach, and it has explicit forms for some special distribution functions. The loss-averse retailer’s order quantity is always less than loss-neutral decision maker’s when the reference dependency is under consideration. However, the optimal order quantity of the loss-averse system with quantity-oriented reference point is more than, equal to or less than that of the classical system. Furthermore, the structural properties and sensitivity analysis of the optimal solution are addressed. Several important managerial insights are presented by extensive numerical experiments, and finally, some conclusions and future work are given.

A Multiproduct Single-Period Inventory Management Problem under Variable Possibility Distributions

In multiproduct single-period inventory management problem (MSIMP), the optimal order quantity often depends on the distributions of uncertain parameters. However, the distribution information about uncertain parameters is usually partially available. To model this situation, a MSIMP is studied by credibilistic optimization method, where the uncertain demand and carbon emission are characterized by variable possibility distributions. First, the uncertain demand and carbon emission are characterized by generalized parametric interval-valued (PIV) fuzzy variables, and the analytical expressions about the mean values and second-order moments of selection variables are established. Taking second-order moment as a risk measure, a new credibilistic multiproduct single-period inventory management model is developed under mean-moment optimization criterion. Furthermore, the proposed model is converted to its equivalent deterministic model. Taking advantage of the structural characteristics of the deterministic model, a domain decomposition method is designed to find the optimal order quantities. Finally, a numerical example is provided to illustrate the efficiency of the proposed mean-moment credibilistic optimization method. The computational results demonstrate that a small perturbation of the possibility distribution can make the nominal optimal solution infeasible. In this case, the decision makers should employ the proposed credibilistic optimization method to find the optimal order quantities.

Distribution-robust single-period inventory control problem with multiple unreliable suppliers

This paper presents a distribution-robust approach to the single-period inventory control problem with multiple unreliable suppliers and stochastic demand. Using the mean and covariance that are assumed to be the only known data, the proposed approach tries to find a solution that performs well independent of the specific distributions. The approach can provide a way to effectively hedge against risks coming not just from uncertainty itself but also from inaccurate estimation. Moreover, the resulting optimization model turns out to be computationally tractable and amenable to mathematical analysis. Using the model, we provide a complete characterization of the optimal sourcing strategies when there are two suppliers: a perfectly reliable supplier and an unreliable supplier. Various interesting issues relevant to sourcing problems, including the value of supplier diversification and yield quality improvement, also are addressed.

The routed inventory pooling problem with multiple lateral transshipments

We consider a single item, single-period inventory problem with two identical retailers who can pool stocks at multiple predetermined points in time. Since routing decisions are often taken at the multi-item level in practice, we use a predetermined route for redistribution at the single-item level. The objective is to determine order-up-to levels and transshipment decisions that minimise the sum of inventory holding, backorder and fixed as well as variable transshipment costs. We present a Dynamic Programming formulation to solve the problem and we compare the performance of our routed pooling policy to situations without pooling and with complete pooling in an extensive numerical study. The results reveal when routed pooling performs well and when multiple pooling moments provide significant benefits.

A novel single-period inventory problem with uncertain random demand and its application

In many real inventory situations of short life-cycle products the decision maker often has to provide a subjective estimate of new demand distribution due to the lack of historical data. Thus, both randomness and uncertainty simultaneously appear in a single-period inventory (newsboy) problem. In this paper, we develop both single-item and multi-item single-period inventory models when market demands are assumed to be uncertain random variables. The objective of this study is to provide theoretical analysis of the models that attains optimality when demand information availability in subjective judgments leading to uncertainty along with random variation. The uncertain random models are transferred to equivalent deterministic forms by considering expected profit and providing more information of chance distributions. Finally, the numerical examples of ordering pharmaceutical reference standard materials are presented to illustrate the models.

The routed inventory pooling problem with three non-identical retailers

We consider a single period inventory problem with three non-identical retailers in which items can be pooled at a predetermined point in time. Since multiple items are often pooled with a single visit to each retailer, we use a predetermined (shortest) route for redistribution. We derive cost expressions for this routed pooling policy as well as for the no pooling and complete pooling policies, which serve as benchmarks. In a numerical investigation we analyze how much of the pooling benefits can be captured if the route for redistribution is fixed. Furthermore, we investigate how stock is distributed among retailers at the beginning of the period and we look into the influence of a retailer׳s size and position in the route on expected costs.

Research on Optimal Policy of Single-Period Inventory Management with Two Suppliers

We study a single-period inventory control problem with two independent suppliers. With the first supplier, the buyer incurs a high variable cost but negligible fixed cost; with the second supplier, the buyer incurs a lower variable cost but a positive fixed cost. At the same time, the ordering quantity is limited. We develop the optimal inventory control policy when the holding and shortage cost function is convex. We also conduct some numerical experiments to explore the effects of the fixed setup cost K and the ordering capacity Q on the optimal control policy.

(s, S) POLICY FOR UNCERTAIN SINGLE PERIOD INVENTORY PROBLEM

The traditional single period inventory problem assumes that the market demand is a random variable. However, as an empirical or subjective estimation, market demand is better to be regarded as an uncertain variable. This paper is concerning with single period inventory problem under two main assumptions that (i) the market demand is an uncertain variable and (ii) a setup cost and an initial stock exist. Under the framework of uncertainty theory, the optimal inventory policy for uncertain single period inventory problem with an initial stock and a setup cost is derived, which is of (s,S) type. Also, some expansions are obtained.

The loss-averse newsvendor problem with random yield

This paper studies a single-period inventory problem with random yield and demand, where the loss-averse preferences are adopted to describe the retailer’s (newsvendor’s) decision-making behavior. When the loss-averse retailer orders, the fraction of good units in a batch is stochastic. He will choose an order quantity to maximize his expected utility. Both shortage cost and no shortage cost are considered, respectively. The retailer’s optimal ordering policies are obtained, then the impacts of loss aversion, price and cost on the optimal order quantity are analysed. For the model without shortage cost, the loss-averse retailer’s optimal order quantity is always less than the risk-neutral retailer’s, and decreasing in the loss aversion level. While for the model with shortage cost, the loss-averse retailer’s optimal order quantity may be larger than the risk-neutral retailer’s, and increasing in the loss aversion level. Moreover, it may be decreasing in selling price and increasing in purchasing cost, which will never occur in the case of zero shortage cost. The numerical experiments are conducted to demonstrate our theoretical results.

The expectation-based loss-averse newsvendor

We modify the classic single-period inventory management problem by assuming that the newsvendor is expectation-based loss averse according to Kőszegi and Rabin (2006, 2007). We show that the expectation-based loss-averse newsvendor orders less than the profit-maximizing quantity. Moreover, the order placed by the expectation-based loss-averse newsvendor features plausible comparative statics of cost and price changes.

Single-period inventory problem under uncertain environment

This paper investigates the single period inventory Newsboy problem in a general uncertain environment. Here it is assumed that the uncertainty appears in the market demand of the product. Uncertain demand is used to describe a subjective estimate (not estimated by random/fuzzy demand), linguistically expressed by “demand is about ξ”. Using identification functions of the uncertain variable we derive the optimum order quantity and finally the expression of total expected profit for a fixed time period. The computational aspects of the model in uncertain environment and their interpretations are illustrated by some examples.

A Price-Dependent Demand Model in the Single Period Inventory System with Price Adjustment

The previous efforts toward single period inventory problem with price-dependent demand only investigate the optimal order quantity to minimize the total inventory costs; however, there is no method in the literature to avoid unwanted costs due to the deviation between the actual demand and the previously estimated demand. To fill this gap, the present paper supposes that stochastic demand rate with normal distribution is sensitive to the selling price; this means that increasing the selling price would decrease the demand rate and vice versa. After monitoring the consumption trend within a section of the period, a new selling price is implemented to change the demand rate and reduce the shortage or salvage costs at the end of the period. Three functions were suggested to represent the demand rate as a function of selling price, and the numerical analysis was implemented to solve the proposed problem. Finally, an illustrative numerical example was solved for different configurations in order to show the advantages of the proposed model. The results revealed that there is a significant improvement in the system costs when price revision is considered.