Underage Costs Research Articles

A comparative analysis of how to handle stockout scenarios: the impact of newsvendor’s risk attitude

The purpose of this paper is to evaluate contrasting approaches for handling excess demand through the lens of a retailer (newsvendor) whose risk attitude (risk-neutral versus risk-averse) is modeled explicitly. We employ representative newsvendor models and provide comparison between two well-established stockout policies when demand exceeds supply. The “while supplies last” policy avoids the need for a secondary production order to satisfy the excess demand but faces potential opportunity cost through lost sales. Conversely, the “accepting backorders” policy relies on recourse production availability which is potentially costly but meets all levels of realized demand. Across distinct parameter classes, we incorporate comparison between the two policies in terms of financial metrics including expected profit and conditional value-at-risk criteria as well as metrics that relate to inventory availability and, hence, customer service, e.g., stockout probabilities and expected excess inventory. Powerful analytical results encompass both financial and inventory metrics and reveal that the outperforming policy is simply determined through relative underage cost values. That is, our insights indicate general advantages of accepting backorders when profit margins are sufficiently large and advantages of ignoring excess demand when profit margins are smaller. Although these extensive analytical takeaways hold in general, our numerical study reveals mean order quantity deviations (decision bias) in addition to which modeling approaches and counterpart optimal solutions maintain outperformance (resiliency) or lead to underperformance (sensitivity) when evaluated across all objective function criteria.

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.

The opportunistic newsvendor problem: Defining the optimal purchase quantity of resalable items, whose value may appreciate

With Newsvendor Problem (NvP) we refer to a specific class of inventory management problems, valid for a single item with stochastic demand over a single period. In the standard version, the newsvendor is allowed to issue a single order, before he or she can observe the actual demand. Since the newsvendor can face both overage and underage costs, due to lost sales or residual stock, the objective is to define the optimal order size that maximizes the expected profit. In this paper, we consider a specific version of the NvP, in which the buyer has the opportunity to make a last and single order for opportunistic reasons. Specifically, we consider discontinued, collectible items, for which demand will not vanish and whose value might appreciate. Hence, the objective is to define the optimal quantity that should be purchased, just before the item is retired from the market or sold-out, and that should be sold as soon as the price rises over a predefined target level. An optimal solution, maximizing the expected profit, is obtained both in case of negligible and non-negligible stockholding costs. In the latter case, to obtain the optimal solution in implicit form, some simplifying assumptions are needed. Hence, a thorough numerical analysis is finally performed, as a way to empirically demonstrate both the robustness and the accuracy of the model, in several scenarios differentiated in terms of costs and customers’ demand.

Inventory Management Practices in Private Healthcare Facilities in Nairobi County

Universal health coverage (UHC) is an integral part of the United Nations sustainable development goals. The private sector plays a prominent role in achieving UHC, being the primary source of essential medicines for many people. However, many private healthcare facilities in low‐ and middle‐income countries (LMICs) have insufficient stocks of essential medicines. Simultaneously, these same facilities carry excessive quantities of other drugs, leading to obsolescence. This suggests poor inventory control. To propose potential remedies it is vital to fully understand the underlying causes. In semi‐structured interviews with managers of private healthcare facilities in Nairobi, we asked them about their (1) inventory control systems, (2) inventory control skills, (3) time/human resource constraints, (4) budget constraints, (5) motivations for inventory control, and (6) suppliers. Our results suggest that the problems are driven by resource limitations (budget and time/human resources), managerial issues (relating to skills and systems), and market mechanisms that limit overage and underage costs. Unavailability at the supplier level and motivations for inventory control are relatively minor issues. We posit that the key causes are interlinked and stem from wider issues in the market and regulatory environment. Our results challenge prevalent beliefs about medicine supply chains in LMICs and lead to novel hypotheses. Testing these hypotheses could improve our understanding of inventory management in private healthcare facilities and aid progress in achieving UHC.

Heuristics and sensitivity analyses to guide replenishment decisions for red blood cells with random transfer

While the transfer of blood is common in practice, research addressing replenishment strategies in the context of random or unscheduled transfers is scarce and the few papers that consider ordering policies with multiple independent sources of supply offer mathematically complex solution approaches that are difficult to implement in practice. There are no simple heuristic approaches to guide ordering decisions in these situations. In this paper, we introduce two near-optimal heuristics to guide replenishment decisions for the fixed lifetime perishable inventory problem with random transfers. Much like the traditional base stock policy, the heuristics are straightforward to calculate and implement. The first heuristic (H1) employs a base stock policy using the convolution of demand and transfer distributions. The second heuristic (H2) employs a transfer adjusted base stock policy. We validate our heuristics using inventory-related cost components (i.e., order, holding, wastage, and underage costs) and demand and transfer distributions based on data provided by a large university medical center. Via simulation, we evaluate the performance of the heuristics by comparing the total costs obtained using each heuristic to the total costs obtained using the optimal ordering policy. Both heuristics perform quite well. We conduct a variety of sensitivity analyses considering the effects of different (1) levels of holding and stockout costs, as these costs are difficult to quantify and can vary dramatically, and (2) percentile transfer adjustments in H2. We observe that the H1 policy consistently results in slightly larger orders than the optimal policy, which leads to a slightly higher inventory, holding costs and wastage rates, yet slightly lower stockout costs. The H2 policy, on the other hand, consistently results in slightly smaller orders than the optimal policy, which leads to a slightly smaller inventory, lower holding costs and wastage rates, yet slightly higher stockout costs. To guide decision making, we discuss a number of management challenges that we encountered as part of this project and offer a five-step process to help decision makers with replenishment decisions.

A Study on the Optimal Inventory Allocation for Clinical Trial Supply Chains

With increasing competition in the pharmaceutical industry, pharmaceutical companies pay more attention to improving the efficiency of clinical trial supply chains to reduce the drug supplying cost, which takes up a considerable part of the total research and development expense. To improve the efficiency of clinical trial supply chains, this study investigates the inventory levels of clinical drugs in each period at a distribution center and clinics considering the reverse replenishment, transshipment, and generalized stockout cost. The inventory allocation problem in clinical trial supply chains is formulated as a rolling horizon-based two-stage stochastic mixed-integer model where the minimal operational cost constitutes the underage cost at the production planning level of clinical trial supply chains. An algorithm extending Benders decomposition is proposed as the solution approach. We also derive several structural results and develop the reformulation method and row generation strategy to improve the efficiency of the optimization process. The effectiveness of our approach is demonstrated in the numerical experiment.

Scenario-based two-stage stochastic programming for a Hybrid Manufacturing-Remanufacturing System with the uncertainty of returns, quality and demand

This paper addresses the optimization of make-to-order hybrid manufacturing - remanufacturing system to make capacity and inventory decisions jointly along with production decisions. The proposed system considers a common production facility and the same assembly/disassembly line to perform manufacturing and remanufacturing operations simultaneously. The current study takes into account an environment where new and remanufactured (reman) products competing to each other that is, the common demand stream for both products but different selling prices. Furthermore, the relative capacity consumed by remanufacturing over the manufacturing is explained in two ways, namely less capacity intensive case and more capacity intensive case. Differently, from previous studies, we consider a scenario with a discounted selling price for reman products, shortage penalty costs, lost sales, disposal and uncertainty in demand, amount and yield of returns. Hence, to handle those uncertainties, a scenario-based stochastic programming model in a two-stage setting is presented. In the first stage, the raw material inventory and production capacity levels are planned and in the second stage, the production, inventory and disposal decisions are determined by balancing overage and underage costs. The results indicate that net values associated with new and reman products can be decisive in choosing either manufacturing or remanufacturing.

The Nonstationary Newsvendor: Data-Driven Nonparametric Learning

We study a newsvendor problem with unknown demand distribution in a nonstationary demand environment over a multi-period time horizon. The demand in each period consists of a time-varying demand level and an additive random shock. Neither the demand level nor the random shock is separately observable. The amount of change in the demand level over the time horizon is measured by a cumulative variation metric. The problem has widespread applications, such as perishable inventory planning, staffing, and medical resource capacity planning in the wake of COVID-19. We design a nonparametric dynamic ordering policy, termed the moving window ordering policy, that tracks the shifts in the unknown demand level while accounting for the unobservable random demand shocks. To compute the order quantity in each period, this policy only needs the past demand observations, without any access to the underlying demand distribution. For a finite variation budget, we prove that our ordering policy is first-order optimal in the sense that its regret grows at the smallest possible rate. We also extend our analysis to the case of asymptotically large variation budgets. Through case studies based on real-life data, we show that our policy can save 20-80% of overage and underage costs, relative to policies widely used for perishable inventory replenishment and nurse staffing.

Leveraging the Newsvendor for Inventory Distribution at a Large Fashion E-Retailer With Depth and Capacity Constraints

Problem definition:We consider the problem of inventory allocation of multiple products, across a network of warehouses, faced by a large fashion e-retailer. The objective is to minimize overall shipment costs and to speed up deliveries to customers accounting for inventory constraints on products and capacity constraints of warehouses. Academic / Practical Relevance: Online retailers increasingly face the problem of optimizing inventory allocation for a wide variety of products, across a large network of warehouses. In most practical cases, demand of these products is unknown, and product level inventory available for distribution across the warehouses is very limited. Nevertheless, to the best of our knowledge, inventory allocation with both capacity and depth constraints has not been previously studied. Methodology: We formulate the inventory allocation problem as a Multi-Product, Multi-Warehouse Newsvendor (MPMWN) problem that balances overage and underage costs across products and warehouses. We then use Lagrangian duality to propose an efficient allocation algorithm (Optimal Distribution Algorithm (ODA)). ODA breaks the central MPMWN problem into two subproblems with either depth or capacity constraints. We show that these subproblems can be efficiently solved using binary search, due to the separability of the objective function and monotonicity of the constraints with respect to the dual variables. Results: Analytically, we show that the inventory allocation from the proposed algorithm converges to the optimal solution of the MPMWN problem. Furthermore, we analyze the rate of convergence of the algorithm to show fast convergence. Numerically, in collaboration with a large fashion retailer, we perform a large-scale real data study to show that the proposed algorithm, combined with a state-of-the-art demand prediction method can reduce inventory costs by as much as 7% and increase In-Class-Fulfillment (ICF) up to 10%. This improvement is also robust to changes in the demand distribution and the overage to underage cost ratio. Hence, the proposed method leads to considerable cost reduction and service improvement, both very important for the retailer. Managerial Implications: E-Retailers increasingly face the task of managing a very wide variety of products across a large network. Adding both capacity and depth constraints to the classical newsvendor problem poses computational challenges that make the current inventory optimization methods either impractical or inapplicable. We solve this problem by proposing an efficient and practical algorithm that combines transaction data for efficient inventory allocation.

Electricity supply chain coordination: Newsvendor model for optimal contract design

This paper delivers an electricity supply chain coordination framework through the newsvendor model to provide an optimal contract design with the aim of maximizing profits. Given retailers’ attitude towards the risk associated with the demand uncertainty, the framework optimally considers overage and underage costs, and discount policy to define the contract share and prices. A novel simulation-optimization approach has also been proposed to provide a global optimal solution for the model using the advantages of the linear transportation model. More analytically, the approach leads to some original and meaningful trade-offs among retailers’ and generation companies’ profits, markets share, overage and underage costs, and the all-unit discount given by retailers. By this means, an almost linear, positive relationship is found between the spot market share and the underage cost. On the contrary, retailers’ sensitivity to overage cost is greater if the share of the spot market is low and the retailer is more risk-averse. In this way, the greater the overage cost, the higher the share of the spot market. And, the lower the overage and underage costs, the greater the retailers profit, and the lower the generation companies’ profit due to the lower retailers’ order quantity. The amount of the discount has a negligible effect on retailers’ order quantity, while lowering prices. However, an increase in the amount of the discount has a negligible but negative effect on the spot market share.

The newsvendor problem: The role of prospect theory and feedback

Experimental studies on newsvendor ordering behavior offer conflicting explanations as to the cause of the deviation from the optimal risk-neutral behavior. With one exception, studies have neither explored prospect theory as possible explanations, nor investigated exactly how this prospecting behavior comes to be. We conduct two experiments and demonstrate that a newsvendor, indeed, exhibits prospecting behavior and that this behavior is triggered by the relative value of the overage and the underage costs. These relative values help create a frame of reference that puts the newsvendor in either a gain-frame or a loss-frame. When the overage cost is less than the underage cost, a newsvendor is in a loss-frame and acts in a risk-seeking manner by ordering more than the optimal, and when the overage cost is more than the underage cost, the newsvendor is in a gain-frame and acts in a risk-averse manner by ordering less than the optimal, as prospect theory suggests. We also show the newsvendor does not use mean demand anchoring with insufficient adjustment heuristic to determine either the initial or the subsequent order quantity. The newsvendor is willing to change the decision in response to changes in parameters, consistent with prospect theory. Two forms of feedback are also supplied; however, feedback does not result in improved decision-making with a commensurate reduction in either systematic bias or prospecting behavior. Surprisingly, the newsvendor becomes more risk-seeking over time rather than risk-neutral. We conclude with a discussion of our findings, managerial insights, and possible future directions.

An Empirical Analysis of Demand-Supply Mismatches in Private Healthcare Facilities in Nairobi County

Universal health coverage (UHC) is an integral part of the United Nations’ sustainable development goals. The private sector plays a prominent role in achieving UHC, being the primary source of essential medicines for many people. However, many private healthcare facilities in low- and middle-income countries (LMICs) have insufficient stocks of essential medicines. At the same time, we find that these same facilities carry excessive quantities of certain drugs, leading to losses due to obsolescence. This suggests poor inventory control. To propose potential remedies, it is key to fully understand the underlying causes. In semi- structured interviews with facility managers from private healthcare facilities in Nairobi we asked them about their 1) inventory control systems, 2) inventory control skills, 3) time/human resource constraints, 4) budget constraints, 5) motivations for inventory control, and 6) suppliers. Our results show that the problems are strongly driven by resource limitations (budget and time/human resources), managerial issues (relating to skills and systems), and market mechanisms that limit overage and underage costs. Unavailability at the supplier level, and motivations for inventory control, are only minor issues. We argue that these key causes are strongly interlinked and stem from deeper issues in the market and regulatory environment. Our results challenge several prevalent beliefs about medicine supply chains in LMICs and lead to hypotheses that require further testing. We also discuss how such testing could improve our understanding of inventory management in private healthcare facilities and aid progress in achieving UHC.

Managing premium wines using an $$(s - 1,s)$$ inventory policy: a heuristic solution approach

Operations research models are increasingly being used to support decision making in the wine industry. However, they have not yet been used to support inventory management decisions. In this paper, we develop a heuristic procedure for managing the stock of premium wines motivated by the operations of a small export-focused winery we worked with. Following an $$(s-1,s)$$ inventory policy, we assume that the decision maker aims to minimize the steady-state expected values of work in process, overage, and underage costs. The developed heuristic is as follows. First, we approximate the dynamics of the labeling process by a group scheduling policy to obtain the mean delays for each labeled product. Then, we address the problem of setting the inventory positions for the whole product portfolio by solving one newsvendor-type problem for each end-product. We provide some theoretical insights, a numerical example, and we analyze the accuracy of our procedure.

Supply Chain Contracts That Prevent Information Leakage

This paper determines categories of contracts that facilitate vertical information sharing in a supply chain while precluding horizontal information leakage among competing newsvendors. We consider a supply chain in which retailers replenish inventory from a common supplier to satisfy uncertain demand and are engaged in newsvendor competition. Each retailer has imperfect demand information. Yet one of the retailers (the incumbent) has a more accurate demand forecast than the other (the entrant). Information leakage among such competing retailers precludes vertical information sharing and is often the reason for many retailers to abandon collaborative forecast-sharing initiatives, leading to suboptimized supply chains. We show that whether a contract can prevent information leakage depends on how the inventory risk (i.e., cost of supply–demand mismatch) is allocated among the supplier and retailers in conjunction with the allocation of profits. We categorize contracts according to how they allocate inventory risk among firms when compared with a wholesale‐price contract. This comparison yields four mutually exclusive and collectively exhaustive categories of contracts. A downside-protection contract is one that effectively reduces retailers’ cost of excess inventory by shifting some of their overage cost to the supplier. Examples of such contracts include buy-back and revenue-sharing contracts. An upside-protection contract is one that effectively increases retailers’ cost of inventory shortage by shifting some of the supplier’s underage cost to retailers. Examples of such contracts include penalty and rebate contracts. A two-sided protection contract combines the properties of the previous two categories. A no-protection contract is one that fails to shift firms’ cost of inventory shortage or excess from one to the other. Examples of such contracts include wholesale-price and two-part tariff contracts. We show that no-protection contracts, which are extensively used in practice, cannot prevent information leakage, whereas others may do so. We also show that preventing information leakage could be costly for the supply chain (i.e., low channel efficiency). We conclude by illustrating how our unified framework to study a variety of contracts can enable a firm to determine the best-performing contract (among many) that precludes information leakage while almost coordinating the channel. For example, we show why buy‐back contracts perform significantly better than revenue‐sharing or rebate contracts. This paper was accepted by Serguei Netessine, operations management.

Risk premiums and certainty equivalents of loss-averse newsvendors of bounded utility

Loss-averse behavior makes the newsvendors avoid the losses more than seeking the probable gains as the losses have more psychological impact on the newsvendor than the gains. In economics and decision theory, the classical newsvendor models treat losses and gains equally likely, by disregarding the expected utility when the newsvendor is loss-averse. Moreover, the use of unbounded utility to model risk attitudes fails to explain some decision-making paradoxes. In contrast, this paper deals with the utility maximization of the newsvendor using a class of bounded utility functions to study the effect of loss aversion on the newsvendor certainty equivalents and risk premiums. New formulas are introduced to find the utility-optimal order quantity of the normal distribution. The results show that when an exponential loss aversion exists, the classical newsvendor optimal quantity serves as a lower bound when the overage costs are high and as an upper bound when the underage costs are high. In addition, we show that high loss aversion entails higher risk premiums. Similar conclusion holds when the overage/underage costs increase. Higher standard deviations, on the other hand, mean lower utility-optimal quantities and higher risk premiums. The presented formulas are advantageous in finding the optimal order quantities and risk premiums of a stochastic short-shelf life inventory when the loss is a key factor in the decision-making process.

Capacitated Supply Chain with Demand Uncertainty

Abstract We consider a manufacturer-retailer supply chain which faces a high demand uncertainty. To mitigate the overage and underage costs caused by the high demand uncertainty, an emergency order is provided by the manufacturer to the retailer. However, due to the limited capacity, the manufacturer would impose a maximum supply commitment on the emergency order. The manufacturer needs to make more initial production or reserve capacity in advance for the supply commitment for the retailer’s emergency order. We find that when the emergency order opportunity is provided, the manufacturer may be worse off although the retailer would be not.

A Meta‐Analysis of Newsvendor Experiments: Revisiting the Pull‐to‐Center Asymmetry

The field of behavioral operations has produced a rich tradition of experiments in newsvendor decision‐making. Our study provides a meta‐analysis of 24 papers in this research area; we confirm that the pull‐to‐center (PtC) effect, where average order quantities in a sample lie in between average demand and optimal order quantities, is a very stable observable phenomenon across studies. However, we also show that the asymmetry in the PtC effect between high‐margin and low‐margin conditions varies significantly from study to study; factors that allow predicting the extent and direction of the PtC asymmetry include the likelihood of obtaining losses, the way underage costs are presented to subjects, and the existence of a decision support system. We validate these factors using a controlled experiment. In conclusion, the PtC asymmetry appears less as a fundamental attribute of human behavior, but rather as a function of the design aspects of the experiment.

Data-Driven Inventory Management: Integrated Estimation and Optimization

We analyze two fundamentally different concepts to considering data for planning decisions using the example of a newsvendor problem in which observable features drive variations in demand. Our work contributes to the extant literature in two ways. First, we develop a novel joint estimation-optimization (JEO) method that adapts the random forest machine learning algorithm to integrate the two steps of traditional separated estimation and optimization (SEO) methods: estimating a model to forecast demand and, given the uncertainty of the forecasting model, determining a safety buffer. Second, we provide an analysis of the factors that drive difference in the performance of the corresponding SEO and JEO implementations. We provide the analytical and empirical results of two studies, one in a controlled simulation setting and one on a real-world data set, for our performance evaluations. We find that JEO approaches can lead to significantly better results than their SEO counterparts can when feature-dependent uncertainty is present and when the cost structure of overage and underage costs is asymmetric. However, in the examined practical settings the magnitude of these performance differences is limited because of the overlay of opposing effects that entail the properties of the remaining uncertainty and the cost structure.

Another piece of the puzzle: Firms\u2019 investment in training as production of optimal skills inventory

BackgroundBy applying the inventory theory to hiring skilled workers under uncertainty, the authors explain how firms decide on their optimum investment in an “inventory of skills.” This paper investigates the conditions under which firms are willing to make investments in a skilled workforce themselves rather than relying on skills produced within the education system or by other companies. By applying inventory theory to investments into apprenticeship training, the authors explain how firms decide on producing an optimum “inventory of skills” today to meet future demand. The authors derive hypotheses on how much firms are willing to invest in having a larger inventory of skilled workers depending on different types of inventory costs (overage costs, underage costs, demand structure).MethodsThe authors use data from the BIBB Cost–Benefit-Survey 2012/2013, which comprises detailed information on different costs and benefits of training investments from the firm’s perspective. The study applies a negative binomial estimation model.ResultsResults are threefold: firms are willing to invest in a larger inventory of skilled workers, i.e., to train more apprentices, first, if the costs of producing and retaining an excessive number of skilled workers (overage costs) are lower, second, if the costs of being short of skilled workers (underage costs) are higher, and third, given an identical cost structure, if it is more likely that the demand for skilled workers may be high in the future. Even more important is the relationship of the three: the combination of a firm’s critical ratio (underage costs in relation to overage costs) with its demand structure (industry volatility) is associated with a higher inventory of skills.ConclusionThe findings (particularly the relation of underage and overage costs, in combination with the demand structure) have important policy implications for firms’ incentives to invest in apprenticeship training.

Bullwhip and reverse bullwhip effects under the rationing game

When an unreliable supplier serves multiple retailers, the retailers may compete with each other by inflating their order quantities in order to obtain their desired allocation from the supplier, a behavior known as the rationing game. We introduce capacity information sharing and a capacity reservation mechanism in the rationing game and show that a Nash equilibrium always exists. Moreover, we provide conditions guaranteeing the existence of the reverse bullwhip effect upstream, a consequence of the disruption caused by the supplier. In contrast, we also provide conditions under which the bullwhip effect does not exist. In addition, we show that a smaller unit reservation payment leads to more bullwhip and reverse bullwhip effects, while a large unit underage cost results in a more severe bullwhip effect. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 203–216, 2017