Stockout Cost Research Articles

The impacts of stockout cost on a stochastic production-inventory system in minimizing total cost conditional value-at-risk

The impacts of stockout cost on a stochastic production-inventory system in minimizing total cost conditional value-at-risk

Estimating Stockout Costs and Optimal Stockout Rates: A Case on the Management of Ugly Produce Inventory

Efficiently managing inventories requires an accurate estimation of stockout costs. This estimation is complicated by challenges in determining how to compensate consumers monetarily to ensure they will maintain the same level of utility they would have obtained had stockouts not occurred. This paper presents an analysis of these compensation costs as applied to the design of optimal stockout rates by an online retailer marketing to consumers aesthetically substandard fruits and vegetables rejected by mainstream grocery chains. Because growers face high uncertainty in their harvesting conditions and in the aesthetic quality of their crops and there are little data on hand to predict the value consumers attach to the availability of subpar produce, it is difficult to optimally match the supply of these products with consumers’ demand. Our analysis draws from a multiple discrete-continuous extreme value (MDCEV) choice model to calculate consumer compensations that the retailer can use to estimate the opportunity costs of stockouts to manage its inventory. We show that not taking into account these compensation costs could unduly inflate the optimal stockout rates for these products. Armed with these compensation cost estimates, we show how these costs can serve as incentives for retailers to source greater inventory amounts of imperfect produce from growers and how this will ultimately translate into less waste in the supply chain. This paper was accepted by Charles Corbett, operations management. Funding: Funding from Agriculture and Food Research Initiative (National Institute for Food and Agriculture, USDA) [Grant 2016-09900] is gratefully acknowledged. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.03174 .

Forecast Horizon of Dynamic Lot Sizing Problem with Perishable Inventory and Multiple Chain Stores: Shipping and Stockout Cost

Perishable products are very common, but managing inventory of perishable products can be very challenging for firms, especially in distribution systems, including multiple chain stores. In this environment, we consider a dynamic lot-sizing problem faced by a distribution center that dis-patches a single perishable product to multiple chain stores. Demand cannot be backlogged, but it does not have to be satisfied; unsatisfied demand means stockout (lost sale). The first step is to transform the total profit function into a special total cost function. Our next step is to explore the properties of the optimal solution and use them to formulate a dynamic programming algorithm to solve the problem. Furthermore, we establish forecast and decision horizon results, which help the operation manager to decide the precise forecast horizon in a rolling decision-making process. Based on the model setting and the methods of dynamic programming, we obtained two interesting findings: (1) the maximized profit objective function is equivalent to the minimized cost objective function, and (2) the famous zero inventory property conditionally holds in the inventory management of perishable products. On an extensive test bed, useful insights were obtained on the impact of the lifetime of the product and cost parameters on the total cost and length of the forecast horizon. Thus, the contributions of this study are as follows: (1) we explore two structure policies in an optimal solution to devise efficient algorithms to reduce computational complexity; (2) we provide a sufficient condition for forecasting and decision horizons; and (3) we determine that, for a given fixed cost, the median forecast horizon first increases with the lifetime of the product and stockout cost and then remains invariable when it reaches a certain level.

An EOQ Model Under the Condition of Permissible Delay in Payments with Allowed Stock-Out Cost and Lead Time

From this present study, derive the two consecutive demands between the time intervals: economic order quantity and total annual variable cost. The solution for this inventory model is optimizing the total annual variable cost. Here, given an arithmetical example and sensitivity analysis for the provision of the inventory model, assume the planning horizon and replenishment rate are infinite. To the best of our knowledge, this is the first study to find out the total annual variable cost using various costs under the condition of a permissible delay in payments with an allowed stock-out cost and lead time.

Stochastic inventory routing with dynamic demands and intra-day depletion

Businesses such as supermarkets face an inventory routing problem with distinct stochastic dynamic demand distributions for various weekdays and times of the day. Most research, however, considers aggregated per-period demand and inventory depletion, thereby oversimplifying actual events. We formulate the problem as a finite-horizon stochastic dynamic program that accounts for the dynamic demand throughout the planning horizon and within each planning period. The models include different levels of information aggregation to decide the replenishment quantities and times by dividing periods into sub-periods with distinct demand distributions. This division helps the supplier create efficient replenishment plans and account for intra-day inventory levels. The modeled characteristics include routing, holding and stock-out costs, delivery time windows, inventory and vehicle capacities, and delivery time windows. The problem is solved using an iterative lookahead algorithm with an adaptive large neighborhood search for the routing and policy learning for the replenishment decisions. Numerical evaluations show the benefit of intra-day planning, effects of instance sizes, different coefficients of variation, and holding costs compared to benchmark replenishment policies. Considering intra-day depletion and demand data for each sub-period helps achieve savings of more than 20% compared to planning for full periods. The savings are obtained by adjusting delivery quantities, incorporating intra-day consumption, creating more efficient delivery routes, and correctly timing replenishments.

Oil price uncertainty and corporate inventory investment

PurposeThis study examines the relationship between oil price uncertainty (OPU) and corporate inventory investments using a sample of 6,072 USA manufacturing firms from 1992 to 2019.Design/methodology/approachThe author's study employs a panel dataset to examine the relationship between OPU and corporate inventory investments. The author uses several alternative specifications such as fixed effects models, an instrumental variable analysis, an impact threshold for confounding variable (ITCV) analysis, alternative measures, additional control variables and the percent bias analysis to account for endogeneity issues.FindingsCorporate inventory investments decrease in response to high OPU. This decrease in inventory investments happens regardless of firms' expected stockout costs, information environment and reliance on external financing. As a potential mechanism, an uncertainty-induced increase in cash holdings contributes to this reduction in inventory investments. Also, the effect of OPU is non-linear and asymmetric. In response to the volatility of positive (negative) oil price changes, inventory investments decrease (increase) up to a certain point and increase (decrease) after that. Further, uncertainty-induced adjustments in inventory investments positively influence the operating performance of firms.Originality/valueThe author's study adds to the growing literature that examines the impact of OPU on corporate outcomes. Inventory investments directly affect business operations and could better reflect firms' responses to an uncertain environment.

Competitive strategies for two-product, multi-period stationary newsvendor problem with budget constraint

In this paper, we study a two-product, multi-period stationary newsvendor problem with budget constraint. In the problem, the inventory of each product is not allowed to be carried between one period and another. At the beginning of each period, the newsvendor has to determine the order quantities of the two products with budget constraint. We apply the weak aggregating algorithm (WAA) to study this problem. WAA, developed in the field of computer science, is a competitive online prediction method of combining expert opinions. By regarding each fixed stock level as an expert opinion and updating its weight according to the cumulative loss it achieves, we first provide an online ordering strategy to decide each period's order quantity. Furthermore, we theoretically prove that this online ordering strategy possess competitive property, i.e., the cumulative loss it achieves is as small as that achieved by the optimal expert. The salvage value and stock-out cost are further considered to obtain extended results. Finally, the numerical analysis illustrates that the online ordering strategies proposed in this paper are competitive whether with or without salvage value and stock-out cost.

A Practical End-to-End Inventory Management Model with Deep Learning

We investigate a data-driven multiperiod inventory replenishment problem with uncertain demand and vendor lead time (VLT) with accessibility to a large quantity of historical data. Different from the traditional two-step predict-then-optimize (PTO) solution framework, we propose a one-step end-to-end (E2E) framework that uses deep learning models to output the suggested replenishment amount directly from input features without any intermediate step. The E2E model is trained to capture the behavior of the optimal dynamic programming solution under historical observations without any prior assumptions on the distributions of the demand and the VLT. By conducting a series of thorough numerical experiments using real data from one of the leading e-commerce companies, we demonstrate the advantages of the proposed E2E model over conventional PTO frameworks. We also conduct a field experiment with JD.com, and the results show that our new algorithm reduces holding cost, stockout cost, total inventory cost, and turnover rate substantially compared with JD’s current practice. For the supply chain management industry, our E2E model shortens the decision process and provides an automatic inventory management solution with the possibility to generalize and scale. The concept of E2E, which uses the input information directly for the ultimate goal, can also be useful in practice for other supply chain management circumstances. This paper was accepted by Hamid Nazerzadeh, big data analytics. Funding: This research was supported by the National Key Research and Development Program of China [Grant 2018YFB1700600] and National Natural Science Foundation of China [Grants 71991462 and 91746210]. Supplemental Material: The online data are available at https://doi.org/10.1287/mnsc.2022.4564 .

The impact of buyback support on financing strategies for a capital-constrained supplier

In this paper, we investigate the optimal operational decisions and financing strategies of a supply chain with one financial-constrained supplier and one reputable retailer. In particular, two pre-shipment financing mechanisms, buyback support buyer-backed purchase order financing (BSBPOF) and buyback support advance payment discount (BSAPD), are chosen to ease the supplier's financial pressures. Both financing methods indicate that the supplier promises to buy back the unsold items after the sales season, but the difference is that the former means that the financial institution lends money to the supplier which the retailer needs to guarantee, while the latter means that the retailer pays in advance. Our research shows that: 1) the difference between the buyback price of the unsold product and its salvage value has an impact on the optimal operational decisions (such as the supplier's capacity level, the discount rate under BSAPD, and the financial institution's interest rate under BSBPOF); 2) when both financing instruments are available, if the buyback price is above a certain level and the difference between the buyback price and the salvage value is less than a certain range, the financing equilibrium is BSBPOF. Otherwise, BSAPD is preferred. Furthermore, the results provide managerial insights on how to address the operational and financing issues, and relevant conclusions are drawn by extending the model to consider stockout costs.

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.

The impact of e-marketplace on the B2b relationships

PurposeConsidering the growing momentum of online marketplaces worldwide, the purpose of this paper is to develop a model to identify the main activities impacted by the implementation of an e-marketplace in the business-to-business relationship and assess the savings on costs for the main actors involved (i.e. manufacturer, distributor and retailer).Design/methodology/approachThe methodology used in the study is a quantitative one. The analytical model used to evaluate B2b e-marketplace's impacts followed three main steps: (1) model settings and general assumptions, (2) cost structure and (3) model simulation.FindingsThe findings reveal that beyond stock-out costs and inventory levels also other operating costs (i.e. transportation, penalty and administrative costs) play a significant role in determining overall impacts of B2b e-marketplace, and as such should be considered by managers in their process of e-marketplace evaluation, selection and performance optimisation. The model shows that compared with the offline scenario the B2b e-marketplace is expected to bring value to the overall supply chain, which tends to increase as the share of e-sales penetration is increased, ranging from a cost reduction of 0.1% (€ 229.2k) in the base-case of 10% e-sales adoption, up to 0.9% (€ −2.2 M) in case of full e-marketplace adoption.Originality/valueThis study aims to shed light and foster the adoption of B2b e-marketplace by providing some practical tools to support (1) research in future studies, filling the existing gaps on the topic, and (2) managers in the process of adoption and execution of e-sales through online marketplaces.

Optimal supplier inventory control policies when buyer purchase incidence is driven by past service

A buyer exposed to a stockout may lose goodwill and be less inclined to select the same supplier in his next procurement. Reversely, an in-stock experience may restore the supplier’s prospect of being selected in the future. What should the supplier’s inventory control policy be in this situation? To address this question, we develop a multiperiod model of a buyer who selects a supplier with a probability that depends on the supplier’s rating. This rating reflects the buyer’s goodwill towards the supplier based on past service, measured in terms of in-stock/out-of-stock incidents, and is updated by the buyer after each service. The supplier’s optimal inventory policy partitions the inventory space in order-up-to and do-not-order intervals for each rating. The optimal decision depends on whether ordering reduces the supplier’s risk of being downgraded enough to offset the increase in her ordering and inventory costs. We derive and evaluate bounds on the optimal policy and expose some of its properties. We obtain conditions for the optimality of basestock policies and show that such policies are optimal if there are only two ratings or if the buyer’s demand is constant. Using our model, we impute the stockout cost in a newsvendor setting. Numerical experiments suggest that (i) the supplier may benefit from holding more inventory in intermediate than in extreme ratings, and from dealing with a buyer who responds less erratically to service, (ii) basestock policies are efficient, and (iii) using an arbitrary stockout cost in the newsvendor setting can significantly hurt profits.

Examining the balance between efficiency and resilience in closed-loop supply chains.

We study a hybrid system where the demand of customers can be satisfied by both manufacturing new products and remanufacturing used products. To manage the serviceable inventory, we implement a proportional order-up-to (POUT) replenishment policy. In this context, we first analyse the system efficiency by assessing its capacity to meet customer demand in a cost-effective manner. To this end, we consider both inventory performance (i.e., the balance between inventory holding and stock-out costs) and production smoothness (by measuring the Bullwhip effect in the supply chain). Second, we investigate the system resilience to demand volatility. In particular, we explore the impact of demand shocks on the inventory and production of the closed-loop system. Interestingly, we find that tuning the POUT controller to optimise efficiency may be problematic in terms of resilience to demand shocks. In this sense, a key trade-off exists that needs to be carefully considered by supply chain managers. Linking efficiency to resilience in such supply chains thus becomes essential to strengthen the transition towards more circular economic models. All in all, our analysis, via control-theoretic and simulation techniques, provides professionals with valuable insights into how to identify the appropriate ‘formula’ for building both efficient and resilient closed-loop supply chains.

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.

Pre-positioning strategies for relief supplies in a relief supply chain

It is vital to pre-position a certain amount of relief supplies at pre-disaster. But governments are often confronted with a dilemma of coordinating inventory cost and stock-out cost in pre-positioning relief supplies. Pre-positioning strategies for relief supplies depend on the natural characteristic of relief supplies and the most urgent needs at post-disaster. Therefore, we classify relief supplies by their natural characteristic and priority, and introduce an option contract into relief supplies pre-positioning system which consists of a single government and an agreement enterprise. Specially, a consumable and relatively urgent relief supplies pre-positioning (C-RUP) model and a non-consumable and urgent relief supplies pre-positioning (NC-UP) model are established. The optimal decisions of the government and the enterprise are derived, respectively. The relief supply chain coordination is achieved with the option contract. Under channel coordination, the two models can not only improve the government’s emergency ability and support capacity, but also reduce the government’s inventory risk when compared to the government single pre-positioning model. Moreover, we give out the conditions that the two sides can reach a win-win situation. Lastly, we propose important managerial insights for pre-positioning strategies related to different types of relief supplies.

A dynamic lot size model with perishable inventory and stockout

This research work deals with the single-item dynamic lot size problem under (i) age-dependent inventory deterioration rates and inventory costs and (ii) stockouts (or lost sales, that is, the demands do not have to be satisfied). Two equivalent forward dynamic programming (DP) algorithms are devised to solve this problem in O(T3) time based on several properties of the optimal solution, where T denotes the length of the problem horizon. Moreover, a special case with no speculative motive cost structures is investigated. Compared to the general time-variant case, two equivalent algorithms for efficient forward DP in O(T2) time are developed. Furthermore, we study the problem under storage capacity constraint and develop a forward DP algorithm to solve this problem. Finally, we offer two useful managerial insights by using a comprehensive test bed of instance: (i) the stockout policy can reduce the total costs when stockout costs are relatively small, and (ii) prolonging the product's lifetime or extending the storage capacity at great financial costs under smaller setup costs and higher holding costs for the firm is not needed.

An integrated MCGP-U and fuzzy-AHP method for enhancing the competitiveness of Taiwan’s forklift industry

The operation of small to medium-sized enterprises (SMEs) is smaller in scope and scale of business that they tend to suffer from financial crises or even bankruptcy when facing an economic downturn [1]. Thus, most research for SMEs today focuses on the formulation and practice of strategies, such as exploring the key success factors and innovation research. Taiwan’s forklift industry (TFI) belongs to SMEs that it is indispensable from construction engineering, but the related research has always been lacking to improve their competitiveness and sustainability. We refer to the relevant literature and expert opinions and use the fuzzy analytic hierarchy process (FAHP) to verify and rank the 18 factors that affect financial factors in TFI. We summarized these factors into four financial facets, including profits, workforce, holding cost, and stock-out cost. Then, the MCGP-U model is used to find the optimal solution for TFI and Komatsu Forklift Taiwan (KFT). In addition, KFT is taken as an example to ensure decision-makers (DMs) remain KFT in a better financial status and competitive advantages under uncertain business environment. As a result, the MCGP-U model optimizes the four financial facets better than by the rule of thumb in KFT, especially in the holding cost section achieving savings as high as 55.9%. Finally, the model runs fast and provides robust results, which is suitable for SMEs, given the characteristics of lacking experts and funds.

Improved MRO Inventory Management System in Oil and Gas Company: Increased Service Level and Reduced Average Inventory Investment

This study proposes a methodology for the oil and gas businesses to keep their production plant productive with a minimum investment in carrying maintenance, repair, and operating inventory planning. The goal is to assist the exploration and production companies in minimizing the investment in keeping maintenance, repair, and operating (MRO) inventory for improving production plant uptime. The MRO inventory is the most expensive asset and it requires substantial investment. It helps in keeping the oil and gas production plant productive by performing planned and unplanned maintenance activities. A (Q, r) model with a stock-out and backorder cost approach is combined with a continuous inventory review policy for the analysis of class A items of oil and gas production plant MRO inventory. The class A items are identified through popular ABC analysis based on annual dollar volume. The demand for the inventory is modeled through Poisson distribution with consideration of constant lead time. The (Q, r) model in both stock-out cost and backorder cost approaches assigned higher order frequency and lower service level to low annual demand and highly expensive items. The stock-out cost approach shows an 8.88% increase in the average service level and a 56.9% decrease in the company average inventory investment. The backorder cost approach results in a 7.77% increase in average service level and a 57% decrease in average inventory investment in contrast to the company’s existing inventory management system. The results have a direct impact on increasing plant uptime and productivity and reducing company maintenance cost through properly managing maintenance stock. The analysis is carried out on the oil and gas production plant’s MRO inventory data, but it can be applied to other companies’ inventory data as well. All the results reflected in this research are based on the inventory ordering policy of two orders per year. The inventory ordering frequency per year may be other than two orders per year depending on the type of organization.

A periodic review policy for a coordinated single vendor-multiple buyers supply chain with controllable lead time and distribution-free approach

In this paper, we study a single vendor-multiple buyer integrated inventory model with controllable lead time and backorders-lost sales mixture. Each buyer adopts a periodic review policy in which the review period is an integer fraction of the production cycle time of the vendor. To reflect the practical circumstance characterized by the lack of complete information about the demand distribution, we assume that only the first two moments of the demand during the protection interval are known. The long-run expected total cost per time unit is derived, which includes stockout costs. The problem is to determine the length of the inventory cycle of the vendor, the produce-up-to level for the vendor, the replenishment policy of each buyer, and the length of lead times that minimize the cost function under the minimax distribution-free approach. Two alternative heuristics are proposed. Numerical experiments have been carried out to investigate the performance of the heuristics and to study the sensitivity of the model.

Determination of lead time arrival of raw materials optimal vannamei shrimp at PT. XYZ Makassar

Inventory control is the efforts made by a company so that the production process can be optimally fulfilled with the smallest possible risk. The problem of raw material requirements and costs incurred for the production process is very important, because with the existence of raw materials the production process can run smoothly. This study aims to determine the amount of economical Vannamei shrimp raw material inventory and to know when the order should be done with PT. XYZ Makassar. Where the need for raw materials in 2017 was 1,855,558 kg. Therefore, companies must control the supply of raw materials that are economical and efficient in order to meet the production process for each specified period, determine the optimal waiting time for the arrival of raw materials and determine the quantity of orders that are economical. Based on the results of research determining the optimal waiting time for arrival of raw materials at PT XYZ Makassar using the Economic Order Quantity (EOQ) method, obtained an economical raw material inventory of 20,672 kg per message with a total inventory cost of Rp.136,586,577 each time message. With the Stock Out Cost (SOC) and Extra Carrying Cost (ECC) method, the optimal waiting time for arrival of raw materials is 3 days with a minimum cost of Rp. 1,836,979,830 and with the Reorder Point (ROP) method, the results of the order are made again at the level inventory in warehouse 18,555 kg.