Base-stock Policy Research Articles

Approximation Algorithms for Dynamic Inventory Management on Networks

We provide the first approximation algorithm for dynamic inventory management on a network with stochastic demand and backlogging. Specifically, under a mild cost condition, we prove the cost of a specially designed base-stock policy is less than 1.618 times the cost of an optimal policy. We develop a novel stochastic programming analysis to prove this result: We carefully calibrate two stochastic programs (providing upper and lower bounds on the optimal policy), and compare their objectives. The upper bound arises from a new class of base-stock policies we define to address the currently unresolved issue of how to assign and fulfill backlogs in a system with fulfillment flexibility. We show the optimal policy in this class takes a simple and intuitive form: backlogs are assigned to their lowest cost activities for replenishment, and the ordered resources for those activities are committed to the backlogs for fulfillment. Next, the lower bound stochastic program is derived through a novel cost accounting scheme that captures the tradeoff between current inventory decisions and future backlog decisions. We then exploit this tradeoff to bound the ratio of the two stochastic program objectives and prove our main result. We also demonstrate our policy’s practicality with numerical simulations that show it performs within 1% of optimal on average across a wide range of problem instances. Finally, we show that our techniques and results extend to more general settings, demonstrating their potential for broader applicability. Importantly, our approach extends to problems with lead times, where we prove an approximation guarantee for base-stock policies that is independent of both the lead time and network structure. Thus, our work provides the new managerial insight that properly designed base-stock policies can be effective in network settings. This paper was accepted by Victor Martínez-de-Albéniz, operations management. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.02965 .

The effect of visibility on forecast and inventory management performance during the COVID-19 pandemic

During the COVID-19 pandemic, healthcare facilities faced significant shortages of critical supplies like personal protective equipment, with dire repercussions. This study evaluates the potential role of decreased data visibility on these shortages, analysing different forecasting methods integrated with a periodic review inventory system (i.e. a base stock policy) on semi-simulated data encompassing several visibility issues. The forecasting methods chosen pertain to different data types: Holt and naïve methods are used as demand-based predictors, while a modified epidemiological model utilises pandemic data for demand forecasting. We scrutinise three prevalent data visibility issues through specifically crafted scenarios examining the effects of delayed, temporally aggregated, and erroneous data on system performance. Generally, our research illustrates that data visibility issues have a detrimental impact on the healthcare supply chain's efficacy. Interestingly, the system performance sees an uptick when these issues spur significantly oversized over-forecasts, e.g. when employing an epidemiological compartmental model for predictions.

Asymptotic optimality of base-stock policies for lost-sales inventory systems with stochastic lead times

We consider the lost-sales inventory systems with stochastic lead times and establish the asymptotic optimality of base-stock policies for such systems. Specifically, we prove that as the per-unit lost-sales penalty cost becomes large compared to the per-unit holding cost, the ratio of the optimal base-stock policy's cost to the optimal cost converges to one. Our paper provides a theoretical guarantee of the widely adopted base-stock policies in lost-sales inventory systems with stochastic lead times for the first time.

An emergency supply policy for an inventory replenishment model with returns and partial backorders

AbstractThis paper studies a continuous-review inventory replenishment model with a limited storage capacity S in an uncertain environment. We assume that the demands and returns follow independent Poisson processes. We further assume a ra1079 shelf life, a random lead time, and early loss. The storage is managed according to the base-stock (S, s) policy for $$s<S,S>0.$$ s < S , S > 0 . In case of overstock, each returned item exceeding S is transferred to a foreign facility. If during the lead time a demand reaches zero stock, we consider two alternatives: either allow partial backordering up to $$L_{B}$$ L B items, beyond which the unsatisfied demand is lost, or call for an immediate and costly emergency supply up to level $$0<Q_{B}^{e}\le S$$ 0 < Q B e ≤ S . Our objective is to study how the thresholds s, S, $$L_{B},$$ L B , and $$Q_{B}^{e}$$ Q B e are impacted by the system’s parameters, such as returns, demands, and costs. Using a Markovian framework, we derive the steady-state probabilities for the inventory level, and construct closed-form expressions for the average cost functions. Then, we numerically investigate the impact of the different parameters on the best policy and on the threshold levels. We compare the two alternatives and identify situations in which calling for an emergency supply is economically profitable.

Conditional Lead-Time Flexibility in an Assemble-to-Order System

Problem definition: We introduce and formalize a concept termed conditional lead-time flexibility (CLF), which refers to the industry practice where a manufacturer requests that its upstream suppliers dynamically adjust the pipeline orders’ remaining lead times. Over a finite horizon, an assemble-to-order manufacturer makes joint decisions on inventory replenishment and lead-time adjustment to minimize the total discounted expected cost. Methodology/results: The problem is formulated as a multiperiod dynamic programming with an enlarged state space to track the adjustable pipeline orders. The replenishment and lead-time adjustment decisions are made sequentially in each period. The analysis reveals that (i) the optimal cost-to-go function is both convex and additively separable, that (ii) both the optimal replenishment and lead-time adjustment decisions follow general base-stock policies, and that (iii) the convexity and additive separability allow us to perform a derivative analysis on the optimality equations and design an efficient algorithm. Managerial implications: Using real industry data, we numerically find that (i) CLF achieves notable cost savings over a wide range of parameters, that (ii) the value of CLF comes from both the order expediting and deferring, and that (iii) CLF outperforms dual sourcing when the unit adjustment cost is less than 40% of the unit ordering cost from the express source. Our findings underscore the importance of CLF. Funding: T. Deng acknowledges financial support from the National Key Research and Development Program of China [Grant 2022YFB3305602] and the National Natural Science Foundation of China (NSFC) [Grant 72188101]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/msom.2023.0520 .

Asymptotic Scaling of Optimal Cost and Asymptotic Optimality of Base-Stock Policy in Several Multidimensional Inventory Systems

Asymptotic Optimality of Simple Heuristic Policies for Multidimensional Inventory Systems Stochastic inventory systems with multidimensional state spaces, such as lost-sales system with positive lead time and perishable inventory system, are challenging to manage because of the curse of dimensionality, and their optimal control policies are extremely complex. In “Asymptotic Scaling of Optimal Cost and Asymptotic Optimality of Base-Stock Policy in Several Multidimensional Inventory Systems,” Bu, Gong and Chao consider three classes of such systems in the regime of large unit penalty cost, and they establish the asymptotic optimality of (modified) simple base-stock policies as well as an explicit expression for the optimal cost rate in each of these systems. These results justify the applications of such policies in real-world applications, and they are achieved by constructing tight newsvendor upper and lower bounds on the systems’ costs and analyzing the asymptotic scaling of newsvendor costs with large unit penalty cost. This approach is expected to be useful in studying other multidimensional stochastic inventory systems.

Reduced food waste through inventory control despite throwing out food before expiration: Online vs. offline retail

Online retailers throw out food that has not yet expired. This gives rise to the question whether online retailers generate more food waste than offline retailers, who typically throw out food only after it has expired. We focus on the food waste at the retailer which inherently ensues from the logistical set-up. We provide a theoretical discussion of the potential increase in food waste as a result of the inventory control policy and throwing out food that has not yet expired, as is the case for online retailers. Note that the online retailer has some advantages over offline retailers as well. Online retailers benefit from full control of order picking, which is instead often done by the consumer in offline retail. Moreover, the online retailer often benefits from the pooling effect, as offline retailers might use multiple stores to satisfy the same demand volume as an online retailer from a single warehouse. Our numerical experiments with a base-stock policy suggests that online retail actually yields less food waste for many products, despite throwing out food before expiration.

Exact evaluation and optimization of integer-ratio policies for stochastic one-warehouse multiple-retailer inventory systems

This paper considers one-warehouse multiple-retailer inventory systems. The retailers are non-identical and face Poisson demand processes. We consider an integer-ratio policy in which each retailer orders in a fixed interval that is either an integer or integer-ratio multiple of the warehouse's reorder interval. Base-stock policy and virtual allocation are assumed. We show that cost evaluations at the retailers are completely separable, leading to a simple approach to develop an optimal integer-ratio policy for a two-level distribution system with heterogeneous retailers.

A Bi-Objective Inventory Model for Strategic Items in a Stochastic Environment with Partial Shortage: A Base-Stock Approach

This paper suggests an ordering policy for strategic items. Based on the base stock policy, we modeled a bi-objective, multi-product inventory control system with partial back-ordering. The model aims to minimize total costs and maximize the average service level, considering stochastic constraints such as storage space, maximum allowable shortage, and maximum allowable lost sales to match real-world conditions. We used three Multi-Objective Decision-Making methods, namely Individual optimization, Desirability function, and Goal attainment, to solve the problem. TOPSIS method showed the Goal attainment method’s superiority over the others. The sensitivity analysis revealed that the mean of storage space had the most significant impact on objective functions. Also, increasing the back-order percentage can reduce the system’s total costs.

Projected Inventory-Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

Inventory Projection and Asymptotic Optimality van Jaarsveld and Arts propose a new policy for the canonical periodic review lost sales inventory problem. Under this policy, orders are placed in each period such that the expected inventory level at the moment of replenishment order arrival is at a fixed level. This single-parameter policy is called the projected inventory-level (PIL) policy. The PIL inherits asymptotic optimality properties from the constant-order policy for long lead time and from the base-stock policy when the cost of losing a sale is large. The PIL policy has lower cost than competing heuristics in a numerical study. The PIL seems to be a promising approach for other inventory systems with a high-dimensional state space, such as the perishable item inventory management problem.

The Proactive Base Stock Policy for Condition Based Maintenance

This paper introduces the proactive base stock policy (ProBSP) that incorporates degradation data into spare parts decision-making processes. The proposed policy aims to anticipate the demand for spare parts by proactively ordering them, instead of ordering each time one is needed. ProBSP involves two decision variables: the initial stock level and the degradation order threshold. To determine the optimal values for these variables, a simulation-based optimization method is developed. More precisely, a discrete event simulation is constructed to evaluate a single point in the parameter space, and an intelligent algorithm is employed to search for the optimal solution by efficiently exploring the solution space, thereby exploiting structural properties of ProBSP. Finally, numerical experiments are conducted to gain insights into the performance of ProBSP. These experiments reveal the effectiveness of ProBSP: the average spare parts stock level is reduced by 68%, with reductions exceeding 90% in specific scenarios.

UCB-Type Learning Algorithms with Kaplan–Meier Estimator for Lost-Sales Inventory Models with Lead Times

Efficient Learning Algorithms for the Best Capped Base-Stock Policy in Lost Sales Inventory Systems Periodic review, lost sales inventory systems with lead times are notoriously challenging to optimize. Recently, the capped base-stock policy, which places orders to bring the inventory position up to the order-up-to level subject to the order cap, has demonstrated exceptional performance. In the paper “UCB-Type Learning Algorithms with Kaplan–Meier Estimator for Lost Sales Inventory Models with Lead Times,” Lyu, Zhang, and Xin propose an upper confidence bound–type learning framework. This framework, which incorporates simulations with the Kaplan–Meier estimator, works with censored demand observations. It can be applied to determine the optimal capped base-stock policy with a tight regret with respect to the planning horizon and the optimal base-stock policy with a regret that matches the best existing result. Both theoretical analysis and extensive numerical experiments demonstrate the effectiveness of the proposed learning framework.

Single-Product Assemble-to-Order Systems with Exogenous Lead Times

Efficient Algorithm for Base Stock Policy Optimization in Single-Product Assemble-to-Order Systems with Stochastic Lead Times Single-product assemble-to-order systems can be commonly observed in industrial settings. For example, firms targeting a niche market often choose to offer a single product; moreover, sole-product rollout is usually a preferable business strategy for manufacturers promoting a brand-new product or trying to penetrate a new market. However, maintaining an effective inventory management for those systems is a notoriously difficult problem, especially when the order lead times exhibit stochastic patterns. In “Single-Product Assemble-to-Order Systems with Exogenous Lead Times,” Muharremoglu, Yang, and Geng investigate the case with a special type of stochastic lead time and utilize a certain analysis technique to develop an efficient algorithm for the performance evaluation of base stock policies. In addition, efficiently computable upper and lower bounds are proved based on the key idea of the algorithm. Extensive numerical studies show that the heuristics and the approximation methods developed from those bounds perform well in base stock optimization.

Joint Discount and Replenishment Parametric Policies for Perishable Products

We consider a joint discount and replenishment problem in a discrete periodic review fashion for the sale of a perishable product, characterized by limited deterministic shelf life, replenishment lead times, and stochastic demand. Customers decide what to buy according to a linear discrete choice model, balancing price and perceived quality, uniquely determined by the residual shelf life. The decisions we consider are: How many new items to order, the age of the items to be discounted, and how much discount to offer. In this context, we compare a set of policies mixing the constant order policy and the base stock one with some easy discounting policies, optimizing their parameters using a simulation-based optimization framework. To evaluate their performance in terms of revenue and quantity of scraped items, we consider four realistic instances for a grocery retailer characterized by products of different shelf life and variance of demand. Experiments show that best results are achieved by a base stock policy that discounts products of different ages based on a threshold: If the quantity of the inventory of a given age is greater than a threshold it applies a discount, otherwise no discount is proposed. In the presented configurations, this policy increases the average reward compared to policies that do not discount.

On the value of multi-echelon inventory management strategies for perishable items with on-/off-line channels

The progress of digitization makes the integration of online and offline sales channels increasingly necessary for retailers. Multichannel and omnichannel multi-echelon networks are gradually more common in responding to customer demands, but their complexity makes the optimization of replenishment and item allocation policies among different channels challenging, especially if products have a short shelf life, as in the case of food retailers, where customer behavior (e.g., first-/last- in-first-out selection) also plays a role. It is not always possible to solve this problem exactly and heuristics are required. We propose a dynamic model and jointly optimize allocation and replenishment policies in the case of perishable goods with stochastic demand, uncertainty in customer selection preferences, and fixed lead times. We study complexity and structure of optimal policies. Furthermore, we explore several intuitive generalizations of base-stock policies over multi-echelon networks, analyzing the effect that potential correlations and imbalances in demand volumes across channels generate on the heuristics and identifying the pros and cons of such solutions. Results show that inventory-pooling effects in multi-echelon models for perishable items are often combined with the allocation of fresher products to offline channels. Generalizations of the well-known constant-order or base-stock policies can be a viable solution that generates benefits and increases system flexibility. They advantageously leverage negative channel correlation, but in the case of unbalanced demand distributions, increased offline demand can impoverish the quality of some heuristics.

Dual sourcing under non-stationary demand and partial observability

We study dual sourcing under stochastic and non-stationary demand. The non-stationarity is modeled through Markov-modulated changes in the underlying demand distribution. The actual demand distribution is not observed directly, yet demand observations reveal partial information about it. We propose a policy where a pre-committed base order from the slow source is complemented with flexible short-term orders from both the fast and slow source. The pre-committed order is cheaper, while flexible orders can be adjusted to the actual inventory needs and the non-stationary demand. By formulating the problem as a partially observable Markov decision process, we show that the optimal flexible orders follow an adaptive dual base-stock policy when the lead time difference between both sources is one period. A numerical validation study reveals how flexible slow source orders reduce the share of expensive orders from the fast source compared to a conventional tailored base-surge policy. In addition, our policy’s ability to adapt decisions to partial information allows for a more effective use of flexible orders. Our findings show the value of incorporating partial information to deal with the non-stationary demand and adding the flexible slow-sourcing option to create a more resilient replenishment policy.

Performance evaluation of a two-echelon inventory system with network lost sales

Inventory systems are largely analyzed in the literature under the common assumption of backorders due to the complexity of lost sales. In this paper, we consider a two-echelon inventory system composed of a central warehouse and multiple local warehouses subject to lost sales. The demand faced by each local warehouse is a Poisson process and the stock in the warehouses is controlled according to a continuous review base-stock policy. This system has been analyzed in the literature under deterministic or exponential lead-times at the central warehouse, deterministic lead times at the local warehouses and approximate performance evaluations have been proposed for two cases: (1) the demand is lost if no items are available in the local warehouse, the central warehouse, or in the pipeline in between (i.e., a waiting time threshold for incoming demand equal to the local warehouse lead time), and (2) when there is a waiting time threshold less than the local warehouse lead time. Based on a queuing network representation of the system, we extend the performance analysis of the system in the first case by considering generally distributed lead times both at the central and local warehouses and by providing the exact closed-form expressions for the inventory performance measures. In the second case, we provide new approximate solutions under generally distributed lead times at the central warehouse. We numerically show that our exact and approximate solutions perform equally or better than those presented in the literature under deterministic lead times.

A periodic review inventory model facing different disruption profiles

We study a periodic review inventory system with alternations of periods with supply availability and unavailability. The system is controlled by a periodic review base stock policy (S,T). While periodic review inventory models have been studied assuming supply disruption, they mainly invoke the limiting disruption probabilities overlooking that these probabilities may correspond to different disruption profiles (ranging from rare-long disruptions to frequent-short ones). In this context, we use a continuous-time Markov chain (CTMC), in order to formulate a periodic review inventory model that can distinguish the different disruption profiles. Through theoretical results, we determine the policy variables (order-up-to level and review interval) that minimize the long-run average cost. We show that when the disruption profile is considered, the optimal order-up-to level, although Newsvendor-styled form, is not always linear in the review interval. We present analytical properties demonstrating the impact of the different disruption profiles (under the same limiting disruption probability) and the impact of the limiting probability on the optimal policy. Furthermore, we propose an approximation to obtain a closed-form (near-)optimal solution for the review interval. Finally, numerical comparisons highlight the impact on system's cost performance of deploying approaches that either use the above mentioned closed-form solution for the review interval or the limiting disruption probabilities instead of the time dependent ones in the cost formulation.

EOQ with supply disruptions under different advance information regimes

In this paper, we consider the impact of advanced delivery information on the performance of supply chains facing endogenous disruptions. We study a single-echelon EOQ-based inventory model with backorders where the supplier could fail to deliver shipments on time following a Bernoulli process, a measure of the supplier service quality. Two extreme advance information regimes are analyzed: (1) full delivery information (FDI), where the timing of the next delivery is always known, and (2) partial delivery information (PDI), where the timing of the next delivery is known if it coincides with the next planned delivery. For both regimes, we use a natural adaptation of the base-stock policy, having multiple order up-to levels, each corresponding to the level of available information when ordering. We then model the long-run average cost and determine the policy variables that minimize this cost. While the analysis of the FDI model proved straightforward, the PDI model involved the solution of a mixed-integer nonlinear optimization problem. We found closed-form solutions for both models. Numerical results show that, by reducing planning uncertainty, advanced information directly reduces operating costs. They also show that the cost of the case of full information is higher than that of the EOQ model, suggesting the importance of finding reliable suppliers for disruption-free operations.

Optimizing pricing and inventory strategies for dietary supplement production under stochastic demand

PurposeThe increasing popularity of ERP solutions has provided dietary supplement manufacturing companies with modules to manage pricing and inventory. However, the decisions made by these modules are often independent and rely on deterministic forecasts. This paper studies a multi-product dietary supplement manufacturing system under stochastic demands. The purpose is to maximize the long-run expected profit by jointly considering pricing and inventory strategies.Design/methodology/approachThe authors investigate both the general cases and three special cases including stable demand, negligible backlog and instantaneous replenishment. A two-stage algorithm named PAS is proposed. In the strategy construction stage, the constructed objective bounds are combined to provide estimates which then help to derive the optimal product prices. In the system operation stage, replenishment decisions are further made based on the prices generated from the previous stage.FindingsIt is proved that base-stock policy is optimal for the studied system, and the optimal based-stock level is provided. The global optimal strategies are obtained for three important special cases. For the general case, theoretical objective bounds are established. These bounds provide quick and reliable performance estimates for practical applications.Originality/valueVery few studies have jointly considered pricing and inventory strategies with uncertainty demands in the dietary supplement industry. The PAS algorithm developed integrates these decisions and consistently generates high-quality solutions even under highly varying demands. Such algorithm could be a valuable add-on to the pricing and inventory management modules in ERP systems.