Stochastic Inventory Control Research Articles

Stochastic inventory control models for single item replenishment with variable demand under constrained and unconstrained conditions

Stochastic inventory control models for single item replenishment with variable demand under constrained and unconstrained conditions

Error Propagation in Asymptotic Analysis of the Data-Driven (s, S) Inventory Policy

Estimating Optimal Inventory Policies: Moving Beyond SAA and Empirical Process Theory In “Error Propagation in Asymptotic Analysis of the Data-Driven (s,S) Inventory Policy,” Zhang, Ye, and Haskell dive into the class multiperiod stochastic inventory control in a data-driven setting. They investigate the statistical properties of the data-driven $(s, S)$-policy obtained by recursively computing the empirical cost-to-go functions. In this setting, the empirical cost-to-go functions for the estimated parameters are not i.i.d. sums because of the error propagation. They establish a novel asymptotic representation for multi-sample $U$-processes in terms of i.i.d. sums. This representation enables them to apply empirical process theory to derive the influence functions of the estimated parameters and to establish joint asymptotic normality. Based on these results, they also propose an entirely data-driven estimator of the optimal expected cost and derive its asymptotic distribution. They demonstrate some useful applications of their asymptotic results, including sample size determination and interval estimation.

Multi-objective continuous review inventory policy using MOPSO and TOPSIS methods

In the dynamic business environment of today, decision-making involves considering various conflicting aspects. Inventory planning problems aim to determine how much and when to order products to satisfy customer demand at the lowest possible cost while maintaining a desirable service level. These problems can be formulated as a MOPSO algorithm, which is used to handle multiple objectives in a continuous review stochastic inventory control system (r, Q). Unfortunately, most multi-objective inventory models have been solved by aggregating objectives using specific weights or by optimizing only one objective and treating the others as constraints. Considering the complexity of real-world inventory control problems, which involves conflicting objectives such as minimizing cost and maximizing service level, the need arises to employ more precise optimizers that can generate better and more diverse non-dominated solutions of reorder point and order size system. In this paper multi-criteria decision-making framework that combines MOPSO algorithm and TOPSIS method to generate a Pareto front of non-dominated solutions and rank them based on decision makers' preferences. Initially, the original MOPSO is applied to the multi-objective inventory control problem, and then the mutation operator is integrated into the MOPSO to maintain diversity in the swarm and explore the entire search space. Next, the leader selection strategy called the geographically-based system (Grids) is replaced by the crowding distance factor to choose the global optimal particle as a leader. Additionally, the ε-dominance concept is employed to limit the archive size and maintain more diversity and convergence in the MOPSO for optimizing the inventory control problem. In conclusion, this work not only pioneers a cutting-edge approach to multi objective inventory control but also underscores its practical value. By facilitating the generation of superior solutions that cater to diverse decision-maker preferences, our methodology resonates deeply with real-world challenges and sets a new benchmark for effective inventory planning.

Inventory Management with Advance Booking Information: The Case of Surgical Supplies and Elective Surgeries

Problem definition: Medical operations require a large volume and variety of consumable supplies that are kept in hospital inventory and replenished on a regular basis. Stringent requirements on the availability of these supplies, together with high variability in their daily usage, contribute to the high inventory costs of the surgical departments in hospitals. We investigate the value of utilizing Advance Booking Information (ABI) on elective surgeries—which are often booked up to months in advance—in reducing inventory costs. Methodology/results: We study a single-item, periodic-review, stochastic inventory control problem, where the item demand in each period is driven by the number and type of surgeries requiring the item, and with the available information on elective surgeries integrated into the ordering decisions. Given that item usage from each case is uncertain and only realized after the surgery, ABI provides imperfect information on future demand. Through exact analysis of a simplified version of the problem, as well as extensive numerical experiments using synthetic and real data, enabled using a state aggregation technique, we provide insights on and quantify the value of using ABI as a function of the number of periods of ABI integrated into the ordering decisions. We identify a relevant parameter regime—namely, high backlog (relative to holding) costs and when surgeries are booked sufficiently in advance—where the value of using ABI could be significant and the majority of the benefits can be gained through incorporating only one period of ABI beyond the order lead time. In a case study conducted using real data, we observe up to 26% reduction in average inventory levels, without violating the service levels. Managerial implications: By incorporating readily available elective surgery schedules into replenishment decisions of surgical supplies, hospitals could significantly reduce inventory costs without compromising the availability of the supplies. Funding: This work was partially funded by The Ontario Ministry of Government and Consumer Services (MGCS). The views expressed in the paper are the views of the authors and do not necessarily reflect those of the Province. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2021.0063 .

AI vs. Human Buyers: A Study of Alibaba’s Inventory Replenishment System

Inventory management is one of the most important components of Alibaba’s business. Traditionally, human buyers make replenishment decisions: although artificial intelligence (AI) algorithms make recommendations, human buyers can choose to ignore these recommendations and make their own decisions. The company has been exploring a new replenishment system in which algorithmic recommendations are final. The algorithms combine state-of-the-art deep reinforcement learning techniques with the framework of fictitious play. By learning the supplier’s behavior, we are able to address the important issues of lead time and fill rate on order quantity, which have been ignored in the extant literature of stochastic inventory control. We present evidence that our algorithms outperform human buyers in terms of reducing out-of-stock rates and inventory levels. More interestingly, we have seen additional benefits amid the pandemic. Over the last two years, cities in China partially and intermittently locked down to mitigate COVID-19 outbreaks. We have observed panic buying from human buyers during lockdowns, leading to the bullwhip effect. By contrast, panic buying and the bullwhip effect can be mitigated using our algorithms due to their ability to recognize changes in the supplier’s behavior during lockdowns. History: This paper has been accepted for the INFORMS Journal on Applied Analytics Special Issue—2022 Daniel H. Wagner Prize for Excellence in the Practice of Advanced Analytics and Operations Research.

Constrained Stochastic Inventory Control Models for Multi-Item with Variable Demand

Constrained multi-item inventory system with variable demands are considered. The demand rates of five selected multi-item - Cowbell, Milo, SMA, Cerelac and Golden Morn were modeled as Weibull, Normal and Lognormal probability distributions respectively with the aid of chi-squared multinomial goodness-of-fit test. The respective probability distributions with estimated location parameters: 491.55, 536.92, 10.5, 2.1926 and 5.3103 were used as the basis of probabilistic inventory models to obtain dynamic EOQ for each item under each constraint subject to Kuhn, Karush and Tucker (KKT) conditions as against the use of simple averages in deterministic inventory models. The optimal values of these constraints: available warehouse space (124sq.ft), specified level of inventory (94 units), limited capital (76,671.52 naira) and number of orders (1/month) were obtained using the optimal EOQ values to establish optimal inventory level and constraints level/capacity for each item in order to avoid shortage or excess stock.

The use of parametric programming and simulation-optimisation approaches for stochastic inventory control in the food markets under fuzzy deterioration rate

In this study, we address the stochastic inventory control problem of green vegetables deteriorating in a fruit and vegetable wholesaler. The problem is to re-order green vegetables periodically to meet demand of the green markets. The aim is to decide the order quantity and the order-up-to level for each period minimising the total inventory cost. In the fruit and vegetable wholesaler, a staff separates the fresh and non-fresh products to sustain freshness in the green vegetable crates. The behaviour of the wholesaler staff on selecting the non-fresh green vegetables is personal reasoning that fuzzy logic can help to deal with the uncertainty. Accordingly, we introduce a stochastic integer linear programming model accounting for the uncertain demand. We represent the deterioration rate indicated in the model by fuzzy numbers and transform the resulting fuzzy model into an α-parametric programming model. As a solution method, we propose a simulated annealing based simulation-optimisation algorithm. The models and the heuristic algorithm are applied to a case study that reflects the real settings of a food market in Turkey. The numerical analysis is conducted on the case study to understand the effect of the fuzziness on the solution quality and time under varying cost parameters and deterioration rates. As a result, the numerical analyses demonstrate that the proposed models allow us better to estimate the total costs and the waste quantity. The heuristic algorithm yields near-optimal solutions. The solutions approach approximately 3% difference on average for the medium and long term decisions. The heuristic algorithm results in significantly shorter computation times compared to the proposed model.

Discrete Convex Analysis and Its Applications in Operations: A Survey

Discrete convexity, in particular, [Formula: see text]‐convexity and [Formula: see text]‐convexity, provides a critical opening to attack several classical problems in inventory theory, as well as many other operations problems that arise from more recent practices, for instance, appointment scheduling and bike sharing. As a powerful framework, discrete convex analysis is becoming increasingly popular in the literature. This review will survey the landscape of the approach. We start by introducing several key concepts, namely, [Formula: see text]‐convexity and [Formula: see text]‐convexity and their variants, followed by a discussion of some fundamental properties that are most useful for studying operations models. We then illustrate various applications of these concepts and properties. Examples include network flow problem, stochastic inventory control, appointment scheduling, game theory, portfolio contract, discrete choice model, and bike sharing. We focus our discussion on demonstrating how discrete convex analysis can shed new insights on existing problems, and/or bring about much more simpler analyses and algorithm developments than previous methods in the literature. We also present several results and analyses that are new to the literature.

Forecast Methods and Periodic Review Inventory Model for Supply Planning to Reduce Food Waste

Food waste is an important economic and resource problem in all countries around the world. Particularly, the restaurant sector highly contributes to food waste and limited efforts or studies have been performed to overcome this problem. In this context, the present study addresses an alternative to improve the supply planning for perishable products in the restaurant sector through the application of specific forecasting methods and a stochastic inventory control model. For this purpose, a real enterprise within this economic sector was considered. Our findings support that monthly forecasts can be more appropriate for accurate demand estimation and supply planning of perishable products, which is important to reduce unnecessary products. Also, the periodic review inventory control model can lead to a more appropriate supply scheme to reduce the waste of surplus food. These findings and the proposed techniques can be used for other economic entities to reduce product waste due to poor supply planning.

Computing optimal ([formula omitted]) policy parameters by a hybrid of branch-and-bound and stochastic dynamic programming

A well-known control policy in stochastic inventory control is the (R,s,S) policy, in which inventory is raised to an order-up-to-level S at a review instant R whenever it falls below reorder-level s. To date, little or no work has been devoted to developing approaches for computing (R,s,S) policy parameters. In this work, we introduce a hybrid approach that exploits tree search to compute optimal replenishment cycles, and stochastic dynamic programming to compute (s,S) levels for a given cycle. Up to 99.8% of the search tree is pruned by a branch-and-bound technique with bounds generated by dynamic programming. A numerical study shows that the method can solve instances of realistic size in a reasonable time.

Resilience toward supply disruptions: A stochastic inventory control model with partial backordering under the base stock policy

This paper examines supply-side disruptions using an inventory management framework to gain insights into the economic performance of buyers who use two conventional costing strategies – end-of-cycle and continuous. The proposed model assumes that a single supplier faces full disruptions with a probability, and therefore, fails to procure all the items ordered. Accordingly, the buyer experiences unmet demand, which is assumed to be partially backordered. To make proper replenishment decisions, two base stock (S,T) periodic review optimization models are developed. The objective functions minimize the expected long-run total costs (i.e., ordering, holding, and shortage). After proving their convexity and obtaining the optimal decisions, computational experiments were carried out to investigate the impacts of the change in parameters. The results highlight the importance of selecting a suitable ratio for backorders during supply disruptions, as it leads to lower costs and reduces the inventory obsolescence and overstocking risks. Moreover, the managerial insights derived from this study aid retailers to make better replenishment decisions (in terms of level and frequency) and to be more resilient in times of disruptions. Retailers can benefit from the provided solution algorithm as a computational application.

On the numerical solution of separable stochastic inventory control problems

Separable stochastic inventory control problems and stochastic quasigradient methods for solving stochastic optimization problems are considered in this paper. Polynomial algorithms are proposed for numerical implementation of projection operation of the current iterate, obtained by the stochastic quasigradient methods, on feasible regions of some inventory control problems. Availability of such efficient algorithms is important because the projection operation is implemented at each iteration of stochastic quasigradient methods. It is proved that the suggested algorithms are convergent, and results of computational experiments are presented.

Provably Near-Optimal Approximation Schemes for Implicit Stochastic and Sample-Based Dynamic Programs

In this paper, we address two models of nondeterministic discrete time finite-horizon dynamic programs (DPs): implicit stochastic DPs (the information about the random events is given by value oracles to their cumulative distribution functions) and sample-based DPs (the information about the random events is deduced by drawing random samples). Such data-driven models frequently appear in practice, where the cumulative distribution functions of the underlying random variables are either unavailable or too complicated to work with. In both models, the single-period cost functions are accessed via value oracle calls and assumed to possess either monotone or convex structure. We develop the first near-optimal relative approximation schemes for each of the two models. Applications in stochastic inventory control (that is, several variants of the so-called newsvendor problem) are discussed in detail. Our results are achieved by a combination of Bellman equation calculations, density estimation results, and extensions of the technique of K-approximation sets and functions introduced by Halman et al. (2009) [Halman N, Klabjan D, Mostagir M, Orlin J, Simchi-Levi D (2009) A fully polynomial time approximation scheme for single-item stochastic inventory control with discrete demand. Math. Oper. Res. 34(3):674–685.].

Optimal Periodic Replenishment Policies for Spectrally Positive Lévy Demand Processes

We consider a version of the stochastic inventory control problem for a spectrally positive Lévy demand process, in which the inventory can only be replenished at independent exponential times. We show the optimality of a periodic barrier replenishment policy that restocks any shortage below a certain threshold at each replenishment opportunity. The optimal policies and value functions are concisely written in terms of the scale functions. Numerical results are also provided.

Simulation-Optimisation Approach to Stochastic Inventory Control with Perishability

In order to tailor inventory control to urgent needs of grocery retail, the discrete-event simulation model with realistic perishability mechanics is proposed in the paper. The model is stochastic and operates with multiple products under constrained total inventory capacity. Besides, the model under consideration is distinguished by quantity discount, uncertain replenishment lags and lost sales. The paper presents both mathematical description and algorithmic implementation. An optimisation framework based on a genetic algorithm is also proposed for deriving an optimal control policy. The proposed approach contributes to the field of industrial engineering by providing a simple and flexible way to compute nearly-optimal inventory control parameters.

Discrete Convex Analysis and Its Applications in Operations: A Survey

Discrete convexity, in particular, L-natural-convexity and M-natural-convexity, provides a critical opening to attack several classical problems in inventory theory, as well as many other operations problems that arise from more recent practices, for instance, appointment scheduling and bike-sharing. As a powerful framework, discrete convex analysis is becoming increasingly popular in the literature. This review will survey the landscape of the approach. We start by introducing several key concepts, namely, L-natural-convexity and M-natural-convexity and their variants, followed by a discussion of some fundamental properties that are most useful for studying operations models. We then illustrate various applications of these concepts and properties. Examples include network flow problem, stochastic inventory control, appointment scheduling, game theory, portfolio contract, discrete choice model, and bike-sharing. We focus our discussion on demonstrating how discrete convex analysis can shed new insights on existing problems, and/or bring about much simpler analyses and algorithm developments than previous methods in the literature. We also present several results and analyses that are new to the literature.

A centralized stochastic inventory control model for perishable products considering age-dependent purchase price and lead time

In this paper, we present a stochastic multi-period multi-echelon $$ \left( {s, S} \right) $$ periodic inventory control model for perishable products in a healthcare environment. We consider age-dependent purchase price, order lead time, and allow for backorder. The model is inspired by a real case where a regional health system operates multiple hospitals in addition to managing a central warehouse. The warehouse centralizes the purchasing of the products and then distributes them among hospitals while demand for products in each hospital is uncertain. We formulate the problem as a stochastic mixed-integer linear programming model and study two purchasing strategies. The first and traditional strategy assumes that the warehouse only orders fresh products, i.e., products with the latest expiry date and most expensive, referred to as purchasing constant remaining life (CRL). The second strategy considers a discount function with a lower purchase price for products with a shorter remaining life, referred to as different remaining life (DRL). The designed models are naturally complex and intractable to obtain optimal solutions by an analytical approach for large instances of the problem. Thus, we developed a genetic algorithm to solve the problem and benchmarked its performance against an exact method. We also verified the results of the stochastic models through simulation. Extensive sensitivity analysis is also conducted to investigate the behaviors of both CRL and DRL strategies about the risk of product shortage, product expiration and the total cost imposed on the system.

The benefit of receding horizon control: Near-optimal policies for stochastic inventory control

In this paper we address the single-item, single-stocking point, non-stationary stochastic lot-sizing problem under backorder costs. It is well known that the (s, S) policy provides the optimal control for such inventory systems. However the computational difficulties and the nervousness inherent in (s, S) paved the way for the development of various near-optimal inventory control policies. We provide a systematic comparison of these policies and present their expected cost performances. We further show that when these policies are used in a receding horizon framework the cost performances improve considerably and differences among policies become insignificant.

Metamodelling of Inventory-Control Simulations Based on a Multilayer Perceptron

Abstract Inventory control problems arise in various industries, and each single real-world inventory is replete with non-standard factors and subtleties. Practical stochastic inventory control problems are often analytically intractable, because of their complexity. In this regard, simulation-optimization is becoming more and more popular tool for solving complicated business-driven problems. Unfortunately, simulation, especially detailed, is both time and memory consuming. In the light of this fact, it may be more reasonable to use an alternative cheaper-to-compute metamodel, which is specifically designed in order to approximate an original simulation. In this research we discus metamodelling of stochastic multiproduct inventory control system with perishable products using a multilayer perceptron with a rectified linear unit as an activation function.

Sampling-Based Approximation Schemes for Capacitated Stochastic Inventory Control Models

We study the classical multiperiod capacitated stochastic inventory control problems in a data-driven setting. Instead of assuming full knowledge of the demand distributions, we assume that the demand distributions can only be accessed through drawing random samples. Such data-driven models are ubiquitous in practice, where the cumulative distribution functions of the underlying random demand are either unavailable or too complex to work with. We consider the sample average approximation (SAA) method for the problem and establish an upper bound on the number of samples needed for the SAA method to achieve a near-optimal expected cost, under any level of required accuracy and prespecified confidence probability. The sample bound is polynomial in the number of time periods as well as the confidence and accuracy parameters. Moreover, the bound is independent of the underlying demand distributions. However, the SAA requires solving the SAA problem, which is #P-hard. Thus, motivated by the SAA analysis, we propose a polynomial time approximation scheme that also uses polynomially many samples. Finally, we establish a lower bound on the number of samples required to solve this data-driven newsvendor problem to near-optimality.