Inventory Replenishment Problem Research Articles

Optimizing omnichannel retailer inventory replenishment using vehicle capacity-sharing with demand uncertainties and service level requirements

This study explores an inventory replenishment problem for an omnichannel retailer selling a product with demand uncertainties and service level requirements in different channels through a capacity-sharing strategy. The omnichannel retailer allows customers to order products online and then pick them up in retail stores. The capacity-sharing strategy is considered to reduce travel costs when the omnichannel retailer delivers products in different channels. With the capacity-sharing strategy, some products can be transferred from the online delivery vehicle to the retail store delivery vehicle. The expectation and the bounds on the online route travel cost of the capacity-sharing strategy are determined, based on which the capacity-sharing rules are established. Optimization models and a solution procedure are developed to solve the omnichannel retailer inventory replenishment problem. To ensure adequate performance, service level requirements are considered when making delivery decisions. Numerical experiments using randomly generated and artificial instances are performed to verify the effectiveness and practicality of the proposed optimization models and the solution procedure. The results show that the proposed models and solution procedure can effectively reduce travel costs, and can provide effective schedule and delivery quantity decision support for omnichannel retailers.

An adaptive GLNPSO method for inventory replenishment supply chain problem with multiple-warehouse policy and budget consideration

This paper presents an efficient computation tool for a multiple-warehouse inventory replenishment lot-sizing problem with supplier selection, quantity discounts, and budget constraint. The cost model of the considered inventory replenishment issue is formulated as a mixed-integer nonlinear programming (MINLP) problem. With the proposed MINLP problem being an NP-hard problem, the MINLP cost model was optimized by using a novel global–local neighbor particle swarm optimization algorithm (TPAGLNPSO), inspired by two-phase self-adaptive inertia weight and improved constraint-handling technique. Apart from introducing the velocity index to switch the search scheme from exploration to exploitation, the constraint-handling technique was utilized to guide and guarantee the particle search toward undiscovered regions in the solution space. The stability analysis for the proposed novel TPAGLNPSO was also conducted using the stochastic process theorem. The corresponding parameter selection ranges were obtained based on the convergent conditions. Finally, eight industry cases were provided as examples to evaluate the performance of the proposed TPAGLNPSO method, after which a sensitivity analysis for the MINLP cost model was performed. The results demonstrate the competitive performance of the proposed TPAGLNPSO optimizer in terms of solution quality (with near-optimal results) than the optimal solutions obtained from Lingo software and computational effort (CPU time). Such findings can provide practitioners marginal insights into the effective management of the supply chain inventory replenishment problem.

Adaptive inventory replenishment using structured reinforcement learning by exploiting a policy structure

We consider an inventory replenishment problem with unknown and non-stationary demand. We design a structured reinforcement learning algorithm that efficiently adapts the replenishment policy to changing demand without any prior knowledge. Our proposed method integrates the known structural properties of a well-performing inventory replenishment policy with reinforcement learning. By exploiting the policy structure, we tune reinforcement learning to characterize the inventory replenishment policy and approximate the value function. In particular, we propose two methods for stochastic approximation on the gradient of the objective function. These novel reinforcement learning algorithms ensure an efficient convergence rate and lower algorithmic complexity for solving practical problems. The numerical results demonstrate that the proposed algorithms adaptively update the policy to changing demand and lower inventory costs compared to various benchmarks. We also conduct a numerical validation for a South Korean retail shop to validate the practical feasibility of the proposed method. Understanding the policy structure is beneficial for designing reinforcement learning algorithms that can address the inventory replenishment problem. These well-designed reinforcement learning algorithms are particularly promising when we require policy updates based on observations without precise knowledge of non-stationary demand. These research findings could be extended to address the various inventory decisions in which policy structures are available.

Inventory replenishment decisions with uncertain price and demand

This paper studies the multiple period inventory replenishment problem for a capacitated warehouse when procurement prices and market demands are both uncertain, with the goal to minimise the procuring and holding costs. We analyse this problem under the framework of competitive analysis, where neither probabilistic distributions nor sets are available to characterise the unknown price and demand parameters. An efficient online real-time replenishment algorithm is developed, which is free of any distribution assumption, and the decisions are made based entirely on past and present information. We derive an instance-independent competitive ratio of the algorithm, which provides a worst-case theoretical performance guarantee, and shows that the proposed algorithm performs well for situations with high volatility uncertainty over time and is naturally risk-averse. Finally, a set of numerical experiments further verifies the effectiveness of the algorithm.

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 .

A min-max policy for multi-item joint inventory replenishment problem: Application to industrial vending machines

Industrial vending machines are often used in manufacturing facilities to offer various items and tools that are required in the manufacturing process. Companies often manage the inventory replenishment for such vending machines based on a min–max or (s,S) policy for each item. When a replenishment arrives, the inventory of all items can be brought up to their maximum levels. This paper studies this unique multi-item joint inventory replenishment problem to determine the optimal min–max policy that maximizes the expected profit in a finite planning horizon. Specifically, a simulation optimization framework is used to determine the optimal inventory decisions. Two discrete-event simulation models are developed in Arena and Python and three optimization approaches are utilized, including OptQuest in Arena simulation, gradient-based methods, and particle swarm optimization algorithms. Moreover, computational experiments are conducted to compare the different solution methods. A simple heuristic is also provided for ease of implementation.

A Monotone Approximate Dynamic Programming Approach for the Stochastic Scheduling, Allocation, and Inventory Replenishment Problem: Applications to Drone and Electric Vehicle Battery Swap Stations

There is a growing interest in using electric vehicles (EVs) and drones for many applications. However, battery-oriented issues, including range anxiety and battery degradation, impede adoption. Battery swap stations are one alternative to reduce these concerns that allow the swap of depleted for full batteries in minutes. We consider the problem of deriving actions at a battery swap station when explicitly considering the uncertain arrival of swap demand, battery degradation, and replacement. We model the operations at a battery swap station using a finite horizon Markov decision process model for the stochastic scheduling, allocation, and inventory replenishment problem (SAIRP), which determines when and how many batteries are charged, discharged, and replaced over time. We present theoretical proofs for the monotonicity of the value function and monotone structure of an optimal policy for special SAIRP cases. Because of the curses of dimensionality, we develop a new monotone approximate dynamic programming (ADP) method, which intelligently initializes a value function approximation using regression. In computational tests, we demonstrate the superior performance of the new regression-based monotone ADP method compared with exact methods and other monotone ADP methods. Furthermore, with the tests, we deduce policy insights for drone swap stations.

A Min-Max Policy for Multi-Item Joint Inventory Replenishment Problem: Application to Industrial Vending Machines

A Min-Max Policy for Multi-Item Joint Inventory Replenishment Problem: Application to Industrial Vending Machines

A stochastic scheduling, allocation, and inventory replenishment problem for battery swap stations

Electric vehicles and drones promise to transform transportation systems and supply chains. However, long recharge times and battery degradation inhibit adoption. To overcome these barriers, swap stations enable quick battery exchange. We introduce a stochastic scheduling, allocation, and inventory replenishment problem which determines the charging, discharging, and replacement decisions at a swap station over time. The decisions are complex because recharging is necessary for short-term operation but causes degradation and the need for future replacement. We model the problem as a Markov Decision Process, solve it using backward induction, and show that the problem suffers from the curses of dimensionality. Hence, we propose two approximate methods, a heuristic benchmark policy and a reinforcement learning method, which provide high-quality solutions. Using a designed experiment, we deduce effective operational insights.

An Optimization-Simulation Framework for Integrated Inventory and Cash Replenishment Problem of Automated Teller Machines in India

An Optimization-Simulation Framework for Integrated Inventory and Cash Replenishment Problem of Automated Teller Machines in India

Technical Note: A Joint Pricing, Supplier Selection, and Inventory Replenishment Model Using the Logit Demand Function*

ABSTRACTWe revisit the joint pricing, supplier selection, and inventory replenishment problem for a single item in a two‐stage system examined by Adeinat and Ventura (2015) and use the logit function to model the price‐sensitive demand. This article provides a detailed analysis regarding the shape and properties of the logit demand function. In this context, we propose a two‐stage piecewise‐linear approximation technique to solve the integrated pricing, supplier selection, and inventory replenishment model. Besides, in this research, we provide sufficient justification for the selection of the logit demand function as well as a comparison with other demand functions. A numerical study further suggests the importance of using a precise demand curve to select the set of suppliers, coordinate inventory, and accurately optimize the profit function.

Inventory Management under Storage and Order Restrictions

Inventory management in most practical settings faces challenges due to various restrictions on storage and replenishment of products. These restrictions may be posed by budget availability, different production/supply schedules for different products, and limited storage space shared by a number of products—very common in retail, food, and the pharmaceutical industry. Motivated by this, we investigate in this study how simultaneous restrictions on shared storage capacity and product‐specific order capacities impact optimal replenishments in a multi‐product system. We formulate the inventory replenishment problem as a multi‐period stochastic dynamic program, where products face stochastic demand with general distributions and excess demand is lost or fulfilled by emergency orders. We first fully characterize the optimal replenishment policy for two‐product systems, and provide a methodology to compute optimal replenishment quantities, which can be described as a dynamic priority‐based replenishment rule. Our results show that for each product, the optimal replenishment priority as well as quantity depends on the inventory levels of both products and all available capacities. More interestingly, the results show that capacity restrictions can flip the stocking priorities of products. Based on the optimal policy for two‐product systems, we develop a heuristic for multi‐product systems whose complexity scales linearly with the number of products. Under moderate storage capacities, our heuristic significantly outperforms the naive heuristics that ignore dynamic priority assignment, and closely captures the benefits of the optimal policy for systems with large number of products.

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

We investigate a data-driven multi-period 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 to 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.

Structural Results for Average‐Cost Inventory Models with Markov‐Modulated Demand and Partial Information

We consider a discrete‐time infinite‐horizon inventory system with non‐stationary demand, full backlogging, and deterministic replenishment lead time. Demand arrives according to a probability distribution conditional on the state of the world that undergoes Markovian transitions over time. But the actual state of the world can only be imperfectly estimated based on past demand data. We model the inventory replenishment problem for this system as a Markov decision process (MDP) with an uncountable state space consisting of both the inventory position and the most recent belief, a conditional probability mass function, about the actual state of the world. Assuming that the state of the world evolves as an ergodic Markov chain, using the vanishing discount method along with a coupling argument, we prove the existence of an optimal average cost that is independent of the initial system state. For our linear cost structure, we also establish the average‐cost optimality of a belief‐dependent base‐stock policy. We then discretize the uncountable belief space into a regular grid and observe that the average cost under our discretization converges to the optimal average cost as the number of grid points grows large. Finally, we conduct numerical experiments to evaluate the use of a myopic belief‐dependent base‐stock policy as a heuristic for our MDP with the uncountable state space. On a test bed of 108 instances, the average cost obtained from the myopic policy deviates by no more than a few percent from the best lower bound on the optimal average cost obtained from our discretization.

Joint Quality Investment and Inventory Decisions for Perishable Items with Reference Quality Effect under the O2O Environment

Reference quality, as a benchmark against which the purchase quality of a product is judged, has an important impact on consumers’ purchase decision, especially perishable items. Thus, how to determine an appropriate quality investment and ordering strategies for perishable items to maximize retailers’ profit is an essential task. A joint dynamic quality investment and inventory replenishment problem for perishable items with consideration of reference quality effect is investigated, where the retailer sells its products using a combination of the offline and online stores, and the sales function is sensitive to products’ quality and consumers’ reference quality. The optimal control model is established to maximize the retailer’s total profit by making a joint quality and inventory strategy. The continuous time dynamic optimal quality investment and inventory replenishment strategies with reference quality effect are obtained by Pontryagin’s maximum principle. Numerical experiments are accounted for the key system parameters on the optimal strategies.

Joint Pricing and Inventory Replenishment Decisions with Returns and Expediting under Reference Price Effects

This paper considers a single-item joint pricing and inventory replenishment problem under reference price effects in consecutive T periods. Demands in consecutive periods are sensitive to price and reference price with general demand distribution. At the end of each period, after the demand realization, a firm can return excess stocks to a supplier or place an expediting order to reduce the loss by shortage. Unfilled demands are fully backlogged. In order to maximize the total expected discounted profit with reference price effects the optimal pricing and inventory replenishment policies for regular order and the inventory adjustment decisions for returning/expediting are derived. The optimal replenishment policy for regular order is a base-stock policy, the optimal pricing policy is a base-stock-list-price policy, and the optimal policy for returning/expediting inventory adjustment follows a dual-threshold policy. Furthermore, the analysis of the operational impacts (from the perspective of adding returning/expediting and reference price effects, respectively) is researched. Numerical results also show that considering both returning/expediting and reference price effects is more profitable than considering only one of them.

Synchronizing Pricing and Replenishment to Serve Forward-Looking Customers with Lost Sales

[Problem Definition] We incorporate heterogeneous customer valuation and the strategic customer behavior in the classical economic order quantity (EOQ) setting. The seller incurs setup costs when replenishing inventory, and can set the prices differently over time and implement capacity rationing. [Academic/ Practical Relevance] While similar ideas of market segmentation and intertemporal price discrimination can be carried over from the travel industries to other industries, there are new aspects when applying these concepts to retail outlets and supermarkets, because they usually face inventory replenishment problems. This makes the joint inventory replenishment and revenue management problem imperative. [Methodology] We adopt the mechanism design and dynamic programming approaches. [Results] We establish the optimality of cyclic intertemporal price discrimination, even if the customers are endowed with homogeneous valuations. Under the optimal policy, the replenishments and price promotions are synchronized, and the seller adopts the highest selling price when the inventory level is the lowest and plans discontinuous price discount at the replenishment point when the inventory is the highest. We also show that, under inventory-based pricing there is a direct mapping between deterministic and stochastic arrivals scenarios, and randomness on the arrivals per se does not alter the structure of the optimal policy. [Managerial Implications] This cyclic pricing scheme offers a stark contrast to the low-price-every-day scheme and achieves overall higher profit because customer strategic behavior offers additional flexibility to the seller in managing his inventory. Furthermore, because strategic customers are willingly backlogged, this creates opportunities for the seller to work with the customers to achieve a lower operational cost and a higher overall profit.

The inventory replenishment planning and staggering problem: a bi-objective approach

To the best of our knowledge, this paper is the first one to suggest formulating the inventory replenishment problem as a bi-objective decision problem where, in addition to minimizing the sum of order and inventory holding costs, we should minimize the required storage space. Also, it develops two solution methods, called the exploratory method (EM) and the two-population evolutionary algorithm (TPEA), to solve the problem. The proposed methods generate a near-Pareto front of solutions with respect to the considered objectives. As the inventory replenishment problem have never been formulated as a bi-objective problem and as the literature does not provide any method to solve the considered bi-objective problem, we compared the results of the EM to three versions of the TPEA. The results obtained suggest that although the TPEA produces good near-Pareto solutions, the decision maker can apply a combination of both methods and choose among all the obtained solutions.

A multi-objective simulation-based optimization approach for inventory replenishment problem with premium freights in convergent supply chains

In this study, a multi-objective simulation-based optimization approach is developed to solve inventory replenishment problem with premium freights in convergent supply chains. In this context, a decomposition-based multi-objective differential evolution algorithm (MODE/D) is used to determine demand forecast adjustment factor, safety stock and supplier flexibility parameters that minimize total holding cost, inbound and outbound premium freight ratios simultaneously. The proposed approach is applied a set of problem instances and the performance of the proposed approach is evaluated in comparison with the performance of non-dominated sorting genetic algorithm-II (NSGA-II). Furthermore, the proposed approach is applied to a multi-national automotive supply chain spread on Europe. The results reveal that the proposed approach is effective in solving inventory replenishment problem with premium freights in convergent supply chains.

EOQ Models with Optimal Replenishment Policy for Perishable Items taking Account of Time Value of Money

The main purpose of this research is to establish replenishment models and develop optimal replenishment policies for perishable items taking account of time value of money. This paper follows the Discounted Cash Flow (DCF) approach to investigate inventory replenishment problem over a fixed planning horizon. We develop model, to establish optimal solutions with and without backlogging and Show that the total variable cost is minimize and convex by the help of software. Numerical examples are to demonstrate the applicability of the proposed models and sensitivity analysis with respect to the parameters of the system is carried out.