Stochastic Inventory Problem Research Articles

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 .

1 A Markov Decision Processes Model for Stochastic Inventory Problem Under Uncertainty in Supply

1 A Markov Decision Processes Model for Stochastic Inventory Problem Under Uncertainty in Supply

Inventory and financing decisions in cross-border e-commerce: The financing and information roles of a bonded warehouse

Cross-border retail firms are often exposed to a lack of working capital for their procurement, especially for sudden increases in demand on special holidays such as Black Friday. This paper studies a cross-border product stochastic inventory management problem where capital-constrained retailers can obtain additional working capital through bonded warehouse financing and entrusted loan financing. This study obtains an optimal inventory policy in which retailers may purchase cross-border products with financing to sell to markets with uncertain demand. The results show that entrusted loan financing helps capital-constrained retailers increase their inventory procurement. Specifically, when capital levels are low, capital-constrained retailers opt for a mixed financing option of bonded warehouse and entrusted loan. Furthermore, the increase in bonded warehouse financing limits could weaken the reliance of capital-constrained retailers on entrusted loan financing. Interestingly, bonded warehouse financing and entrusted loan financing enable the formation of a liability network among retailers. While there is no risk contagion in the liability network when they sell heterogeneous products, the risk of losses due to fire sales remains. This paper further characterizes the payment and clearing model and derives the optimal payment-clearing strategy with fire sales of stagnant products. The results suggest that managers can utilize our designed procurement system with bonded warehouse financing and entrusted loan financing to purchase products without worrying about insufficient financing.

On the stochastic inventory problem under order capacity constraints

We consider the single-item single-stocking location stochastic inventory system under a fixed ordering cost component. A long-standing problem is that of determining the structure of the optimal control policy when this system is subject to order quantity capacity constraints; to date, only partial characterisations of the optimal policy have been discussed. An open question is whether a policy with a single continuous interval over which ordering is prescribed is optimal for this problem. Under the so-called “continuous order property” conjecture, we show that the optimal policy takes the modified multi-(s,S) form. Moreover, we provide a numerical counterexample in which the continuous order property is violated, and hence show that a modified multi-(s,S) policy is not optimal in general. However, in an extensive computational study, we show that instances violating the continuous order property do not surface, and that the plans generated by a modified multi-(s,S) policy can therefore be considered, from a practical standpoint, near-optimal. Finally, we show that a modified (s,S) policy also performs well in this empirical setting.

Application of a Distributionally Robust Optimization Approach for Single-Period Stochastic Inventory Problems with Different Carbon Policies

While single-period stochastic inventory problems have been studied in academia and industry, the impacts of both carbon emissions reduction and partial distribution information have not been investigated. In this paper, we consider carbon emission reduction in a single-period inventory problem where both product price and demand are stochastic. When only partial information on the first and second moments of the two stochastic elements is specified, we use the max–min criterion to construct two optimization models under cap-and-trade and carbon tax policies. For each model, we prove the existence of the optimal robust decisions on production quantity and cleaning equipment investment. By comparing the profit and carbon emission between these two models, we identify certain conditions that improve the economic and environmental performance of the manufacturer. Finally, we conduct a numerical study to test the robustness of the optimal operational decisions under each carbon policy.

The stochastic inventory routing problem on electric roads

In this work we introduce a green inventory routing problem termed the Stochastic Inventory Routing Problem on Electric Roads (S-IRP-ER), in which a hybrid vehicle navigates a road network with charging opportunities in some road sections, to cover the non-stationary stochastic demand of a single product for a set of retailers in the network. We model the problem using isochrone graphs to represent the real road network. In an isochrone graph nodes are located such that the time to travel any arc is constant all over the network. This allows for tracking the battery level of the vehicle serving retailers, as it charges and discharges continuously while travelling. We formulate a mathematical programming heuristics and prove its effectiveness. We use our model on a realistic instance of the problem, showcasing the different strategies that a vehicle may follow depending on fuel costs in relation to the costs of electricity.

Optimizing food logistics through a stochastic inventory routing problem under energy, waste and workforce concerns

The trend towards sustainable operations management makes it inevitable for companies to carry out their operations by considering environmental and social externalities. This tendency has implications also in the food logistics industry. This study addresses a single-period closed Inventory Routing Problem under environmental and social sustainability concerns in daily food logistics systems. In particular, the study focuses on reducing CO2 emissions in a refrigerated transportation system, collecting and disposing of waste, and offering employees more enticing work schedules, that have not been simultaneously addressed in the literature. The problem has been mathematically defined as a Mixed Integer Linear Programming model. A solution approach based on a clustering algorithm has been proposed to solve large-sized cases. The applicability of the proposed decision support models and the potential practical benefits obtained from their use are shown by performing numerical analyses on an industrial case and a set of larger instances. The results show that simultaneously respecting workforce constraints, waste collection/disposal, and demand uncertainty provide improved economic, environmental and social outputs for food logistics companies. Due to workforce constraints, the delivery time is shortened by 5.5 h, which allow the manufacturing to start later. Respecting waste collection and disposal as well as demand uncertainty enables cost reductions of %40.9 and %6, respectively.

A sampling-based matheuristic for the continuous-time stochastic inventory routing problem with time-windows

This article considers a continuous-time variant of the stochastic inventory routing problem. In most of the articles present in the literature related to inventory routing, customers reveal their demands at the end of each period, which is when the inventory level is calculated. In the variant of the problem at hand, the demand that each customer experiences on each period, results in a continuous decrease of the inventory for the customer during the period. This characteristic strongly affects the quantities that can be delivered to each customer and, if the deliveries are not sufficient or arrive too late, they can cause some stock-out situations within the periods. In the inventory routing problem, the vendor manages all the replenishment decisions of the vendees and, therefore, creates delivery plans for a planning horizon, aiming to reduce the routing, consistency, inventory and lost-sales costs. We formulate the problem as a two-stage mathematical program. Customers experience a continuous stochastic demand within each period and present information about inventory level and capacity at each period, as well as the time windows in which deliveries can take place. To solve this problem, we develop a matheuristic solution approach based on an adaptive large neighborhood search algorithm. In addition, we evaluate the impact of applying recourse actions to deal with expected lost sales during the planning horizon. We compare the performance of the algorithm with adapted variants of the multiple scenario approach and the branch and regret algorithms from the literature. Samples based on the stochastic demands are considered in the algorithms, to find robust solutions that can minimize the objective function. We evaluate the solutions by means of a sample average estimator procedure, and we compare the efficiency of the algorithms as well as the impact of different levels of stochasticity.

A new data-driven robust optimization approach to multi-item newsboy problems

<p style='text-indent:20px;'>A newsboy problem is a typical stochastic inventory management problem and has extensive applications in the fields of operational research, management sciences and marketing sciences. One of the challenges underlying such problems is to handle the uncertainty of demands. In the existing results, it is often to assume that the demand distribution is given to facilitate solution of the problems. In this paper, a novel data-driven robust optimization model for solving multi-item newsboy problems is proposed by combining the absolute robust optimization with a data-driven uncertainty set, and the latter is leveraged to address the uncertainty of demands. For the single-item situation, a closed-form solution is obtained and influences of parameters on the optimal solutions are analyzed. Owing to complexity of the multi-item situation, a uniform smoothing function is leveraged to smooth the proposed model. Then, an algorithm, called a modified Frank-Wolfe feasible direction algorithm, is developed to solve a series of smooth subproblems. Numerical simulation demonstrates that the proposed model in this paper can reduce over-conservation of robust optimization methods and is more robust than other similar well-established methods in the literature. By numerical simulation and sensitivity analysis, it is concluded that: (1) The proposed method can provide more stable optimal order policy and profits than the existing ones; (2) For a product with a higher unit purchase price, the optimal order quantities are more sensitive to its change; (3) In view of profitability, the newsboy should not to be too risk-averse.</p>

Scalable Approximately Optimal Policies for Multi-Item Stochastic Inventory Problems

Scalable Approximately Optimal Policies for Multi-Item Stochastic Inventory Problems

Stochastic inventory routing with time-based shipment consolidation

Inspired by the retail industry, we consider a stochastic inventory routing problem where retailers are replenished from a central warehouse using a time-based shipment consolidation policy. Such a time-based dispatching policy, where retailers facing stochastic demand are repetitively replenished at fixed times, is essential in practice. It allows for easy incorporation with dependent up- and downstream planning problems such as personal staffing and warehouse operations, and has become a standard part of transportation contracts. We provide a new chance-constrained model that determines an optimal clustering of retailers in groups, their associated routing and shipment interval, and each retailers’ optimal inventory level. A newly developed branch-price-and-cut algorithm solves our model to optimality. Its efficiency comes from a tailored labeling algorithm for solving the pricing problem that relies, among others, on an optimality pruning criterion based on the approximate solution of a 0,1-knapsack problem. Computational experiments show that our exact method can solve instances of up to 60 retailers to optimality. Besides, we accommodate practitioners by providing a fast heuristic that provides excellent solutions with an optimality gap of less than 1%. Finally, we show that incorporating uncertainty already in the planning process is essential for stochastic inventory routing with time-based shipment consolidation, as it results in overall cost-savings of 7.7% compared to the current state-of-the-art.

A mathematical programming-based solution method for the nonstationary inventory problem under correlated demand

This paper extends the single-item single-stocking location nonstationary stochastic inventory problem to relax the assumption of independent demand. We present a mathematical programming-based solution method built upon an existing piecewise linear approximation strategy under the receding horizon control framework. Our method can be implemented by leveraging off-the-shelf mixed-integer linear programming solvers. It can tackle demand under various assumptions: the multivariate normal distribution, a collection of time-series processes, and the Martingale Model of Forecast Evolution. We compare against exact solutions obtained via stochastic dynamic programming to demonstrate that our method leads to near-optimal plans.

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.

A multi-stage stochastic inventory management model for transport companies including several different transport modes

ABSTRACT This paper deals with modeling and solving a multi-stage stochastic inventory management problem for transport companies, including several different transport modes. This model aims to determine the amount of stored cargo and transport containers and trucks to the appropriate locations. Due to the uncertainty of environmental conditions, the demand and transfer costs parameters are considered uncertainly in different scenarios in the proposed model. Since the uncertain model is insoluble, a new robust-fuzzy-probabilistic method has been used to control the model’s parameters. As a result, the final model minimizes the total cost of maintaining cargo and transporting trucks and containers. Three genetic algorithms, particle swarm optimization and gray wolf optimization have been employed to solve the proposed stochastic inventory management model. The results of the problem analysis show that the increase of uncertainty rate in different scenarios due to the increase in the amount of demand from cargo, transmission, and maintenance costs have increased. In return, the total network costs have also increased.

Scalable Approximately Optimal Policies for Multi-Item Stochastic Inventory Problems

Scalable Approximately Optimal Policies for Multi-Item Stochastic Inventory Problems

A multi-period multi-product stochastic inventory problem with order-based loan*

This paper investigates a multi-period multi-product stochastic inventory problem in which a cash-constrained online retailer can leverage order-based loans provided by some Chinese e-commerce platforms to speed up its cash recovery for deferred revenue. Sample average approximation (SAA) and moment-matching scenario tree are adopted to solve this multi-stage problem with the objective of maximising the retailer's expected profit over the planning horizon. We conduct numerical tests based on crawling real data from an online store. The results show that the solutions of the two stochastic modelling approaches are very close. Moreover, the retailer tends to use order-based loans when its initial available cash is limited or it is facing a long revenue delaying length. Practitioners can make use of the modelling techniques in this paper to estimate whether it is beneficial to apply for an order-based loan.

Solving inventory routing with transshipment and substitution under dynamic and stochastic demands using genetic algorithm and deep reinforcement learning

In this paper, we investigate a two-level supply chain consisting of a company which manufactures a set of products and distributes them via its central warehouse to a set of customers. The problem is modelled as a dynamic and stochastic inventory routing problem (DSIRP) that considers two flexible instruments of transshipment and substitution to mitigate shortages at the customer level. A new resolution approach, based on the hybridisation of mathematical modelling, Genetic Algorithm and Deep Reinforcement Learning is proposed to handle the combinatorial complexity of the problem at hand. Tested on the 150 most commonly used benchmark instances for single-vehicle-product DSIRP, results show that the proposed algorithm outperforms the current best results in the literature for medium and large instances. Moreover, 450 additional instances for multi-products DSIRP are generated. Different demand distributions are examined in these experiments, namely, Normal distribution, Poisson distribution for demand occurrence, combined with demands of constant size; Stuttering Poisson distribution and Negative Binomial distribution. In terms of managerial insights, results show the advantages of promoting inventory sharing and substitutions on the overall supply chain performance.

A competitive stochastic bi-level inventory location problem

ABSTRACT This paper aims to address an inventory competitive facility location problem with the order quantity in a stochastic environment. In this problem, the facility location, customer design, and inventory control decisions have been integrated for two decision makers, i.e. the leader and the follower. To this end, a bi-level nonlinear nonconvex mixed integer mathematical model was proposed. Next, an alternative bi-level mixed-integer linear model was obtained. The enumeration branch-and-cut method in the field of bi-level linear programming was developed to come up with optimal or near-optimal solutions. To determine the branching choice and specialized cuts, a preference function was used. Computational results of some data tests were reported, and the results were compared with those of previous famous methods to show the efficiency of the algorithm. According to the computational results, the proposed algorithm could find effective solutions for solving such problems, which could compete with other well-known published algorithms.

Analysis of an inventory system with emergency ordering option at the time of supply disruption

This paper studies a continuous-review stochastic inventory problem for a firm facing random demand and random supply disruptions. The supplier experiences operational (on) and disrupted (off) periods with exponentially distributed durations. The firm adopts an order-up-to level policy during the on period and additionally can release an emergency order based on the inventory level just before disruption. This inventory policy is described by a continuous-time Markov chain model. We analyze the model for two different lead time scenarios and suggest solution approaches yielding the optimal policy parameters. In a numerical study, we explore the value of exercising such a policy and show that an emergency ordering opportunity at the disruption time brings substantial cost savings in cases with high lost sales cost, long off period, and low percentage of supplier’s availability.

Dynamic Inventory Management with Inventory‐based Financing

This study considers a stochastic inventory management problem where a capital‐constrained firm can obtain additional working capital through inventory‐based financing (IBF) by pledging its inventory to obtain loans from a lender. We show that the firm's optimal inventory policy in each period may order new inventory up to a state‐dependent order‐up‐to level subject to the firm's capital and IBF loan constraints, or salvage existing inventory down to a state‐dependent salvage‐down‐to level. We further partially characterize the structures of the two state‐dependent levels in each period. Through analytical and numerical studies, we offer a number of new insights regarding the optimal inventory management for a capital‐constrained firm with access to inventory‐based financing. In particular, we find that when the firm anticipates a shortage of capital with which to meet high demands in a future period, it may strategically over‐stock its inventory in earlier periods in order to secure the necessary capital. Through extensive numerical studies, our study also demonstrates how some of the key parameters may affect the optimal inventory policy and the value of IBF.