On-hand Inventory Research Articles

A Model for Decision-making to Parameterizing Demand Driven Material Requirement Planning Using Deep Reinforcement Learning

Abstract Demand-Driven Material Requirements Planning (DDMRP) is an emerging inventory management approach that has garnered significant attention from academia and industry. Numerous recent studies have highlighted the advantages of DDMRP compared to traditional methods such as material requirement planning (MRP), Theory of constraint (TOC), and Kanban. However, the performance of DDMRP relies on several parameters that affect its effectiveness. Parameterization models and the optimization of control variables have significantly contributed to the field of inventory management and have proven to be effective and practical in addressing challenges by providing a structured approach to handling complex variables and constraints. This paper introduces an innovative parameterization model that leverages deep reinforcement learning (DRL) to parameterize a DDMRP system in the face of uncertain demand. The main objective is to dynamically determine the optimal values for the variability and lead time factors within the DDMRP framework, to maximize customer service levels and optimize inventory efficiency. The results of this study emphasize the effectiveness of DRL as an automated decision-making approach for controlling DDMRP parameters. Additionally, the findings highlight the potential for enhancing the performance of the DDMRP approach, particularly in terms of on-time delivery (OTD) and average on-hand inventory (AOHI) by adjusting the variability and lead-time factors.

Uncertain random optimal control model for deteriorating inventory with the finite horizon

This paper examines a deteriorating inventory model with combined pricing and production during a limited selling time in an uncertain random setting. Demand is influenced by market size and price, which are portrayed in terms of random variables. The uncertainty factors affecting the inventory are represented by multiple Liu processes. Inventories deteriorate by a certain percentage and back-orders for inventories are permitted. This study aims to determine the optimal level of production rate and pricing that maximizes the producer’s total expected profit through the application of uncertain random optimal control theory, which is based on uncertain theory and probability theory. Numerical examples are used to compare joint pricing dynamic production model with dynamic production model under an optimal static price, highlighting the benefits of implementing joint pricing dynamic production model. Furthermore, it is evident that an increase in deterioration rate results in decreased on-hand inventory, yet higher production rate and price. It should also be noted that different levels of probability expectation of demand can have an impact on production inventory problem.

How good must failure predictions be to make local spare parts stock superfluous?

Thanks to Industry 4.0 technologies, predictive algorithms can provide advance demand information on spare parts demand. Understanding how the goodness of predictions affects on-hand inventory and costs is important for decision makers before integrating these models into existing systems. We consider a spare parts inventory problem for multiple technical systems that are supported by one local stockpoint. Each system has a single critical component that is subject to random failures. Signals are generated to predict component failures. The signal that corresponds to a failure is generated a certain amount of time before the failure, referred to as the demand lead time. However, not every signal results in a failure and some failures are undetected. A component is replaced from the stock when a failure occurs. In case of stock-outs, an emergency shipment takes place. We formulate a discrete-time Markov decision process model to optimize the replenishment decisions with the objective of minimizing the long-run average cost per period. We investigate the effect of precision (i.e., the fraction of true signals among all signals) and sensitivity (i.e., the fraction of detected failures among all failures) of the predictions and the demand lead time on the costs, order-up-to levels, average on-hand inventory and emergency shipments under the optimal policy. In the worst case, the precision, sensitivity or demand lead time is zero. We show analytically that the optimal policy and optimal costs only depend on the sensitivity and the demand lead time through their product. In numerical experiments, we observe a Pareto principle for the reduction of costs in precision (e.g., a 30% perfectness in precision brings a 70% reduction in optimal cost compared to the worst case) and an inverse Pareto principle in the product of sensitivity and demand lead time (e.g., 70% perfectness in the sensitivity or demand lead time only brings 30% reduction in optimal cost compared to the worst case). Finally, we observe that the local spare parts stock only becomes superfluous when the signals are really close to perfect.

MAP/PH/1 Üretim Envanter Modeli

In this study, a production inventory model with phase type service times where customers join the system occur according to a Markovian arrival process is discussed. When the inventory level is positive, if an arriving customer finds the server idle gets into service immediately. Served customer leaves the system and the on-hand inventory is decreased one unit of item at service completion epoch. Otherwise, the customer enters into a waiting space (queue) of infinite capacity and waits for get served. The production facility produces items according to an (s,S) policy. The production is switched on when the inventory level depletes to s and the production remains on until the inventory level reaches to the maximum level S. Once the inventory level becomes S, the production process is switched off. Applying the matrix-geometric method, we carry out the steady-state analysis of the production inventory model and perform a few illustrative numerical examples includes the effect of parameters on the system performance measures and an optimization study for the inventory policy.

A first attempt to enhance Demand-Driven Material Requirements Planning through reinforcement learning

Production planning methods, which are meant to schedule efficiently production orders to meet costumer demands, offer the possibility to fix some parameters to better fit to a specific industrial context. These parameters can be fixed either according to the user's prior knowledge, or according to decision support tools. Optimization algorithms, which require prior knowledge of costumer demand, are most-commonly used for decision-support. Fewer decision-support tools based on reinforcement learning and requiring no prior knowledge of costumer demand have also been suggested in recent years to parameterize most common production planning systems. This paper investigates such a reinforcement-learning approach to parameterize Demand-Driven Materials Requirements Planning (DDMRP), which is a recent production planning method proven to be successful to avoid stockouts while minimizing the on-hand inventory. Despite approximate and exact optimization methods have been suggested in literature to parameterize DDMRP, a reinforcement learning approach remains to be investigated. We suggest a SARSA (State–action–reward–state–action) algorithm to the problem and test it on a randomly-generated instance. The first results are promising in regards to the use of a reinforcement learning approach for the dynamic parameterization of the DDMRP.

Optimal dynamic pricing and production policy for a stochastic inventory system with perishable products and inventory-level-dependent demand

In this paper, we consider a joint dynamic pricing and production policy for a stochastic inventory system with perishable products. The demand is stochastic and dependent on the price and the level of the on-hand inventory. Combined dynamic pricing and production control, a stochastic dynamic optimization model that maximizes the total discounted profit is built. Applying the stochastic optimal control theory, we formulate the problem of finding the optimal joint dynamic pricing and production schedule as the problem of solving a Hamilton-Jacobi-Bellman (HJB) equation. By solving the HJB equation, analytical solutions for optimal pricing and production rate are obtained. In addition, a numerical example is given to illustrate the validness of the theoretical results and sensitivity analysis on major system parameters is carried out.

An alternating direction method of multipliers for optimizing (s, S) policies in a distribution system with joint replenishment volume constraints

In this paper, we study a two-echelon distribution system in which multiple products are jointly replenished at each stocking location and the inventory of each product at each location is controlled by an (s, S) policy. The transportation capacity in volume of products for each joint replenishment is limited, and linear rationing policies are used for both on-hand inventory and transportation capacity allocation in the system in case of shortage. We propose a novel scenario-based model for the optimization of the (s, S) policies in the system that considers the rationing policies. Because of its high complexity when the number of scenarios is large, an Alternating Direction Method of Multipliers is proposed to solve the model. Based on real data, forty instances were generated and tested to evaluate the model and the solution method. Our numerical experiments show that for these instances this method could find a better solution in a much shorter computation time compared with CPLEX 12.9, whereas the latter often runs out of memory for large-size instances on a personal computer. Moreover, the inventory policies found by this scenario-based optimization approach can reduce costs by 5.1% and improve fill rates by 9.7% on average compared with those currently used in Alibaba.

Load balancing in a network of queueing-inventory systems

We study a supply chain consisting of production-inventory systems at several locations which are coupled by a common supplier. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted (“lost sales”). To satisfy a customer’s demand a server at the production system needs raw material from the associated local inventory. The supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. The routing of items depends on the on-hand inventory at the locations with the aim to obtain “load balancing”. We show that the stationary distribution has a product form of the marginal distributions of the production subsystem and the inventory-replenishment subsystem. For the marginal distribution of the production subsystem we derive an explicit solution and for the marginal distribution of the inventory-replenishment subsystem we deduce an explicit solution or a recursive algorithm for some special cases.

Parameterisation of demand-driven material requirements planning: a multi-objective genetic algorithm

Demand-Driven Material Requirements Planning (DDMRP) is a recent inventory management method that has generated considerable interest in both academia and industry. Many recent papers have demonstrated the superiority of DDMRP over classical methods like MRP or Kanban, an observation confirmed by companies that have implemented DDMRP. However, DDMRP depends on many parameters that affect its performance. Only general rules are given by the authors of the method to fix these parameters but no algorithm. The present paper aims to fill this gap by proposing a multi-objective optimisation algorithm to fix a set of eight identified parameters. The suggested genetic algorithm is coupled with a simulation algorithm that computes the objective functions. Two opposing objective functions are considered: first, the maximisation of orders delivered on-time to the customer and, second, the minimisation of on-hand inventory. A set of data instances was generated to test the suggested method. Fronts of non-dominated solutions are found for all these instances.

Queuing Models for Analyzing the Steady-State Distribution of Stochastic Inventory Systems with Random Lead Time and Impatient Customers

In material management, the inventory systems may have good management aspects in terms of materials; however, this negatively affects the relationship between the facility and customers. In classical inventory models, arriving demands are satisfied immediately if there is enough on-hand inventory. Traditional inventory models consider optimization problems and find the optimal policy of decision variables without computing the stationary distribution of the inventory states for random demand. Hence, a detailed analysis of inventory management systems requires a joint distribution of system stock levels and the number of requests to be investigated thoroughly. This research provides a new stochastic mathematical model for inventory systems with lead times and impatient customers under deterministic and uniform order sizes. The proposed model identifies the performance measures in a stochastic environment, analyzing the properties of the inventory system with stochastic and probabilistic parameters, and finally, validating the model’s accuracy. To analyze the system, balance equations were derived from a mathematical characterization of the underlying queuing model dependent on the Markov chain formalism. The precise performance was achieved by examining the graphical representation of the service process in a steady-state as a function of both arrival distribution and the customer patience coefficient, while it was challenging to derive an optimal curve fit in a three-dimensional space that features two input variables and a single output variable.

Economic Production Quantity Model for Deteriorating Items under the Constant and Non Linear GHG Emission

Industry is becoming the largest source of GHG emissions, requiring action from industrialists. The model provided here is developed to address two different scenarios of GHG emission. This paper examines a model for producing inventory to meet the demand rate intended to operate on an infinite planning horizon where the demand rate for deteriorating items is determined by a function based on the on-hand inventory, given that the production rate is linearly related to the demand rate. In the forward manufacturing system, linear and nonlinear GHG emission costs are compared to observe the effects of nonlinearity in emission costs. At last numerical verification is used to illustrate the mathematical expressions, and the sensitivity of the different parameters is examined to draw some managerial conclusions.

A simulation-optimization approach to parameterize Demand-Driven Material Requirements Planning

Since its inception ten years ago, many researchers have shown Demand-Driven Material Requirements Planning (DDMRP) to be an efficient production planning method in terms of customer satisfaction and operating costs. DDMRP introduces a novel Net Flow Equation (NFE) to decide when to launch an order and how much to order. DDMRP relies on many parameters that affect the NFE and therefore the supply orders. The present paper investigates how to fix these parameters. We formulate this problem as a multi-objective optimization problem. The minimization of the average on-hand inventory is considered simultaneously with the maximization of customers’ orders delivered on-time (OTD: On-Time Delivery). To solve the formulated optimization problem, a multi-objective metaheuristic (NSGA-II: Non-dominated Sorting Genetic Algorithm) is coupled with a simulation algorithm. The front of non-dominated solutions is analysed for a given randomly-generated data instance. Other experiments are to be held on data provided by a private company.

A novel Markovian queueing-inventory model with imperfect production and inspection processes: A hospital case study

This paper studies an imperfect production process in an M/M/1 queueing system with an attached inventory screened by an imperfect inspector. The production system follows a Poisson process, and it may produce defective items that are supposed to be detected by an inspection process. The items form an M/M/1 queue in the inspection system. Moreover, the inspector is prone to type 1 and type 2 misclassifications. According to a Poisson process, customers arrive at the system and leave it after service with precisely one item. Provided that items are out-of-stock, the customers in the system must wait while the freshly arriving customers are lost. For the first time, this paper investigated the effect of the imperfect production process on the queuing-inventory system with an inspection process that may involve both type 1 and type 2 misclassifications. Under stationary conditions, we prove that the number of customers in the system, the on-hand inventory, and the number of items in the inspection system are independent, which led to driving the joint stationary distribution in explicit product form. A single variable nonlinear programming model (SVNLPM) is developed to minimize the expected total cost concerning the production rate using long-run performance measures. A mathematical proof identifies the beneficial properties of the expected total cost. We also evaluate the impact of essential parameters such as defective probability, type 1 and type 2 misclassifications, customers arrival rate, etc., on the optimal production rate and the expected total cost through extensive numerical examples and sensitivity analysis. We also apply our model to a real case study of blood inventory management in a hospital in Tehran. Finally, remarkable managerial and industrial implications are presented.

Exploring the Connections between Backrooms, Inventory Record Inaccuracies, and Waste

This paper explores the impact of retail store backrooms on inventory record inaccuracies (IRI) and waste. A trend in the retail industry is operating in the absence of a backroom. Benefits of operating without a backroom can include more employee presence on the sales floor, quicker replenishment (or the elimination of traditional backroom to shelf replenishment entirely), lower on-hand inventory, and the reduction of waste in the form of time, labor, cashflow, and product obsolescence. By conducting a literature review of the published literature on retail backrooms, this paper explores two additional unstated benefits to retailers operating without a backroom; specifically, the reduction of IRI and waste—an angle that has been previously understudied in the current academic literature. The objectives of this paper include defining a link between the existence of a backroom and waste/IRI, presenting an opportunity for future research in this area of study, and providing practical advice for corporations that wish to operate with or without a backroom.

Involvement of controllable lead time and variable demand for a smart manufacturing system under a supply chain management

The concept of controllable lead time and variance is critical issues for the smart supply chain management. This study concerns about variable lead time and variance under controllable production rate and advertise-dependent demand. Managers of any supply chain always improve their performance by reducing lead time and its variance. This paper explores and quantifies these benefits of such lead time reduction for commonly used lot size quantity, production rate, safety factor, reorder point, advertisement cost, vendor’s setup cost. Instead of expected total cost equations, this study provides an exact total cost equation built on an inherent relationship between on-hand inventory and backorder. The marginal value analysis on lead time and its variance achieve more accurate results. The analytical results show that the total supply chain cost is a convex function of both lead time and variance. In other words, the cost savings on both lead time and its variance reduction decrease when lead time becomes larger. Two continuous investments are implied to reduce setup costs and improve the reliability of the production process. The expected backorder and inventory for the buyer uniformly distributed throughout reorder point. Moreover, a smart production process is developed under stochastic demand and flexible production rates. The global optimality of the cost function and decision variables are validated through classical optimization. The numerical examples confirm analytical results and sensitivity analysis is provided for different parameters. Some special cases along with graphical representations are given to validate the model.

Two-Echelon Inventory Model With Service Consideration and Lateral Transshipment

This paper considers a two-echelon inventory system with service consideration and lateral transshipment. So far, researchers have not extensively considered the use of lateral transshipment for such systems. Demand arrivals at both echelons follow the Poisson process. We introduce a continuous review base stock policy for the system in steady state, which determined the expected level for on-hand inventory, expected lateral transshipment level and expected backorder level. We showed that the model satisfied convexity with respect to base stock level. Computational experiments showed that the model with lateral transshipment performed better that the model without lateral transshipment.

Stochastic Decomposition of Geo/Geo/1 Production Inventory System

This paper considers an (s, S) inventory system with production in which demand occurs according to a Bernoulli process and service time follows a geometric distribution. The maximum inventory that can be accommodated in the system is S. When the items in the on-hand inventory are reduced to a pre-assigned level of s due to service, production is started. The production time follows a geometric distribution. The production process is stopped as soon as the inventory level reaches the maximum. Customer who arrives during the inventory level is zero is assumed to be lost. Using the stochastic decomposed solution obtained for the steady-state probability vector, we analyzed the inventory cycle. A suitable cost function is defined using the performance measures. Numerical experiments are also incorporated to highlight the minimum value of the cost function against the parameter values.

Distributing Publicly-Funded Influenza Vaccine-Community Pharmacies' Perspectives on Acquiring Vaccines from Public Health and from Private Distributors in Ontario, Canada.

Objectives: To explore community pharmacies’ experience with two models of distribution for publicly-funded influenza vaccines in Ontario, Canada—one being publicly-managed (2015–2016 influenza season) and one involving private pharmaceutical distributors (2016–2017 season). Methods: Online surveys were distributed to community pharmacies across Ontario during the 2015–2016 and 2016–2017 influenza seasons with sampling proportional to Ontario Public Health Unit catchment populations. Quantitative data were analyzed descriptively and inferentially and qualitative data were summarized for additional context. Results: Order fulfillment appeared more responsive with the addition of private distributors in 2016–2017, as more pharmacies reported shorter order fulfillment times (p < 0.01); however, pharmacies reported significantly more days with zero on-hand inventory in 2016–2017 (p < 0.01), as well as more instances of patients being turned away due to vaccine unavailability (p < 0.05). In both seasons, a similar proportion of pharmacies reported slower order fulfillment and limited order quantities early in the season. Improved availability early in the season when patient demand is highest, more vaccines in a pre-filled syringe format, and better communication from distributors on product availability dates were recommended in qualitative responses. Conclusions: Introducing private distributors for the management and fulfillment of pharmacies’ orders for the publicly funded influenza vaccine appeared to have mixed results. While key concerns surrounding the frequency, responsiveness, and method of delivery were addressed by this change, challenges remain—in particular, acquiring sufficient vaccine early in the season to meet patient demand. As pharmacies become more prominent as vaccination sites, there are several opportunities to ensure that patient demand is met in this setting.

Optimal policies for inventory model with shortages, time-varying holding and ordering costs in trapezoidal fuzzy environment

This paper proposes the optimal policies for a fuzzy inventory model considering the holding cost and ordering cost as continuous functions of time. Shortages are allowed and partially backlogged. The demand rate is assumed in such to be linearly dependent on time during on-hand inventory, while during the shortage period, it remains constant. The inventory problem is formulated in crisp environment. Considering the demand rate, holding cost and ordering cost as trapezoidal fuzzy numbers, the proposed problem is transformed into fuzzy model. For this fuzzy model, the signed distance method of defuzzification is applied to determine the average total cost (ATC) in fuzzy environment. The objective is to optimize the ATC and the order quantity. One solved example is provided in order to show the applicability of the proposed model. The convexity of the cost function is verified with the help of 3D-graph.

The Effect of Lead-Time Variability on Inventory: Expected On-Hand Inventory Vs. Safety Stock

The Effect of Lead-Time Variability on Inventory: Expected On-Hand Inventory Vs. Safety Stock