Constant Lead Time Research Articles

Predictive Feedback Control for Inventory Systems Subject to Delays and Constraints

In this paper, we discuss the inventory regulation problem of a logistic system composed of a production unit and inventory unit. The production system is characterized by a constant lead time, and the storage unit presents fixed losses due to perishable products. In this study, the system is subject to finite production resources, limited storage capacities, and the customer demands are uncertain in a given range. We address a control strategy to the input time delay system that is subject to positive and saturation constraints and to bounded disturbances. We apply a linear prediction feedback control strategy, in order to stabilize the closed-loop system and to fulfill the system constraints, so that necessary and sufficient conditions for the existence of an admissible control law are formulated.

Performance bound for myopic order-up-to inventory policies under stationary demand processes

We consider a single-item infinite-horizon inventory system operating in discrete time and study the performance of the popular myopic order-up-to policy when demand is driven by a general autoregressive moving average (ARMA) stationary process. We derive a suboptimality bound for a system that operates under full demand backlogging, linear holding and backordering costs, and a constant replenishment lead time. We illustrate our results for the case in which demand follows an ARMA(1,1) process, which includes two commonly used demand models, MA(1) and AR(1), as special cases.

Establishing inventory measurements using intermittent demand forecasting

Demand forecasting is a fundamental element in industrial problems. Forecasts are crucial for accurately estimating intermittent demand to establish inventory measurements. The demand estimation by the Croston method gives less accurate values, which increases the standard deviation value. This increase indicates that the forecasted method is an inappropriate method of intermittent demand data because of the zero values. However, real data were adopted in an industrial sector for three years with constant lead-time. Furthermore, an integration of Bernoulli distribution and geometric distribution has been done to establish the new formulation, then extracting the mean equation and the standard deviation equation of intermittent demand during lead-time. Relying on it, the optimal quantity of safety stock and reorder levels have been obtained. Furthermore, the proposed modified forecasting method was evaluated based on the criteria of CV and the results that obtained gives a less ratio dispersion of data thus accurate results. These procedures are very important to the industrial sectors in drawing future inventory policies.

Supply planning and inventory control under lead time uncertainty: a literature review and future directions

The majority of publications in the scientific literature investigate stochastic demand processes with constant order lead times. In practice, inventory management software like MRP is used by companies even if ignored the uncertainty of lead times. In this work, we investigate the influence of this type of uncertainty and existing solutions proposed in the scientific literature. To do this, ARTIREV tool is used to identify the major schools of thought competing in the filed and highlight the current and emerging research themes. One conclusion is obvious from this preliminary work. Even though lead times are very disruptive to supply chain, as seen during the Covid crisis, most of the work is still only interested in the uncertainties related to demand.

데이터기반 재고관리를 위한 DDPG기반 심층강화학습 알고리즘 연구

We develop a modified version of deep deterministic policy gradient(DDPG) algorithm, which is one of the most popular deep reinforcement learning algorithms dealing with continuous action spaces, and apply it to the infinite-horizon newsvendor problems with constant lead time. Reflecting the key features of the inventory management problems, our algorithm, named as Inventory based DDPG (IDDPG), is differentiated in the state variables, action spaces, and cost functions compared to the DDPG. By conducting numerical experiments and comparing the performances, we found that when applied to the inventory management problems, IDDPG is able to find the near-optimal solutions and outperforms the DDPG in most cases. We also found that our IDDPG can be applied to a inventory management problem whose optimal solution is not known.

Algorithm of the automatic synchronizer operation

When connecting powerful synchronous electric machines (SM) to the power system uses automatic synchronizers with constant lead time. It is necessary to improve their accuracy and performance for the success of synchronization on the technological requirements of production. METHODS. For SM change the angle of the rotor is determined in the three phases of the synchronized voltages. This allows to increase the number of measurements per unit of time. The least-squares method is used for extrapolating the function values at the interval forecast. REZULTS. The proposed algorithm for automatic synchronizer uses to predict the set of values of the functions change the angle of the rotor. This distinguishes it from the known algorithms, where the forecast is based on the three rotor angle values determined over the same time interval. This property improves the accuracy, reduces the time interval determine the forecast considers possible change of the acceleration slip angle of the rotor. Using the least-squares method allows to abandon the traditional derivative calculation of the angle of the rotor, which is associated with increased interference. In addition, this method characteristic filter properties. CONCLUSIONS. The developed algorithm allows to quickly define the time of synchronization and improves the conditions of the SM by keeping dynamic stability.

Inventory model for multi-perishable goods with limited storage capacity

The warehouse has an important role, namely storing finished products as well as semi-finished, especially in the Agrifood Supply Chain (ASC) which has special characteristics such as limited shelf life, changing variations in demand and prices that can be adjusted to make ASC look more complex and more difficult than other supply chains. In this study, various thoughts are offered to fit the real conditions. Stochastic demand distribution, the presence of constant lead time on each product, exponential decay rates, to limited storage space capacity. Related to this assumption, the ongoing review (Q, r) is aimed at supply policies that are relevant to the agricultural-food supply chain problem. The development of a mathematical model with decision variables Q and r to minimize costs on warehouse procurement is then analyzed using a comparison using parameter ordering costs, storage costs, and shortage costs that have been determined in this study. on items with limited warehouse capacity. In previous research, the process of storing and procuring multi-products did not contain short-lived products. Also, other studies also explain the storage of products in a short shelf life does not contain a shortage of limited storage capacity. It can be done on research that will be carried out adjusted to conditions that occur in the real world It is estimated that it will make a practical contribution and be a reference model of inventory policies for warehouses that have relevant requirements.

Ordering Depletion in Inventory Policy with Imperfect Products and Backorder Rebate

This study presents an inventory model for imperfect products with depletion in ordering costs and constant lead time where the price discount in the backorder is permitted. The imperfect products are refused or modified or if they reached to the customer, returned and thus some extra costs are experienced. Lately some of the researchers explicitly present on the significant association between size of lot and quality imperfection. In practical situations, the unsatisfied demands increase the period of lead time and decrease the backorders. To control customers' problems and losses, the supplier provides a price discount in backorders during shortages. Also, an order’s policies may result in including some imperfect products in arrival lots. A discount on price may be offered by the supplier on the out-of-stock products to manage the backorder problems. The study aims to develop a model with imperfect products by permitting the price discount in backorders, and the cost of ordering is considered a decision variable. First, it is assumed that the demand for lead time is followed by a normal distribution and then stops it and assumed that the first two moments of demand for lead time are known. Further, the minimax distribution method is used to solve this model, and a separate algorithm is designed. In this study, two models are discussed with and without a normally distributed rate of demand. The current study verified with the help of some numerical examples over various model parameters.

Improved MRO Inventory Management System in Oil and Gas Company: Increased Service Level and Reduced Average Inventory Investment

This study proposes a methodology for the oil and gas businesses to keep their production plant productive with a minimum investment in carrying maintenance, repair, and operating inventory planning. The goal is to assist the exploration and production companies in minimizing the investment in keeping maintenance, repair, and operating (MRO) inventory for improving production plant uptime. The MRO inventory is the most expensive asset and it requires substantial investment. It helps in keeping the oil and gas production plant productive by performing planned and unplanned maintenance activities. A (Q, r) model with a stock-out and backorder cost approach is combined with a continuous inventory review policy for the analysis of class A items of oil and gas production plant MRO inventory. The class A items are identified through popular ABC analysis based on annual dollar volume. The demand for the inventory is modeled through Poisson distribution with consideration of constant lead time. The (Q, r) model in both stock-out cost and backorder cost approaches assigned higher order frequency and lower service level to low annual demand and highly expensive items. The stock-out cost approach shows an 8.88% increase in the average service level and a 56.9% decrease in the company average inventory investment. The backorder cost approach results in a 7.77% increase in average service level and a 57% decrease in average inventory investment in contrast to the company’s existing inventory management system. The results have a direct impact on increasing plant uptime and productivity and reducing company maintenance cost through properly managing maintenance stock. The analysis is carried out on the oil and gas production plant’s MRO inventory data, but it can be applied to other companies’ inventory data as well. All the results reflected in this research are based on the inventory ordering policy of two orders per year. The inventory ordering frequency per year may be other than two orders per year depending on the type of organization.

Numerical Validation of the Continuous Time Markov Chain Approximation as a Service Level Estimation Method for Heterogeneous Customer Demand Classes

In this article, we study a threshold level based inventory allocation and replenishment problem for two priority-demand classes under the lot-for-lot replenishment policy. Demands of low-priority class are backordered when on-hand stock is at or below a certain threshold level, while high-priority class demands are lost in case of stock-out situations. We assume a continuous review lot-for-lot ordering policy with both deterministic and stochastic replenishment lead times. Both priority classes exhibit mutually independent, stationary, Poisson demand processes. There is no exact solution yet in the literature except for the special case of exponentially distributed lead times. In this complementary study, we aim to numerically validate the Continuous-Time Markov Chain (CTMC) approximation as a service level approximation method by thoroughly analyzing the effect of the type of lead time distribution, lead time variability, and value of system parameters on the quality of the class-specific service level estimations. As long as expected lead times are identical, we also show empirically the near-insensitivity of the effect of the type of lead time distribution and the lead time variability on the achieved service levels. The CTMC approximation works well under variety of system parameters and lead time distributions. For the cases considered in the constant lead time scenarios with service levels which we expect to see in practice (with fill rate requirements at least 60 % and 90 % for the low-priority and high priority customer classes, respectively), the average absolute errors for the CTMC approximations are calculated as 0.09 % (for the low-priority class fill rate) and 0.05 % (for the high-priority class fill rate); while the maximum absolute errors for the CTMC approximations are calculated as 0.37 % (for the low-priority fill rate) and 0.18 % (for the high-priority fill rate). The CTMC approach also provides quality approximations for the Erlang, lognormal and gamma distributed lead times.

Anticipated rationing policy for inventory systems with two demand classes and backlogging costs

This paper studies a periodic-review, infinite-horizon, backlogging inventory model with two demand classes and a constant lead time, where inventory replenishment follows a base-stock policy. We consider an anticipated rationing policy which reserves inventory for future high-priority demands with higher backlogging costs by taking the coming delivery of the next period into consideration. Due to the lack of nice properties such as convexity, both the optimal base-stock level and the optimal critical level when minimising inventory costs have to be found by an exhaustive search. Instead, we study a single-period problem truncated from the original infinite-horizon problem and derive its optimal reservation level with a closed-form expression. Surprisingly, the solution form of the single-period problem coincides exactly with the anticipated rationing policy and hence this solution serves as a good approximation for the optimal critical level of the infinite-horizon problem. An empirical study further demonstrates that our closed-form approximation is quite attractive in both solution accuracy and computation efficiency based on spare parts inventory data from a petrochemical plant in China.

Capacity-driven production planning

Traditional material requirements planning systems (MRP) schedule production orders for on-demand items without considering limited capacities of production resources. This article introduces a production planning approach which also incorporates consumption-based items and addresses capacity planning when planned orders are generated. The framework consists of three steps: drafted job list generation, capacity-driven forward scheduling and purchase order generation. Fewer predefined parameters for internally produced items than in MRP are necessary. No lot-sizing policy is applied. Lot-sizes are arranged in a forward scheduling procedure. No predefined constant lead times are used because lead times are also calculated dynamically in the planning procedure. The approach allows a (semi-) automatic finite-capacity production planning and capacity adjustment. The functionality of the approach is illustrated by a simple case study throughout the article.

A simulation-based decision-making framework for construction supply chain management (SCM)

The conventional economic order quantity (EOQ) model used for calculating re-order point in construction material procurement cycle is fundamentally limited by the assumed constant lead time. In real construction scenario, the lead time is hardly ever constant. This study uses a PERT-based simulation model to calculate optimum re-order point and order size with an objective of minimizing the average inventory level and downtime due to non-availability of material. The simulation is run on the STROBOSCOPE simulation framework developed by the researchers at the University of Michigan. The duration data collected from a construction project are used to model each step of the procurement process. The results from the simulation are analyzed to study the relationships between order size, re-order point, average inventory level and work–idle time. A decision-making framework is proposed to choose the optimum order size and re-order point (minimum inventory threshold) for efficient use of storage space and minimum idling.

A rolling horizon simulation approach for managing demand with lead time variability

This paper proposes a rolling horizon (RH) approach to deal with management problems under dynamic demand in planning horizons with variable lead times using system dynamics (SD) simulation. Thus, the nature of dynamic RH solutions entails no inconveniences to contemplate planning horizons with unpredictable demands. This is mainly because information is periodically updated and replanning is done in time. Therefore, inventory and logistic costs may be lower. For the first time, an RH is applied for demand management with variable lead times along with SD simulation models, which allowed the use of lot-sizing techniques to be evaluated (Wagner-Whitin and Silver-Meal). The basic scenario is based on a real-world example from an automotive single-level SC composed of a first-tier supplier and a car assembler that contemplates uncertain demands while planning the RH and 216 subscenarios by modifying constant and variable lead times, holding costs and order costs, combined with lot-sizing techniques. Twenty-eight more replications comprising 504 new subscenarios with variable lead times are generated to represent a relative variation coefficient of the initial demand. We conclude that our RH simulation approach, along with lot-sizing techniques, can generate more sustainable planning results in total costs, fill rates and bullwhip effect terms.

Managing the essential medicines stock at rural healthcare systems in India

PurposeThe purpose of this paper is to eliminate the medicine stock-out problem by building an optimum medicine stock in rural healthcare centers in India.Design/methodology/approachData associated with inflow and outflow of a specific medicine (folic acid tablets) arer collected from all consecutive supply chain stages during the survey. While conducting the survey, it is found that several medicines are out of stock owing to uncertain lead time and demand. Integrating with quantity discount and min–max (s, S) inventory policy, two models are developed using system dynamics: one is Model 1 with constant lead time and uncertain demand, and the other is Model 2 with both uncertain lead time and demand.FindingsBoth models are simulated for a period of one year on Stella 9.1 platform. The results are compared with actual data, and the comparison shows significant improvement of the medicine stock at all downstream stages, while maintaining a certain safety stock. Further, Model 2 suggests a larger stock than Model 1 at each point of time.Practical implicationsDespite numerous issues, the stocks of medicine in rural healthcare systems can be improved as suggested by the models. The models depict the behavior of inventory stock at each stage of the supply chain and act as a function of time that could be used in the form of a prediction tool for the policymakers.Originality/valueThis paper is one of the first papers that had developed the model of the medicine supply chain in rural parts of a developing country. It provides a generic framework for the stock assessment and improvement throughout the supply chain.

Continuous Review Inventory Model with Normally Distributed Fuzzy Random Variable Demand

A fuzzy random continuous review inventory model is developed in this paper in order to illustrate a means of quantifying both imprecision and stochastic uncertainty simultaneously when there is significant information (imprecise and/or otherwise) available. Here the annual customer demand is assumed to be continuous fuzzy random variable following normal distribution, because in real life inventory situations, normal distribution is most often used to quantify customer demand information. The associated probability density function of the annual demand is also taken to be fuzzy in nature. The lead-time demand is also taken to be a normally distributed continuous fuzzy random variable by connecting it to the annual demand through the length of the constant lead-time. Under these assumptions, a methodology is proposed to minimize the crisp equivalent of the expected total annual cost and determine the optimal values of the re-order point and order quantity in the process. A numerical example is also presented to illustrate the proposed model and provide managerial insights.

Joint order (1, T ) policy for a two-echelon, single-item, multi-retailer inventory system with Poisson demand

Abstract This study considers a two-echelon inventory system with one central warehouse and a number of non-identical retailers with Poisson demands, constant lead times, and lost sales for a single item. The warehouse works as a cross-docking terminal with no inventory and coordinates shipments to retailers. We apply the Joint order (1, T ) policy in such an inventory system. In the standard (1, T ) policy , the warehouse sends one unit of the item to each retailer in a fixed cycle time, which is calculated by considering each retailer separately. In the joint order (1, T ) policy, the warehouse decides to replenish one unit of the item for each retailer in a cycle time which is adjusted to be an integer multiple of a base cycle time . Thus, under such an ordering policy, the warehouse can better adjust shipments to retailers so that they can be batched with other retailers’ orders, which results in overall savings in ordering, shipping and stock out costs for the entire system on average. We calculate the total cost of the system, and present a procedure to obtain near optimal values of the base cycle time and the integer multiples of the base cycle in which retailers should be served.

Determination of Economic Lot Size between Suppliers and Manufacturers for Imperfect Production System with Probabilistic Demand

This study aims to develop a combined economical lot size model between supplier and manufacturer for imperfect production processes with probabilistic demand patterns and constant lead times. The supplier side produces the product within a certain time interval then sent to the manufacturer with a certain amount of lot size. Imperfect supplier production systems are characterized by the probability of defective product (γ). The model decision variables are the lot size of the manufacturer's ordering, supplier lot size, and the reorder point of the manufacturer. The optimal decision variables are obtained by minimizing the total expected cost of the combined costs between the suppliers and the manufacturers borne by both parties. The model is built compared to the transactional partnership model, in which the supplier does not participate in the efficiency of its inventory system. A numerical example is given as an illustration of the JELS model and the transactional partnership model. Sensitivity analysis of the model is done by changing the parameters aimed at analyzing the behavior of the developed model.

Emergency orders in the periodic-review inventory system with fixed ordering costs and stochastic lead times for normal orders

This paper presents various periodic review policies for inventory control of a single item facing compound Poisson demand. Emergency orders are controlled by a reorder point policy with a target stock level, whereas normal orders are issued according to a reorder point policy with a fixed order quantity. We assume that emergency orders have a short constant lead time and are more expensive than normal orders for which the extra lead time is specified as a stochastic multiple of the review period. In addition to variable and fixed costs for emergency orders and fixed costs for normal orders, our model includes linear holding and backlogging costs.Pure policies issuing either emergency orders or normal orders are used for benchmarking and initialization purposes of two combined policies, OPT and SIMP, which allow at most one normal order with remaining lead time longer than the lead time for emergency orders. The combined policies are computed by applying Markov decision models and, for some model-exogenous control variables, neighborhood search. The numerical study shows a large potential for cost improvement from using normal orders and emergency orders in combination. The relative cost increase of the new SIMP compared with the previously studied OPT is often about 1%. Because SIMP is easier than OPT to administer and explain, it is more appropriate than OPT for practical applications.

The impact of stochastic lead times on the bullwhip effect – a theoretical insight

ABSTRACTIn this article, we analyze the models quantifying the bullwhip effect in supply chains with stochastic lead times and find advantages and disadvantages of their approaches to the bullwhip problem. Moreover, using computer simulation, we find interesting insights into the bullwhip behavior for a particular instance of a multi-echelon supply chain with constant customer demands and random lead times. We confirm the recent finding of Michna and Nielsen that under certain circumstances lead time signal processing is by itself a fundamental cause of bullwhip effect just like demand-signal processing is. The simulation also shows that in this supply chain the delay parameter of demand forecasting smooths the bullwhip effect at the manufacturer level much faster than the delay parameter of lead time forecasting. Additionally, in the supply chain with random demands, the reverse behavior is observed, that is, the delay parameter of lead time forecasting smooths bullwhip effect at the retailer stage much faster than the delay parameter of demand forecasting. At the manufacturer level, the delay parameter of demand forecasting and the delay parameter of lead time forecasting dampen the effect with a similar strength.