Lead Time Demand Research Articles

Supply chain model having stochastic lead time demand with variable production rate and demand dependent on price and advertisement

In this present study, a single-manufacturer and single-retailer supply chain management model are formulated for a single product. This study specifically looks at a supply chain with variable production rate, stochastic lead time demand, and price- and advertisement-dependent demand. By incorporating these complex aspects into a model, which enables to examine their combined effects on supply chain performance, this study adds to the body of knowledge. The study reveals unique insights into the complex interplay between pricing tactics, advertising efforts, production dynamics, and the variability brought on by stochastic lead times through meticulous study and modelling. Finally, the total system profit is calculated and optimized with all the decision variables. A classical approach is performed to obtain the optimized solution of the joint profit function along with the decision variables. Two models are discussed in the study: (1) the model with normally distributed lead time demand and (2) the model with distribution-free lead time demand. The joint profit of the supply chain is found to be lesser by 1% for the normally distributed lead time demand than the distribution free pattern. The comparison of the shipment policies and the safety factors for the different distribution patterns of the lead time demand are shown. Though the huge increment in the safety factor for unknown leadtime demand distribution may help in reducing the uncertainity factor and disruptions in the supply chain, but also it may unnecessarily tie up more capital which can be invested in other sectors of the supply chain.

Optimization of Neutrosophic EOQ Model for Effective Demand Management in Uncertain Environment Using Genetic Optimization

Inventory management is characterized by a continuous struggle to lower goods levels and related costs while also providing customers with the goods they need. However, reducing costs while simultaneously striving for ideal inventory levels is difficult, notably in the current situation of high unpredictability of goods demand and lead time. Traditional inventory models are not strong enough to endure changes like goods demand and lead-time demand. As a result, it must be adjusted to achieve results. The oeuvre below presents a new kind of inventory model that deals with uncertainty in the demand for goods and lead time. In this regard, the presented work, the novel Neutrosophic Economic Order Quantity approach is a mechanism to account for the likely imprecision in the model. Specifically, the Neutrosophic set theory is integrated into the EOQ model so that it can handle variations in the demand and lead-time pattern successfully. An objective function is established for obtaining economical order quantities that include demand, lead-time, and other necessary components’ irregularities. The process variables in the model are given the final values using genetic algorithms and simulated annealing. To highlight the impact of the proposed Neutrosophic approach, it is then applied to several realistic examples. This will provide the audience a sense of how effective inventory management may be in high-uncertainty situations. The rapid evolution of organizations necessitates innovative inventory control tactics to meet growing demands

When is the next order? Nowcasting channel inventories with Point-of-Sales data to predict the timing of retail orders

Slow-moving goods are common in many retail settings and occupy a vast part of retail shelves. Since stores sell these products irregularly and in small quantities, the replenishing distribution center may only place batched orders with manufacturers every few weeks. While order quantities are often fixed, the challenge for manufacturers facing such intermittent demand is to forecast the order timing. In this paper, we explore the value of Point-of-Sales (PoS) data to improve a food manufacturer’s order timing forecast for slow-moving goods. We propose an inventory modeling approach that uses the last order, PoS data from retail stores, and the expected lead time demand to estimate the retailer’s channel inventory. With this dynamic estimate, we can ‘nowcast’ the retailer’s inventory and predict his next order. To illustrate our methodology, we first conduct an experimental simulation and compare our results to a Croston variant and a moving average model. Next, we validate our approach with empirical data from a small German food manufacturer that serves a grocery retailer with a central distribution center and 53 hypermarkets. We find that, on average, our approach improves the accuracy of order-timing predictions by 10–20 percent points. We overcome a shrinkage-induced bias by incorporating an inventory correction factor. Our approach describes a new way of utilizing PoS data in multi-layered distribution networks and can complement established forecasting methods such as Croston. Particular applications arise when the order history is short (e.g., product launch) or represents a bad predictor for future demand (e.g., during COVID-19).

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.

Inventory Policies and Supply Chain Coordination under Logistics Route Disruption Risks

Predictable logistics disruptions due to scheduled lockdowns for large-scale events such as the Olympic Games may not only reduce supply chain profits, but also increase carbon emissions. To help solve these problems, an emergency transit policy to be applied to the logistics path is an effective solution. However, optimal inventory control is needed. This paper proposes an optimization model to control ordering and inventory policies for decentralized and centralized supply chains. The model considers the logistics path damping coefficient, the logistics path acceleration coefficient, and the vehicle loading capacity ratio in emergency transit. Our major findings include the following. First, supply chain profits under centralization are confirmed to be higher than under decentralization. Second, a price discount mechanism can achieve supply chain coordination. Third, the manufacturers in a centralized supply chain are more inclined to choose a logistics path with a high acceleration coefficient in order to let their cargo arrive quickly and to reduce the impact of the lead time demand fluctuations. Finally, the implications of our research results for carbon emission reductions are discussed.

A nonparametric approach for setting safety stock levels

In practice, lead time demand (LTD) can be skewed, multi‐modal or highly variable, and these factors compromise the validity of typical approaches used for setting safety stock levels. Motivated by encountering this problem at our industry partner, we develop an approach for setting safety stock levels using the bootstrap, a widely used statistical procedure. Existing bootstrap approaches for inventory management either operate directly on observed LTD or assume deterministic lead times, permitting direct application of the bootstrap approach for univariate quantile estimation. As LTD is a convolution of multiple random demands over a random lead time, a multivariate bootstrap approach is required. As we demonstrate, when lead times are stochastic, our multivariate approach provides improved safety stock estimates. We develop a multivariate central limit theorem for the bootstrap mean and bootstrap quantile—components of the safety stock calculation—highlighting why the generalization of these bootstrap methods is critical for inventory management. These results provide a theoretical underpinning for the bootstrap estimator of safety stock and permit the construction of confidence intervals for safety stock estimates, allowing decision makers to understand the reliability with which the desired service level will be achieved. Building on our theoretical results, and supported by numerical experiments, we provide insights on the behavior of the bootstrap for various LTD distributions, which our results demonstrate are critical when employing the bootstrap method. Implementation of our approach with our industry partner resulted in an inventory investment reduction of $1.17 million combined with an overall increase in service level. Our approach is general and can be implemented without modification in other settings.

نموذج المراجعة المستمرة المقيد للمخزون مع توزيعات داجوم وكوماراسوامي – داجوم

The main objective of this paper is to minimize the expected total cost using Lagrange multiplier approach with decreasing varying holding cost for probabilistic continuous review single-item multi-source inventory model under a restriction on the storage space. The optimal order quantity and the optimal reorder point for the best source which achieve the goal when lead time demand follows Dagum and Kumaraswamy-Dagum distributions of obtained. Also, an application is analyzed and reach the goal of minimizing the expected total cost with simulation data.

Developing trust among players in a vendor-managed inventory model for random demand under environmental impact.

Retailers play a vital role in supply chain management because they deal directly with consumers. Occasionally, retailers may cover the entire system's statistics and not disclose these data to the manufacturer. Therefore, asymmetry is generated in the data throughout the system. The main motive of this research was to prevent unreliability throughout the system using a vendor-managed inventory policy. This research shows that by applying a cap and trade policy, the total carbon emitted from the production and transportation sectors can be controlled in the atmosphere. Finally, numerical and sensitivity analyses, along with pictorial representations of various parameters, are performed to examine the optimal results of this study. In addition, the retailer's lead time demand for items is assumed to be random rather than fixed and follows uniform and normal distribution functions. Under these two distribution functions, the optimal retailer lot size, service provided by the retailer to customers, and retailer reorder points are assessed. Furthermore, an evaluation of the total carbon released from an environmental viewpoint is illustrated using numerical findings. The numerical results show that this research is 50.24% more economically beneficial than the methods used in previous studies, whereas the mean value of demand follows a uniform distribution.

Estimating the cumulative distribution function of lead-time demand using bootstrapping with and without replacement

Forecasting of the cumulative distribution function (CDF) of demand over lead time is a standard requirement for effective inventory replenishment. In practice, while the demand for some items conforms to standard probability distributions, the demand for others does not, thus making it challenging to estimate the CDF of lead-time demand. Distribution-free methods have been proposed, including resampling of demand from previous individual periods of the demand history, often referred to as bootstrapping in the inventory forecasting literature. There has been a lack of theoretical research on this form of resampling. In this paper, we analyse the bias and variance of CDF estimates obtained by resampling, both with and without replacement. Counterintuitively, we find that the ‘with replacement’ approach does not always dominate ‘without replacement’ in terms of mean square error of CDF estimates. Closed-form expressions are given for the components of Mean Square Error, with and without replacement. For shorter lead times, of two or three periods, these may be used directly to identify series that may benefit from resampling without replacement. Inventory performance implications are evaluated on simulated and empirical data. It is found that marked differences may arise between ‘with replacement’ and ‘without replacement’ bootstrapping approaches. The latter method can be more beneficial for lower target Cycle Service Levels, longer lead times and shorter demand histories.

Fuzzy Random Periodic Review Mixture Inventory Model With Shortage Dependent Backorder Rate

In most real-life inventory situations, it is observed that, during stock out period, an increase in the amount of shortage results in a decrease in the rate of backorder incurred. Therefore, backorder rate is dependent on shortages, and it may be assumed to be inversely proportional to the shortages. The present research describes a periodic review inventory model with a mixture of backorder and lost sales where the backorder rate is a control parameter. Furthermore, to incorporate two different types of uncertainties i.e., fuzziness and randomness, here the annual customer demand, lead-time demand and the lead-time plus one period's demand have been assumed to be continuous fuzzy random variable following the normal distribution with associated fuzzy probability density functions. An algorithm has been proposed to find the optimal backorder rate, the optimal period of review along with the target inventory level so that the crisp equivalent of the fuzzy random total annual inventory cost is a minimum.

Estimating the reorder point for a fill-rate target under a continuous review policy in the presence of non-standard lead-time demand distributions

Skewed and multimodal lead-time demand (LTD) distributions can be present in supply chains. Under these conditions, logistics managers find that conventional approaches, which assume standard LTD distribution shapes, yield unreliable estimates of a single item’s reorder point (ROP) in relation to meeting fill-rate targets under a continuous review inventory policy. Furthermore, logistics managers have limited data available from which to determine the true shape of the underlying LTD distribution. In this study, I present a non-parametric bootstrap approach to set a least-biased estimate of the ROP. In addition, to deriving bootstrap expressions for non-standard LTD shapes, I derive expressions for standard distribution shapes to estimate the ROP across a range of fill rates. Thus, eliminating the double counting of stockouts with conventional fill-rate measures. Using Monte Carlo simulation experiments, I show that in comparison to the conventional state-of-the-art approaches the non-parametric bootstrap approach yields the least-biased ROP estimates robust to both the shape of the LTD distribution and the sample size. This research offers more accurate ROP estimators, which can serve as a basis for expanding the scope of future inventory management research and enabling logistics managers to reduce inventory while maintaining and even improving fill rates.

Quantifying the Bullwhip Effect in a Reverse Supply Chain: The Impact of Different Forecasting Methods

The reason for this study is that the bullwhip effect can pose very serious consequences for enterprises, such as increased production costs, additional manufacturing costs, excessive inventory levels, excess storage costs, large capital overstocking, and excessive transportation costs. Thus, the problem for this study is that quantifying the bullwhip effect in a reverse supply chain and comparing the impact of different forecasting methods on it. The objective of this paper is the bullwhip effect (BE) in a reverse supply chain (RSC). In particular, this study proposes a quantitative expression of the BE in a RSC, that is, B E R = V a r q t / V a r r t , and analyzes the impact of different forecasting methods (e.g., the moving average technique (MA), the exponential smoothing technique (ES), and the minimum mean square error forecasting technique (MMSE)) on the bullwhip effect. We evaluate the conditions under which the collector should select different forecasting methods based on the BE. We use simulation date and get some conclusions that, in some cases when using the MMSE method, the BE does not exist in a RSC. This finding is significantly different from the results on the BE in a forward supply chain. Moreover, the MMSE method can reduce the lead-time demand forecast error to the greatest possible extent, which allows the BE to reach the lowest level.

On the stationary stochastic response of an order-constrained inventory system

We investigate the stochastic response of a base stock inventory system where the order quantity is either upper- or lower-constrained. This system can represent many real-world settings: forbidden returns, minimum order quantities, and capacity constraints for example. We show that this problem can be translated into a stopping time problem where the distributions of orders and inventory can be represented by a countably infinite mixture of truncated and convoluted demand distributions. This result can be extended to the cases of arbitrary lead time and auto-correlated demand. A state space algorithm is developed to approximate the first- and second-order moments of the order quantity and inventory level. Via a numerical analysis, we investigate the performance of the approximation, as well as the operational and economic impact of the order constraint. In particular, the constraint impacts order and inventory variances via different combinations of the mixture and truncation effects. We show how tuning the constraint can improve the operational and financial performance of the inventory system by acting as a smoothing mechanism.

A two-tier supply chain model under two distributions with MTTF, rework, variable production rate and lead time

This article considers the two-level supply chain model incorporating an imperfect production process under a variable lead time. The cost of producing a unit item is calculated as a function of the production rate. In addition, two alternative production functions (linear and quadratic functions) are used to relate process quality and production rate. Lead time demand follows two different distributions, based on which two mathematical formulations are described in this paper. In the first model, the lead time demand follows a normal distribution. In the second model, the lead time demand doesn't follow any particular distribution, but the mean and the standard deviation are known. The lead time length is minimized by incorporating the lead time crashing cost. This research aims to analyze the optimized total cost of the supply chain under two different distributions.

Dynamic Discrete Inventory Control Model with Deterministic and Stochastic Demand in Pharmaceutical Distribution

This paper presents an inventory control problem in a private pharmaceutical distribution company from the Republic of Serbia. The company realizes that distribution within nine neighbouring countries and inventory control in the pharmaceutical supply chain is centralized. In order to constitute a conceptual model of the problem, we propose the modern control theory concept. The conceptual model is based on the specific practical assumptions and constraints of the supply chain. Thereafter, a dynamic discrete mathematical model of inventory control is formulated to reflect elements of the system and their relations. The model considers multiple pharmaceutical products, variable lead time, realized stochastics and deterministic demand, and different ordering policies (Lot for Lot and Fixed Order Quantity). Deterministic demand is represented as a sales forecast for each product per month, while stochastic demand is generated as a random variation of sales forecast in a range of ±20%. Two objective functions are defined as the maximization of the difference between planned average inventory level and realized average inventory level, and the minimization of stock-out situations. We develop a procedure for the determination of reorder points and the number of deliveries to achieve proposed objective functions. The model overcomes shortages of theoretically-based distribution requirements planning models and offers solutions to the limitations in inventory control practice. Real-life data, collected over two years, are used for the validation of the proposed model and the solution procedure. Numerical examples illustrate the model application and behaviour.

Involvement of smart technologies in an advanced supply chain management to solve unreliability under distribution robust approach

<abstract><p>The proposed study described the application of innovative technology to solve the issues in a supply chain model due to the players' unreliability. The unreliable manufacturer delivers a percentage of the ordered quantity to the retailer, which causes shortages. At the same time, the retailer provides wrong information regarding the amount of the sales of the product. Besides intelligent technology, a single setup multiple unequal increasing delivery transportation policy is applied in this study to reduce the holding cost of the retailer. A consumed fuel and electricity-dependent carbon emission cost are used for environmental sustainability. Since the industries face problems with smooth functioning in each of its steps for unreliable players, the study is proposed to solve the unpredictable player problem in the supply chain. The robust distribution approach is utilized to overcome the situation of unknown lead time demand. Two metaheuristic optimization techniques, genetic algorithm (GA) and particle swarm optimization (PSO) are used to optimize the total cost. From the numerical section, it is clear the PSO is $ 0.32 $ % more beneficial than GA to obtain the minimum total cost of the supply chain. The discussed case studies show that the applied single-setup-multi-unequal-increasing delivery policy is $ 0.62 $ % beneficial compared to the single-setup-single-delivery policy and $ 0.35 $ % beneficial compared to the single-setup-multi-delivery policy. The sensitivity analysis with graphical representation is provided to explain the result clearly.</p></abstract>

The Research on Distribution of Lead-Time Demand on the Basis of Multivariate Higher-Order Markov Chain

Inventory management is an important part of supply chain management: inventory shortages could result in reduced delivery speeds and response speeds while excess inventory could lead to increased inventory and operating costs. Therefore, finding ways to efficiently control inventory has become an issue companies are most concerned about. Choosing a proper inventory management method based on the lead-time demand distribution fitted from historical data has become the key criteria to solve this issue. However, it is difficult to determine the lead-time distribution based on the limited amount of historical data directly. Thus, the method this report introduces uses a multivariate higher-order Markov chain to reconstruct historical data in order to expand the amount of data used to fit the lead-time distribution of demand, which is significant for inventory management.

The new evidence reasoning based pharmaceutical inventory models with stochastic deterioration rates and lead times using PSO and GA

Pharmaceutical inventory management is critical because insufficient pharmaceutical items and their misusage affect the lives of humans and cause financial losses. Conversely, deteriorating items and lead-time have special importance in pharmaceutical inventory issues, especially as uncertainty appears in both. Different procedures are considered to deal with uncertainty, including fuzzy systems as well as probabilistic techniques. The present study develops a novel technique according to the evidential theory approach, aimed at solving an inventory model with stochastic deterioration rates and lead-times appearing in a single-vendor (pharmaceutical company) multi-buyer (hospitals) inventory system. It seems that the evidence approach is effective in dealing with interval, imperfect, inaccurate, and missing (ignorance) data. The lead time demand of the hospitals is log-normal, and the shortage of hospitals is thoroughly back-ordered. Particle swarm optimization (PSO) and genetic algorithm (GA) solve this problem. Ultimately, the results are illustrated using the numerical example and the impacts of the main parameters. Highlights Develop the new pharmaceutical supply chain models based on the evidential theory approach Design single-vendor (pharmaceutical company) multi-buyer (hospitals) system with stochastic deterioration rates and lead times Considering interval, incomplete, imprecise and missing (ignorance) data in healthcare systems for make decision in the inventory problem Using genetic algorithm (GA) and particle swarm optimization algorithm (PSO)

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.

Impact of uncertain demand and lead-time reduction on two-echelon supply chain

This paper develops a continuous-review vendor-buyer supply chain (SC) model wherein the lead-time (taken as replenished) is considered as a factor affected upon by the time stamp required for setup and production followed by transportation. Here, the production time indicates the interaction between the lot-size and lead-time. Assuming the existence of an opportunity with the buyer of reducing the replenishment lead-time. The buyer receives normally distributed stochastic lead-time demands from its customers. Due to the stochastic nature of lead-time demand, shortages may arise at the buyer’s side which is fully backlogged. We presume imperfection production at the vendor’s end, which leads to the generation of a certain ratio/percentage of defective products, which results in additional warranty costs for the vendor. This study intends to uncover the best policy that minimizes the system’s total expected cost. A solution algorithm with some lemmas is provided which helped in finding the optimal solution and to prove the uniqueness of the solutions. Findings demonstrate that a reduction in lead-time can effectively lower safety stock as well as the total cost.