Stochastic Lead Times Research Articles

Forecasting of lead-time demand variance: Implications for safety stock calculations

Lead-time demand forecasting constitutes the backbone of inventory control. Although there has been a considerable amount of research on forecasting the mean lead-time demand, less has centered around forecasting lead-time demand variance, especially in the case of stochastic lead-times. This represents an important gap in the literature, given that safety stock calculations rely explicitly on the lead-time demand variance (or equivalently the variance of the lead-time demand forecast error for unbiased estimators). We bridge this gap by exploring the viability of three strategies to estimate the variance of the lead-time demand forecast error under stochastic lead-times: (1) aggregating the per period variance of forecast errors over the lead-time, which is the classical approach; (2) considering the variance of the aggregated (over the lead-time) forecast error; (3) considering the variance of the forecast errors resulting from temporally aggregated (over the lead-time length) demand. Analytical results are derived for a first order autoregressive moving average ARMA(1,1) demand process for both a single exponential smoothing and the minimum mean squared error forecasting method. A numerical investigation assesses the effects of demand autocorrelation and lead-time variability on the accuracy of each strategy, and the conditions under which one outperforms the others. The results show that the classical strategy presented in textbooks appears to be the least accurate one, except for cases with a high negative demand autocorrelation. An analysis of the inventory control performance also reveals that the classical strategy often leads to higher inventory costs and lower service levels for positive autocorrelation.

Advance payment based vendor–buyer production inventory model with stochastic lead time and continuous review policy

In this paper, a multi-cycle vendor–buyer supply chain production inventory model is conceptualized. Products in the system are considered to be deteriorated at a constant rate. Before replenishment of the order quantity, the buyer paid the purchase price in advance to the vendor in multiple time with an interest. In the lead time of buyer, the market demand is stochastic. Vendor’s production cost of the item depends on the production rate, labor and technology used for the production. During the production period and shipment of quantity, a green-house gas $$(CO_2)$$ is emitted at a constant rate to the environment. Finally, numerical examples and sensitivity analysis are provided to illustrate the presented model and also corresponding discussions and conclusion are presented.

Impact of Information Sharing on Bullwhip Effect in a Non-Serial Supply Chain with Stochastic Lead Time

Impact of Information Sharing on Bullwhip Effect in a Non-Serial Supply Chain with Stochastic Lead Time

WITHDRAWN: Fuzzy EOQ model with stochastic lead time using yager’s technique

Abstract The inspiration driving here to look at the Economic order quantity model with the impact of stochastic Lead time decline on stock cost underneath hybrid. For this inventory models stock size is constant, We utilize exponential lead times to show that diminishing average lead time has an optional decrease of the difference because of request hybrid. Here we determine a methodology for diminishing the average and change for lead times. In this paper fuzzy done in holding cost and deficiency cost coefficients using yager’s ranking method.

Optimization of a repairable deteriorating system subject to random threshold failure using preventive repair and stochastic lead time

This paper presents a preventive repair / replace strategy for a repairable deteriorating system with stochastic lead time using phase type quasi-renewal processes. The aim of this study is to indicate improvement in the system performance when adopting preventive repair. Employing the standard results of the renewal reward process, an explicit expression for the long-run average cost rate and the operational availability of the system are derived to obtain an optimal replacement policy N* analytically, for the proposed model. Numerical illustrations are provided to show the effectiveness in the long-run average cost rate and operational availability, which depict the advantage of adopting a preventive repair with stochastic lead time.

A hybrid genetic algorithm for a multilevel assembly replenishment planning problem with stochastic lead times

This paper on replenishment planning for multi-level assembly systems with several components at each level deals with the problem of calculating planned lead-times when the real lead-times for all components are assumed to be stochastic. This problem is already treated in the literature by using a recursive procedure and a Branch and Bound algorithm. Here, in order to decrease the computation time, a novel generalized probabilistic model based on an iterative approach is developed. The proposed model calculates the expected total cost, which is composed of the inventory holding cost for components and the backlogging and inventory holding costs for the finished product. An iterative approach and a hybrid genetic algorithm are introduced to determine the planned order release dates for components at the last level of the bill of materials that minimizes the expected total cost. Experimental results show that the proposed optimization algorithm efficiently finds good-quality approximate solutions regardless of the type of assembly system, the number of components at the last level and the variability of the finished product-related costs.

The Markov model for base-stock control of an inventory system with Poisson demand, non-crossing lead times and lost sales

We study base-stock control of a continuous review single-item inventory system with Poisson demand and lost sales. The item is supplied by an exogenous and sequential system with stochastic lead times (LTs) specified by their mean and standard deviation (SD). Define R as the square of mean/SD and define r as the smallest integer which is at least R. When R<r, we introduce a novel tractable LT distribution called Extended Erlangian. When R=r then Extended Erlangian is the same as pure Erlangian and the simple Markov model presented by Johansen (2005) makes it easy to compute and minimize the long-run average cost per unit time. We present an algorithm to compute the steady state distribution of a new Markov model for base-stock control with Extended Erlangian LTs. For fixed base-stock S, this algorithm can be applied to compute the average cost and it is straightforward (but burdensome for large r) to compute the optimal S and the minimum average cost. We also suggest a reasonable S computed in closed form from simple models with pure Erlangian LTs. The reasonable S is easy to compute and it performs well. Our numerical study illustrates that the average cost goes up as SD goes up, which is in sharp contrast to independence of SD when the LTs are i.i.d.

A Discrete Event Simulation Analysis of the Bullwhip Effect in a Multi-Product and Multi-Echelon Supply Chain of Fast Moving Consumer Goods

Timely delivery is the major issue in Fast Moving Consumer Good (FMCG) since it depends on the lead time which is stochastic and long due to several reasons; e.g., delay in processing orders and transportation. Stochastic lead time can cause inventory inaccuracy where echelons have to keep high product stocks. Such performance inefficiency reflects the existence of the bullwhip effect (BWE), which is a common challenge in supply chain networks. Thus, this paper studies the impact of stochastic lead time on the BWE in a multi-product and multi-echelon supply chain of FMCG industries under two information-sharing strategies; i.e., decentralized and centralized. The impact was measured using a discrete event simulation approach, where a simulation model of a four-tier supply chain whose echelons adopt the same lead time distribution and continuous review inventory policy was developed and simulated. Different lead time cases under the information-sharing strategies were experimented and the BWE was measured using the standard deviation of demand ratios between echelons. The results show that the BWE cannot be eliminated but can be reduced under centralized information sharing. All the research analyses help the practitioners in FMCG industries get insight into the impact of sharing demand information on the performance of a supply chain when lead time is stochastic.

Joint pricing and lot sizing model with statistical inspection and stochastic lead time

In many real-world situations, there are a fraction of defective items in a received lot whose quality should be evaluated before storage. In this article, we address the joint ordering, pricing, and inspection planning problem for a retailer facing price-sensitive demand and stochastic supply lead-time. The fraction of nonconforming items in a received lot follows a beta distribution and the buyer considers different kinds of inspection policies that include no inspection, inspection and sampling. Moreover, a novel non-linear optimization model is developed in order to determine optimal ordering, pricing and inspection policies. An analytical solution procedure based on mathematical properties of the model is proposed to find optimal decision variables. Numerical studies are conducted in order to show the applicability of the developed model and effectiveness of the proposed algorithms.

Coordination Supply Chain Management Under Flexible Manufacturing, Stochastic Leadtime Demand, and Mixture of Inventory

The necessity of coordination among entities is essential for the success of any supply chain management (SCM). This paper focuses on coordination between two players and cost-sharing in an SCM that considers a vendor and a buyer. For random demand and complex product production, a flexible production system is recommended. The study aims to minimize the total SCM cost under stochastic conditions. In the flexible production systems, the production rate is introduced as the decision variable and the unit production cost is minimum at the obtained optimal value. The setup cost of flexible systems is higher and to control this, a discrete investment function is utilized. The exact information about the probability distribution of lead time demand is not available with known mean and variance. The issue of unknown distribution of lead time demand is solved by considering a distribution-free approach to find the amount of shortages. The game-theoretic approach is employed to obtain closed-form solutions. First, the model is solved under decentralized SCM based on the Stackelberg model, and then solved under centralized SCM. Bargaining is the central theme of any business nowadays among the players of an SCM to make their profit within a centralized and decentralized setup. For this, a cost allocation model for lead time crashing cost based on the Nash bargaining model with the satisfaction level of SCM members is proposed. The cost allocation model under Nash bargaining achieves exciting results in SCM coordination.

Warehouse Location in An Emerging Country: A Win–Win Proposition?

Warehouse solutions in emerging countries near suppliers have been adopted to achieve cost efficiency in offshore procurement. Previous academic literature ignores logistics operations costs in supply chain contracting. In this paper, we study contracting between a retailer in a developed country and a supplier in an emerging country while incorporating total landed cost (including logistics operations costs) in contracting. The retailer faces stochastic demand and stochastic lead time and determines the warehousing strategy. She can hold cycle stock and safety stock at the retail location (developed country warehousing) or allow the supplier to hold second‐tier cycle stock at a warehouse in the emerging country in addition to her holding inventory at the retail location (emerging country warehousing). We study the retailer’s optimal warehousing strategy in a centralized supply chain and a decentralized supply chain with the retailer as the Stackelberg leader. When emerging country warehousing is adopted in the decentralized supply chain, the retailer and supplier could achieve a win–win or a win–lose outcome compared to developed country warehousing. Our results show that the retailer’s warehousing strategies in the centralized and decentralized supply chains could be different. We further study the retailer’s optimal warehousing strategy under the Nash bargaining framework where the wholesale price and logistics decisions are negotiated simultaneously given the warehousing strategy. We compare this contract to that where logistics costs are excluded from contract negotiation. Our results show that by including logistics costs into contract negotiation the retailer and supplier could achieve lose–win, win–win and win–lose outcomes.

A manufacturer-buyers integrated inventory model with various distributions of lead times of delivering equal- sized batches of a lot

The single manufacturer multi-buyer integrated inventory supply chain problem with deterministic lead time of delivering batches (sub-lot) of a lot has received considerable attention. Because of influences by various factors, usually deviations occur in the times of setup of machines, inspection, loading, transportation, unloading etc., which result deviation in the lead time of delivering batches of a lot. Although the single-manufacturer single-buyer integrated supply chain problem with a particular distribution of lead times has received some attention, a model considering various distributions of lead times is unavailable. Also, the single-manufacturer multi-buyer integrated supply chain problem with stochastic lead time has received no attention from researchers. To fill up these gaps, here we develop a single-manufacturer multi-buyer integrated inventory supply chain model with various distributions of lead times of delivering equal-sized batches of a lot. Then an optimal solution technique to the model is developed, and illustrated with numerical examples. The significant potential benefit is highlighted by comparative study on solutions to numerical problems. Sensitivity analyses on the effects of various parameter values upon the minimal total cost solutions are carried out. The shortcomings of the current solution method are highlighted along with the indication of future research scope.

Supply chain information sharing under consideration of bullwhip effect and system robustness

Supply chain system experiences variance amplification in order replenishment and inventory level, leading to severe inefficiencies of the system. Information distortion is universally known as a fundamental reason for the variance amplification phenomenon. The purpose of this paper is to study the effect of demand information sharing in reducing bullwhip effect and improving the robustness of supply chain systems. The “automatic pipeline inventory and order-based production control system, APIOBPCS” is adopted to model supply chains with different information-sharing strategies. The stochastic factors in the supply chain system lead to poor performance in system robustness. Taguchi design is adopted to find out the optimal setting of ordering parameters in the APIOBPCS model for a robust supply chain. An extension of Taguchi design is adopted to solve the multi-response problems. The weighted signal-to-noise ratio is used as the performance index of the overall performance of the supply chain, including inventory cost, customer service level, and inventory variance amplification. The results show that full demand information transparency helps to improve the overall performance of supply chain. Furthermore, the sensitivity analysis of stochastic lead times verifies the results. This research gives some insights to improve the overall performance of supply chain via information sharing.

A vendor–buyer inventory model with lot-size and production rate dependent lead time under time value of money

The paper studies an integrated vendor–buyer model with shortages under stochastic lead time which is assumed to be variable but depends on the buyer’s order size and the vendor’s production rate. The replenishment lead time and the market demand uncertainty are assumed to be reduced by changing the regular production rate of the vendor at the risk of paying additional cost. Shortages are partially backlogged and the backlogging rate depends on the length of the buyer’s replenishment lead time. The proposed model is formulated to obtain the net present value (NPV) of the expected total cost of the integrated system through optimization of (i) the buyer’s order quantity, (2) the buyer’s safety factor, and (3) the vendor’s production rate. Theoretical results are derived to demonstrate the existence and uniqueness of the optimal solution. Through extensive numerical study, some valuable managerial insights are obtained.

The Single-Vendor Multibuyer Integrated Production-Delivery Model with Production Capacity under Stochastic Lead Time Demand

In this paper, we consider an integrated production-delivery model in which a vendor supplies the same product to multiple buyers. Unlike existing study, in this proposed model, we assume that the sum of all buyers’ demand rates is larger than the vendor’s production rate under normal work, but less than that under overtime. All buyers are independent of each other. For each buyer, the lead time demand is stochastic and the shortage during lead time is permitted. The main objective of this model is to determine the optimal production and delivery policies and the optimal overtime strategy, which minimize the joint expected annual cost of the system. Based on the genetic algorithm, we develop a solution procedure to find the optimal production, delivery, and overtime decision of this model. Computational experiments show the error rate between the objective values obtained by the proposed solution procedure and the solutions solved by the exhaustive method. The results indicate that the proposed mixed genetic algorithm is more effective and adoptable in comparison with the exhaustive method as it can be able to calculate the optimal solutions for at least 96% for the instances. Ultimately, an adequate numerical example is given to show the detailed process of the solution procedure, and sensitivity analysis of main parameters with managerial implication is discussed.

Hybrid differential artificial bee colony algorithm for multi-item replenishment-distribution problem with stochastic lead-time and demands

In this paper, by assuming a B2C e-business company with several regional distribution centers (DCs), an extension of multi-item joint replenishment-distribution problem (JRD) is raised with stochastic lead-time and demands to investigate their mutual impacts to the JRD system. For the proposed JRD, the objective comprising four types of costs, namely, the ordering cost, the inventory holding cost, the lost sale penalties and the transportation cost is minimized by jointly deciding the basic cycle time, the replenishment frequencies and safety stock factors of all items. A hybrid differential artificial bee colony (DABC) algorithm, which combines the superiorities of the differential evolution (DE) algorithm in global search and the artificial bee colony (ABC) algorithm in fine search, is presented to solve the proposed JRD model. Numerical experiments and parameter sensitivity analyses are conducted. The computational results have testified that DABC is faster than that of DE (16%) and two hybrid ABC-DEs (18% and 9%), more effective than that of genetic algorithm (GA, 0.15%), ABC (0.03%) and ABC-DE1 (0.015%) and robust than that of GA (99%), DE (71%), ABC (0.97%) and two hybrid ABC-DEs (86% and 88%). Most importantly, different uncertainty significance of lead-time and demands to JRD are revealed and analyzed. Furthermore, management insights, such as the magnitudes of the problem-related parameters and the mutual effects of the two stochastic variables to the system cost, are indicated in the replenishment process.

A note on the stochastic nature of lead times in multi-echelon supply chains

Recent supply chain research has concluded that stochastic lead times are a significant source of bullwhip effect in reorder-based supply chains. Despite this, the study of lead times and their nature has received remarkably little attention in literature. In this research we prove there exists an interdependency between lead time and service level measure, and thus the magnitude of the bullwhip effect. In a multi-echelon supply chain setting, the decision maker can experience disproportionate bullwhip effect. One cause of this is the fact that lead time distribution may likely stem from skewed and peaked distributions. As a member of a multi-echelon supply chain, a firm can experience an order variance that depend on the total number of echelon and information about their lead-time dependencies. These results correspond well with the few contributions found in literature showing actual lead times.

Analytical Solution and Optimization of serial supply chains with multiple nodes, lost sales, continuous review replenishment policies, stochastic lead times and external demand

Analytical Solution and Optimization of serial supply chains with multiple nodes, lost sales, continuous review replenishment policies, stochastic lead times and external demand

Supply Chain Model for Expiring Items Following Ramp-Type Demand With Stochastic Lead Time Under Crisp and Fuzzy Environment

Supply chain models with deteriorating items, season pattern demand, expiration and uncertain lead time, though common in practice; had received little attention from researchers. In this article, the authors proposed a collaborative system with ramp type seasonal pattern demand rate for expiring items with supplier's random lead time under crisp and fuzzy environment considering the effect of inflation and time value of money. For the seasonal kind of items, demand rate follows the combination of increasing-steady-decreasing demand patterns. A supplier's lead time is a stochastic function of his managing cost; thus, the extra costs incurred on the retailer due to the uncertainty in lead time in terms of shortages costs and lost sales costs are owed by the supplier. Numerical examples are cited to illustrate the results and its significant features. Finally, to study the effect of change of parameters sensitivity analysis is presented and necessary observations are made.

The Impact of Lead Time Uncertainty on Supply Chain Performance Considering Carbon Cost

In supply chain operation practices, lead time uncertainty is a common management issue. Uncertain lead time can lead to increased inventory costs and unstable service levels, which will directly affect the overall operation performance of the supply chain. While considering environmental performance in supply chain, it is important to understand how an uncertain lead time will affect sustainable performance. In this paper, we constructed a supply chain model with stochastic lead time and explored the relationship between uncertain lead time and supply chain performance. We considered carbon cost, inventory cost, and service level as a supply chain performance. System dynamics methodology was employed to observe and explore the dynamic change trend of the overall performance in the complicated supply chain model. This was done under both different levels of lead time standard deviation and different order policies. The results demonstrate how stochastic lead times can significantly increase inventory costs and carbon costs. Therefore, we propose appropriate ordering policies which mitigate the negative impacts of stochastic lead times.